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Laser spectroscopy
Laser spectroscopy II.Applications in quantum VS.
metrology
LETOKHOV
Applications of sub-Doppler optical resonances to the spectral lines of atoms and molecules giving laser standards of wavelength and frequency are presented. The problems of precise measurement of length and absolute measurement of light frequency are considered. Prospects of elaborating fundamental experiments with laser ultra-stable frequency are discussed.
Methods of non-linear high resolution laser spectroscopy without the Doppler broadening of spectral lines in gases (sub-Doppler spectroscopy) have found extensive use in optical quantum metrology. Moreover, at the initial stage of development of these methods in the late sixties, the development of narrow optical Doppler-free resonance was motivated by, among other things, the prospects of elaboration of new and more precise frequency standards in the optical range. The ways of producing non-linear narrow resonances are considered in more detail elsewhere.lm3 In this article consideration is given to the application of sub-Doppler optical resonances to the spectral lines of atoms and molecules giving laser standards of wavelength and frequency. Such an application of non-linear laser spectroscopy in optical quantum metrology has been mentioned elsewhere in this series.“ Here, the attendant problems of precise measurement of length and absolute measurement of light frequency will also be discussed. In the conclusion of the prospects for a unified quantum standard of length and time are briefly considered as well as some other fundamental physical experiments with frequency ultra-stable lasers. The accuracy of determination of the unit length available at present is insufficient for a number of precision measurements*. The accuracy of determination of such important physical constants as the velocity of light, Rydeberg constant, etc are also limited. The primary task is therefore to create a source of electromagnetic vibrations in the optical range to reproduce the light wavelength with an accuracy comparable at least to that of the adopted atomic frequency standard?. ;;6Thewavelength of
the optical spectral line *P,o - 5d6 of the Kr atom fh = 605.7802105 nmj has been adopted as the international length standard. The international metre contains 1 660 763.73 radiation wavelengths at this transition. The accuracy of the orange line wavelength by the krypton primary standard is 3 x 10-g. tThe international standard of physical time measurement is a caesium atomic beam passive frequency standard based on the transition between the hyperfine l”;v&fs F = 4, mF = 0 + F = 3, mP = 0 of the ground state of the Cs atom in the absence of external fields, the frequency value being 9 192 631 770.0000 Hz. The caesium frequency standard reproduces the frequency of this transition accurately to (1 - 2) x 10-l? The author is at the Institute of Spectroscopy, USSR Academy of Sciences, 142092 Moscow Region Troitrk. Received 8 April 1981.
0030-3992/81/040203-07 OPTICS AND LASER TECHNOLOGY.
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1981
Such a source can serve, in principle, as the length and frequency standard at the same time. The optical frequency standard also allows a considerable reduction in frequency measuring time to a required precision, since the precision of measurement during the time interval is proportional to the frequency. A source of coherent radiation with a narrow spectral line, ie a gas laser, forms the basis for the optical quantum standard of frequency and wavelength. The frequency of such a laser is tuned (stabilized) by an automatic control system to the peak of a narrow reference line to a high precision. Like any frequency standard, the laser standard is characterized by the accuracy of reproduction of frequency and by the frequency stability. The latter means the degree to which the standard adheres to the chosen value of frequency during a given time. Usually it is characterized by the relative mean-square frequency shift from its average value Kduring the measuring time T. In determining the frequency stability it is necessary for the averaging time intervals r and frequency measurement T to be indicated. For a very short observation time the frequency stability depends on the spectral width of laser radiation. Methods of frequency
stabilization
of lasers
In frequency-stabilized lasers the following elements are common for all systems: a frequency discrimination (internal or external) which transforms the laser frequency shift to a time-varying error signal; a servo-system to detect and amplify this signal; and a controlling element tuning the laser frequency towards a decrease in error signal (Figs. 1 and 2). The long-term laser frequency stability in such a system is not better than the optical discriminator zero stability, and the response of the system to short frequency fluctuations depends on the transmission band of the servo-system. A controlling element regulates the laser frequency usually by varying the length of its cavity using a piezo effect, magnetic striction, electromagnetic effect or an electromechanical drive. Atomic and molecular resonances, in some cases the transmission maxima of an interferometer, are usually used as optical discriminators. The main requirements for the atomic or molecular reference spectral line are that its frequency must be stable and reproducible to at least the accuracy required of the optical quantum standard, and that the rela$02.000
1981 IPC Business Press 203
P
O”,
1
-2r
77
linear interaction between the laser light field and the moving atoms or molecules in a low pressure gas which gives rise to narrow resonances of saturated absorption and density of excited particles.) Figure 1 shows some widely used methods of laser frequency stabilization. In these schemes narrow saturation resonances are used as the reference line.
Fig. 1 Typical methods of laser frequency stabilization with narrow non-linear resonances. a - internal saturated absorbing cell giving standing light wave; b -external saturated absorbing cell giving quasi-running wave; c - saturated fluorescent call giving standing wave within(out) cavity. 1 -photodetector; 2 -frequency servo control; 3 -driving (PZT) element; 4 -optical isolator; 5 - semitransparent mirror; 6 - unidirectional element. 2r is the homogeneous line width Driving element
Absorbing
Amplifying cclI
Cdl
Laser frequency servo control systems operate on the usual principle of servo control systems, tuning the length of the cavity so that it corresponds to the top of the peak (dip) in the intensity-frequency curve. In practice it is possible for the zero of the fust derivative (Fig. 2) or the central zero of the third derivative of a narrow resonance to serve as a discriminator. Recording the error signal at the higher harmonics of the reference frequency makes it possible to reduce considerably the strong background of general change in radiation intensity which causes the frequency shift of the narrow resonance from its real position. This occurs particularly when the narrow resonance is far from the centre on the intensity profile slope. The total gain coefficient of the feedback loop depends on the value of frequency drift under free generation, the photodetector sensitivity, the discrimination curve gradient and the required degree of frequency stability. In practice it may be as high as 10’ . The servo system transmission band depends on the spectrum of suppressed frequency fluctuations of the laser. Frequency-stabilized
lasers
In the HeNe laser at 0.63 p with an iodine cell the amplification line coincides with some absorption lines in the electronic-vibrational spectrum of vapour-phase lz7 I2 and ‘29 I, to produce narrow resonances of output powersT6. At 0.1 Torr the power peak contrast constitutes 0.1% and the width varies from 3 to 5 MHz. The typical dimensions of the system are as follows: the laser cavity length is about 300 mm, the ’ 29I2 cell is 30 mm long and the beam diameter is 1 mm (Fig. 3). The required pressure of saturated iodine vapour is controlled by the temperature of the cell. The laser frequency stabilized with the central zero of the third derivative of narrow resonance can be 2 x lo-l2 with an average sample time T = 10 s (Fig. 4). The measured frequency reproducibility of the system is 5 x 10-l’ .7 The 3 He” Ne laser stabilized with the ith component of 12’12, with a wavelength in vacuum of 632 991.399 If: 0.0025 pm was recommended in 1973 by the Comite’ Consultatif pour la Ddftition du Mdtre as a secondary standard to be used in precision interferometric measurements.
v. Frequency,
Y i
Fig. 2 Schematic and principle means of output power peak
of laser frequency
stabilization
by
tive width of the reference line does not exceed the required values of stability by more than IO2 to IO4 times (this condition depends on the quality of the servo system). Spectral absorption lines with the reproducibility and stability at their centres of from 10”’ to lo-l3 exist at many quantum transitions of atoms and molecules, the initial and final levels of which are very weakly disturbed by external fields and gaseous inter-particle collisions. Narrow reference lines with their relative width of about 10” to 1Ode can be produced on any long-lived transitions by ehminating the Doppler broadening. (This arises due to non-
In a HeNe laser at 3.39 Mm with a methane cell the output power peak in absorption saturation of the component F,(2) of vibrational-rotational transition P(7) of the u3 methane band was used as the reference for frequency stabilization.* The importarit feature of the component F2 (2) here is that there is a magnetic hyperfine transition structure formed mainly of three strong components of different intensity with frequency intervals between the adjacent components of 11.4 and 14.2 kHz.9 The influence of the light field in the cavity and the pressure of methane in the cell on the position of narrow resonance can be reduced substantially by using resonances with their half-width r of the order of the hyperfine splitting value A for frequency stabilization and by applying the radiation frequency modulation with frequency f - A and a small modulation index (91).
OPTICS AND LASER TECHNOLOGY
. AUGUST
1981
End plate
Plasma tube and carrier
Steel hall Quartz absorption
Adjustment screw
Retainer screw
Piezoelectric translator Rubber compression ring
Inva: rod
Mirror‘carrier
Plasma t&e carriage
Thermoelectric coder
Silicone oil filled aluminium cup
Fig. 3
Design of
HeNe laser (A = 633
nm) with “‘12
absorbing cell6
the COs /CO2 system are as follows: cavity is 1 m long, the length of the intra-cavity fluorescent cell is between 50 and 100 mm, the COZ pressure in the cavity is 2 x 10T2 Torr and the beam diameter is 10 mm. To increase the fluorescence signal a highly sensitive, cooled (Ge :Cu ,4 K) large area photodetector (up to 20 x 20 mm) is used.
I IO
-3
I -2
IO
I
I
I
I
10-l
IO0
IO
100
1000
Sample time (5) Fig. 4
Frequency stability nm as a function
at h = 633
(Allan variance plots) of HeNe 12’12 of sample time6
laser
Such an idea has been used experimentally’0 in a system with long absorbing (3 m) and amplifying (2 m) cells where the parameters of saturation are matched by increasing the beam diameter of the CI-L, cell up to 10 mm. With the CH,J pressure in the region of 10-j Torr, the output power peak comes to several milliwatts with a width of 30 to 50 kHz and a contrast above 50%. At present the HeNe laser with a CH, cell enables the highest values of frequency reproducibility to be obtained with long-term stability (Table 1):
In the CO2 laser with an external, non-linear absorption cell the narrow resonances of saturated absorption within the Doppler line of some vibrational-rotational transitions of the v3 band in heavy, highly symmetrical molecules such as SF, and 0~0~ can be used as a reference frequency. For a typical CO2 /SF6 or CO2 /Os04 system, the CO2 laser output power required for absorption saturation is about 0.1 W the absorbing gas pressure is 10m3 to 10m2 Torr, the external cell length is 1 to 3 m, the beam diameter is several centimetres, the intensity ratio of saturating and probing waves is about 1O:l and the width of probe wave transmission resonances is about 100 kHz. For the CO2 laser, frequency stabilized with the central zero of the third derivative of narrow resonance of SF6, the long-term frequency stability
The CO* laser with a COs saturated cell fluorescing at 4.3 pm” has an important advantage in practice. This is that there is the possibility of generating sufficient power at more than 100 vibrational-rotational lines of the P and R branches of both bands (at 9.6 and 10.6 pm) over a frequency range from 27 to 33 THz. By non-linear mixing of the frequencies of two stabilized COs lasers it is also possible to produce several thousand harmonic frequencies over a range from 0.025 to 100 THz. Typical dimensions of Table 1. 1.
Frequency stability of HeNeKH4
The stability of such a laser has been improved12 by using an external CO2 absorbing cell, a 4.3 pm fluorescence collector cooled by nitrogen and a better detector. All these measures have given an increase in the signal-to-noise ratio of two orders of magnitude and a frequency stability of the two independent lasers, each 1.5 m long, of about o/2% N 6 x 10-r’/ 2;‘) where 7 denotes the averaging time. With r varying from 20 to 30 s the frequency stability was about 10-12, and the authors hope that this can be increased tenfold with further technical modifications. It must be added that the use of a sealed CO2 laser and CO2 absorbing cells with other isotopic molecules (I3 Cl6 02, I3 Ci802) enables the number of lines in the infra-red range with a highly stable frequency to be increased considerably.r2
laser systems10
Averaging time, 7 (s)
lo-3
lo-2
10-l
loo
10
100
2.
Measurement, T (min)
30
30
30
120
120
120
3.
Average differency of frequencies of two lasers (Hz)
-
-
-
3
2
-
FraFtional standard* deviation per laser u/2 av
6 x lo-l2
3 x lo-l2
5 x IO-l3
IO-l3
3 x lo-l4
5 x lo-l5
4.
~Fteproducibilitv
of frequency
during 30 independent
OPTICS AND LASER TECHNOLOGY.
measurements
AUGUST
1981
was 3.5 x 16-14
205
attained on the P(18) line of COZ was the maximum for CO2 lasers (better than 10”2)13~14. The expected values of frequency stability and reproducibility for the CO2 /Os04 system are higher smce the vibrational-rotational spectrum of monoisotopic Os04 molecules with even-numbered isotopes of OS has no hyperfme nuclear structure. Lasers with very narrow frequency-stable output
spectral
For more accurate fixing of the laser frequency to the molecular reference line, the signal-to-noise ratio of the servo-system should be increased by narrowing its transmission band. The ultimate transmission band of the servosystem is governed by fast laser frequency fluctuations, ie its short-term frequency stability. The minimum spectral width of laser radiation due to spontaneous emission is given by
-6
-8 -
-loiY -12
Au min
=
8rlhvAv2,/P,
(1)
1 -10
-8
-6
I -4
‘I
I -2
0
w -w
c
I
I
I
I
I
2
4
6
8
IO
J 12
b
rb
where Au, is the cavity line half-width at frequency v and P is the laser output power. A greater contribution to frequency instability is made by the fluctuations of lowfrequency spatial modes excited by the thermal fluctuations in the material of the laser cavity. Their relative average value is
CL L
Fig. 6 Dependence of the oscillation frequency w of a gas laser with non-linear absorption on the cavity frequency shift around the centre of the absorption line ~b. 2rb is the homogeneous idth of absorbing w6 line andqb is the non-linear frequency PUlhTg faCtOr
” lo-l4 to lo-‘5,
where i-is the temperature, V is the volume of the bars in the cavity and Y is Young’s modulus. The main contribution to the frequency instability of laser systems is made by technical effects. The use of the various methods makes it possible to narrow the spectral width of laser radiation lines, for short times (lOa to 10”s) to several Hz @v/v 2 lo-rO/lo~s). It is possible to produce an extremely narrow radiation spectrum in frequency-stabilized lasers in which technically introduced frequency fluctuations are eliminated by all
1
possible means. l5 In experiments by V. Chebotayev the frequency beating signal of the two independent frequencystabilized HeNe/CH, lasers was recorded with a characteristic beat frequency of just several Hz, conditioned by a frequency difference of the lasers. The spectral width of the beat signal was only 0.4 Hz (!). Figure 5 shows the beat signal spectrum of two independently stabilized lasers of this type. Its width is again about 0.4 Hz. Thus, a laser with its frequency stabilized to a narrow resonance of nonlinear absorption in CH4 is the most monochromatic oscillator of electromagnetic radiation at present available The requirement of simultaneous high short- and longterm frequency stability can be met with the use of combined systems of frequency servo control having the advantages of frequency reproduction by an atomic (molecular) reference line, and the high sensitivity and short-term frequency stability of a Fabry-Perot interferometer. The modulation frequency and transmission band of the loop consisting of a laser and an interferometer must be relatively high (up to 10’ Hz), and the loop including both optical discriminators and compensating for slow, thermal frequency drifts of the Fabry-Perot interferometer has a narrow band of 0.1 to 1 Hz. In another version, the interferometer resonance frequency is stabilized by an additional frequency controlled laser, for example a 3.39 pm HeNe laser with a methane cell. High short-term laser frequency stability can also be attained by tuning its beat signal frequency to another laser, the frequency of which is stabilized to a high accuracy using a wide band servo loop. The gain of the servo system may be as high as lob’, and the band width several MHz. Such laser heterodynes, without frequency modulation of radiation, form the basis for most measurement methods (comparison) of the laser frequency and its stability.
1 Fig. 5 Sp trum of beats of two independently CH4 lasers”
206
stabilized
HeNe/
To eliminate fast laser frequency fluctuations it is potentially very effective to use the frequency self-stabilization effect, particularly in combination with a narrow-band loop of frequency servo tuning with an atomic or molecular reference line.lb This effect manifests itself by a non-linear distortion of a laser frequency w with an internal absorbing cell to the centre of an absorption line ab. The degree of
OPTICS AND LASER TECHNOLOGY.
AUGUST
1981
distortion depends (Fig. 6) on the slopes of the curve W-U,, =(w, -c+,)(l +Q,)~ at thepointw=Wb. With considerable self-stabilization (qb 5 lo), frequency hysteresis can be observed. Furthermore, absolute frequency self-stabilization is possible when, regardless of the variation of the cavity frequency w, , laser action appears at longitudinal modes such that its frequency lies completely within the homogeneous width 2I’ near the centre of the absorption line. The frequency self-stabilization time coincides with the transient time of laser field amplitude in the cavity and may be as small as IO-’ - 10e6 s. Methods of laser wavelength
measurement
To measure (compare) the wavelengths of two different etalon lasers it is possible in some cases to measure the orders of interference of light from one type of laser heterodyne in the cavity, the length of which is tuned on transmission resonance to the frequency of a laser heterodyne of another type. The orders of interference are counted by scanning the frequency fo the first laser heterodyne relative to the reference laser and by measuring their difference in frequency. The use of laser heterodynes with etalon lasers not only allows elimination of the effect of stabilized lasers but also makes it possible to overcome the problem of scanning the interferometer length. To reduce the effect of different phase shifts during beam reflection the measurements must be carried out in series with two interferometers of different length. The measurement accuracy of wavelength is determined by the signal-to-noise ratio. With prolonged observation it may beashighas lO+ and at ordinary observation durations (about 1 s) it is 10”. A more important restriction on the reproducibility is caused by the diffraction of a light wave with a limited diameter. To obtain a reproducibility of 10” it is necessary for the divergence of light beam to be around lOa rad. To obtain this value for a Gaussian beam with diameter 20, the condition 20~5 104Xln must be satisfied. For the wavelength A = 0.63 m the beam diameter should be 20~ >” 2 mm and for h = 10.4 w 20~ 5 30 mm. An increase m beam diameter appears to be of low efficiency since it becomes difficult to align the optics. It can pay for itself only in unique metrological set-ups. Because of the wide use of tunable lasers with narrow radiation lines in spectroscopy, several reasonably simple laboratory wavemeters have recently been devebped for laser radiation over the range from 1 to 10 MHz, ie AX z IO” IO-‘. They all are based on a comparison between the wavelength measured and that of stabilized NeNe& laser.‘*-** The use of an array of photodiodes (usually 1 024 elements) makes is possible to record the interference pattern electronically and thereby to automate completely the data
AUGUST
1981
photodiode orray
:
‘02as
Beam exponding
4
Fig. 7
Absolute measurements of wavelength in stabilized lasers are consistent with interferometric comparison to the wavelength of the krypton standard. In this arrangement the light beam from the laser is made to coincide with that from a s6Kr lamp and is passed through a linearly frequencyscanned Fabry-Perot or Michelson interferometer. The interferometer resonances are simultaneously recorded from each source and compared. The measurement accuracy of laser wavelength depends mainly on the accuracy of the krypton standard and the lenarity of interferometer frequency scanning. The scanning linearity can be improved by servo control tuning of the interferometer length by means of the additional laser heterodyne, the frequency of which is scanned slowly relative to the frequency of the etalon laser.
OPTICS AND LASER TECHNOLOGY.
Linear
t-20
collimator
seconds of arc
Fizeau wavemeter
of laser radiation*’
processing. Figure 7 shows schematically a laser wavemeter with a Fizeau interferometer. *I The instrument consists of an optical system for the laser beam, a collimator widening the light beam, a simple Fizeau interferometer, a linear array of 1 024 photodiode elements, electronics for signal processing and a microcomputer for calculation and digital display of wavelength values. The wavelengths measured by the instrument are in the range 0.4 to 1 .l pm; the measurement accuracy is about 3 x lo-‘. The wavemeter can operate with continuous or pulsed operation and is fairly simple as far as its optics and mechanics are concerned. Recently commercial wavemeters have come into the market with accuracies of about 10”. These can be suitable for routine operation with tunable lasers. The WA-20 type wavemeter produced by Burleigh Instruments23 is an example. It is designed to measure continuous radiation wavelengths accurately to 10 d in the region 0.4 to 4.0 pm. The measurement time is 1.6 s and the result can be seen on an illuminated indicator display. Similar parameters of wavelneters can be obtained not only for continuous but also for pulsed radiation. For example, the French firm Sopra SA23 have introduced a wavemeter with an accuracy of about 10d in the range 0.3 to 1 .O pm for pulsed and continuous laser radiation. Commercial wavemetres with a higher accuracy for precision metrological measurement on the basis of a reference HeNe/I, laser are expected to be
develaped . Methods of laser frequency
measurement
Laser frequency measurement is based on multiplying laser frequency microwave oscillators, known with a high accuracy, up to laser radiation frequencies and on their subsequent comparison by frequency mixing. To realize this process a set of frequency-stabilized sub-milllmetre and infra-red lasers must be used as well as non&near elements (mixers), inertia-less up to optical frequencies. The chain of synthesis of the frequency of optical-range lasers has been described.24*25 In this chain laser radiation of an unknown frequency (VL) serves as the reference oscillator signal in heterodyne detection of the weak signal of the high-harmonic klystron radiation (nv,) and of other lasers (IQ, mv,), the frequencies of which (v, , vI, v,) are measured initially. The radio frequency signal passing through the diode mixer can be expressed as vd = VL - (Iv, f mv, + nv,,) where 1, m, n are the numbers of frequency harmonics. Absolute measurement (synthesis) of frequencies is accomplished in several steps. The first step of the frequency synthesis is to measure the frequency of the standard lines R(10) at 9.33 cun and R(30) at 10.18 lun of the stabilized CO2 laser (narrow resonance of fluorescence in CO2
207
serves as a reference frequency). In the second stage the frequencies of the standard lines serve as a basis from which to measure the frequencies of the rest of the COZ laser lines. Third, frequency-stabilized CO? lasers are used to measure the frequency of the absorption line P(7) of methane to which a HeNe 3.39 pm laser is stabilized. Fourth, HeNe and COa lasers are used for frequency synthesis and measurement in the near infra-red range. The frequencies of HCN, DCN, Ha 0 and Dz 0 lasers are measured using silicon point-contact diodes. The highest frequency measured is about 3 THz. To detect infra-red frequencies up to 200 THz25 point-contact metal oxidediodes can be used. The design of such diodes is a pointed (up to 100 pm) thin (several microns) tungsten wire antenna which is in mechanical contact with a nickel plate. This contact is realized through a thin oxide fh several angstroms thick which serves a a barrier in quantum-mechanical electron tunelhng. The laser radiation is focused onto the wire antenna directly at the point of contact, and the microwave signal from the klystron is also fed to this contact. The best stability of characteristics over the entire cycle of frequency measurement can be ensued using another diode design in which the point contacts with the infra-red antenna are printed on a sapphire sub-stratum photolithographicall.26 Absolute measurement of laser frequency is being developed in two directions. First, the high-frequency limit of absolute frequency measurement is increasing continuously. In the very first experiments in 1967 the 890 GHz radiation frequency of a HCN laser2’ was measured and ten years later it has become possible to measure the 260 THz frequency of radiation at the 1 .15 pm wavelength of a aeNe laser and the absolute frequencies of certain spectral lines of 12’12 in the visible range at nearly 520 THz.~* The accuracy of such measurements of absolute frequency varies between lo+ and 10-lo in accordance with the measurement accuracy of sub-millimetre laser frequencies. The second direction of progress is connected with an increase of frequency measurement accuracy. The following scheme29 for transfer of standard frequencies from the caesium frequency standard to the optical spectral region has been realized: Cs standard & HCN (337 m) -% COa/Os04
(10.53 m)
& Dz 0 (84 pm) -+
% CO2 (10.18 pm) -+
(3)
-% HeNe/CH4 (3.39 run) The measurement accuracy of the HeNe/CH4 laser frequency was 1O-1o and for the CO,/OsO,, laser 3 x lo-” . Such an increase in accuracy has been made possible by using a more rational structure for frequency synthesis with the introduction of D2 0 and CO2 /Os04 lasers. This allows the order of frequency multiplication to be decreased while increasing the signal-to-noise ratio in frequency conversion. The sub-milhmetre laser frequency was stabilized through phase locking by the Cs standard of microwave frequency. In this case the first three oscillators in the chain of frequency synthesis have frequency values defined to an accuracy of 10-13. With the use of the eighth harmonic of the D2 0 laser it is now possible to determine the COZ /OsOd laser frequency with the same accuracy. In the work of reference 29 the frequency measurement accuracy (3 x lo-“) was governed only by the frequency instability of the CO2 / 0~0~ laser itself. This value is expected to be increased in
208
future up to lo-l3 with the possibility a fairly high frequency stability.
of using a laser with
Conclusion and prospects In the past ten years the methods of laser Doppler-free spectroscopy have resulted in considerable progress in optical quantum metrology of length and frequency. Measurements of wavelength accurate to 1Om8are quite possible now, not only in metrological but also in physical laboratories. They are based on the use of a highly frequency-stabilized HeNe/ I2 laser as reference. In combination with methods of nonlinear spectroscopy, without Doppler broadening of the quantum transitions of the hydrogen atom, the Rydberg constant has been determined more accurately. It has become possible to carry out absolute measurements of light oscillation frequency with an accuracy of better than lo+. On the basis of independent measurements of light wavelength and frequency, the light velocity in vacuum has been also measured to a higher accuracy. The values obtained for the Rydberg constant and light velocity are given in Table 2. The possibility of absolute measurement of light frequency and precise measurement of light velocity have opened the way for the creation of a joint standard for time and length instead of two independent standards based on the spectral lines of the 133Cs and 86Kr atoms. This is one of the primary goals of optical quantum metrology where the latest advances in laser spectroscopy are used. It is now possible to carry out absolute measurement of frequencies in the infrared range accurate to 10-l’ on the basis that the CO, laser and the frequency of molecular vibration transitions can be measured with the same accuracy. We can hope for further increasing accuracy up to lOA using individual metrological laser set-ups. This offers considerable scope for comparison between the frequencies of atomic and molecular transitions, ie between the atomic and molecular time scalesT9 Such experiments based on the advances in laser spectroscopy are of fundamental importance for quantum metrology Some fundamental problems of quantum metrology, such as how to achieve frequency stability and reproducibility much better than 10 13 , stimulate the development of methods to produce very narrow optical resonances. It is difficult to overcome the barrier 6v/v Z lo-l3 1lo-l4 principally because of broadening and shift of the frequency of spectral lines, including narrow non-linear resonances, due to the second-order Doppler effect Table 2. Values of physical constants obtained with the use of frequency-stabilized lasers
Constants
Relative measurement accuracy
Value
Light velocity in vacuum,24,25 c (m s-1 ) 299 792 456.2 + 1 .l
k3.5 x lo*
Rydberg constant= R km-‘)
+3x
Note:
In 1973 the Comiti
recommended (k/c
109 737.31476
the following
+ 0.00032
Consultatif
pour la Dhfinition
10-e du M’etre
value: c = 299 792 458 m s-1
= f 4 x 10-Y.
OPTICS AND LASER TECHNOLOGY
. AUGUST
1981
6V __=__= V
V2
-
2
4.6 x lo-r4 T
2c2 The numerical value here is given for the atomic mass A = 200, T is the temperature of particles in gas. One of the main possibilities for elimination of this effect is based on particle cooling to temperature below several K. Deep cooling of ions by laser radiation has been demonstrated3’ and some schemes have been put forward3’ for using highquality (Q = 1O-l3 /l 0-14) spectral lines of cooled ions in a trap to establish an optical frequency standard. Finally, among interesting applications of laser frequency standards we should point out the possibility of measurement of small displacements and creation of gravitational wave detectors by this technique. Indeed, the measurements of the laser oscillation phase or frequency at small displacements of the mirror can be performed with the use of narrow optical resonances and highly frequency-stabilized lasers. Published recently33 are results of the first successful experiments of this kind in which the relative sensitivity of length measurement was AL/L E 10-16. The experiments were carried out with a HeNe laser at X = 3.39 pm. The nonlinear resonances in methane were 50 kHz in width and low3 W in intensity. One of the mirrors of the laser cavity was fed with a periodic perturbation. The absolute sensitivity of measurements with L = 500 cm was as high as 6 x 10” A. The minimum detectable deviation in cavity length depends on the photon noise of laser radiation. In case of a narrow non-linear resonance with width 2r the detectable displacement AL,,,i, is determined from the expression33
3 4 5 6 7 8 9 10 11 12 13 14 15
16
17 18 19 20 21 22 23 24 25
AL min 26
where v,,, = c/U, is the mode spacing, k, is the narrow resonance contrast in the laser output power PO, Af is the band width measurement. As compared to the method of Michelson interferometry, the use of a laser stabilized by a narrow resonance allows an increase in sensitivity by factor v,/I’ E 103. The estimation of ALmh under the experimental conditions33 gives A.L,h N lo-l6 cm Hz-“‘. The real sensitivity is about two orders worse because of technical fluctuations.
24 (1974)
29
Hacker, L.O., Javan, A. et aZAppZ Phys Lett 10 (1967) 147 Jennings, D.A., Petersen, F.R., Evenson, K.M. in Laser sepctroscopy IV’ edited by H. Walther, K.W. Rothe Optical Sciences 21 (Springer-Verlag. 1979) 39 Domnin, YS., Kosheliaevs&i, NJ. et al pis’ma Zh Eksp
30
Goldsmith, J.G.M.,Web& E.W., Jansch~T.W. Phys Rev Lett
27 28
Teor Fiz 30 (1979)
41 (1978)
31 32
References 1
Letokhov,VS.
Opt Laser TechnollO
OPTICS AND LASER TECHNOLOGY.
33 (1978) 15
AUGUST
1981
Shimoda, K. ed High resolution laser spectroscopy in ‘Topics in applied physics’ 13 (Springer-Verlag, 1976) Letokbov, VS., Chebotayev, VP. Non-linear kser SPeCtroscopy’ in Optical sciences 4 (Springer-Verlag, 1977) Letokhov, VS. Opt Loser Technol 11 (1979) 13 Hanes, G.R., Dahlstrom, C.E.AppZ Phys Lett 14 (1969) Schweitzer, W.G., Kessler, E.G., Deslattes, RD., Layer, H.P.,Whetstone, J.R.AppZ Opt 12 (1973) 2927 Rowley, W.R., Wallard, AJ. JPhys E: Sci Instr 6 647 Barger, R.L., Hail, J.L. Phys Rev Lett 22 (1969) 4 Hall, JJ,., Borde, C. Phys Rev Lett 30 (1973) 1101 Bagaev, S>J., Chebotayev, VS. Appl Phys 7 (1975) 7 1 Freed,C. Javan. A.ApplPhys Lett 17 (1970) 53 Freed; C., O’Ddnne1,R.G. Proc 2nd symp frequency standards and metrology (5-7 July 1976, Colorado, USA) 279 Gusev, V.M., Kompabetz, ON. et al Kvantovaya Elektronika (in Russian) 1 (1974) 2465 C&iron, A.,Henry, L. Compt Rend 279B (1974) 419 Chebotayev, V.P. in ‘Metrology and fundamental constants LXVIII’ Corso of quantum electronics (Sot Italiana di Fisica, Bologna, Italy, 1980) 683; Proc 1st national school of laser applications in atomic, molecular and nuclear physics (21-31 August 1978, Vilnius, USSR) Science (1979) 177 Letokhov, VS.Pis’ma Zh Eksp Teor Fiz (in Russian) 6 (1967) 597 (JETP Lett 6 (1967) 101) Comm Atom Molec khys i(l97i) 181 Giacomo, P. ‘Laser spectroscopy III’ edited by J.L. Hail, J.L. Car&en 3rd Optic Sciences 7 (Springer-Verlag, 1977) 410 KowaIski, F.V., Demtroder, W., Schawlow, AL. in reference 17 412 Byer, R.L., Paul, J., Duncan, MD. in reference 17 414 Jacquinot, P., Juncar, P., Pinard, J. in reference 17 417 Snyder, JJ. in reference 17 419 Lee, &A., Hall, J.L. in reference 17 421 Luser Focus 16 (1980) 70; ibid 97 Evenson, KM., WeIls, JS., Petersen, F.R. et al Appl Phys Lett 22 (1973) 192 Evenson, KY., Petersen, F.P., in ‘Laser spectroscopy of atoms and molecules’ edited by H. Walther ‘Topics in applied physics’ 2 (Springer-Verlag, 1976) 352 SmaIl, J.G., Elchinger, GM., Javan, A. et al AppZ Phys Lett
269:ibid
30 (1979)
273
1525
Winelend, DJ., Drullinger, R.E., Walls, FL. Phys Rev Lett 40 (1978) 1639; Neuhauaer, W., Hohenatatt, M., Toachek, P., Dehmelt, H. Phys Rev Lett 41 (1978) 233 Strumia, F. Proc 32nd annual frequency control symposium (31 May-2 June 1978, New Jersey, USA) 44 Bagaev, SN., Dichkov, AS., Chebotayev, V.P. Rs’ma Zh Eksp Teor Fiz (in Russian) 33 (1981) 85
209
metrology
LETOKHOV
Applications of sub-Doppler optical resonances to the spectral lines of atoms and molecules giving laser standards of wavelength and frequency are presented. The problems of precise measurement of length and absolute measurement of light frequency are considered. Prospects of elaborating fundamental experiments with laser ultra-stable frequency are discussed.
Methods of non-linear high resolution laser spectroscopy without the Doppler broadening of spectral lines in gases (sub-Doppler spectroscopy) have found extensive use in optical quantum metrology. Moreover, at the initial stage of development of these methods in the late sixties, the development of narrow optical Doppler-free resonance was motivated by, among other things, the prospects of elaboration of new and more precise frequency standards in the optical range. The ways of producing non-linear narrow resonances are considered in more detail elsewhere.lm3 In this article consideration is given to the application of sub-Doppler optical resonances to the spectral lines of atoms and molecules giving laser standards of wavelength and frequency. Such an application of non-linear laser spectroscopy in optical quantum metrology has been mentioned elsewhere in this series.“ Here, the attendant problems of precise measurement of length and absolute measurement of light frequency will also be discussed. In the conclusion of the prospects for a unified quantum standard of length and time are briefly considered as well as some other fundamental physical experiments with frequency ultra-stable lasers. The accuracy of determination of the unit length available at present is insufficient for a number of precision measurements*. The accuracy of determination of such important physical constants as the velocity of light, Rydeberg constant, etc are also limited. The primary task is therefore to create a source of electromagnetic vibrations in the optical range to reproduce the light wavelength with an accuracy comparable at least to that of the adopted atomic frequency standard?. ;;6Thewavelength of
the optical spectral line *P,o - 5d6 of the Kr atom fh = 605.7802105 nmj has been adopted as the international length standard. The international metre contains 1 660 763.73 radiation wavelengths at this transition. The accuracy of the orange line wavelength by the krypton primary standard is 3 x 10-g. tThe international standard of physical time measurement is a caesium atomic beam passive frequency standard based on the transition between the hyperfine l”;v&fs F = 4, mF = 0 + F = 3, mP = 0 of the ground state of the Cs atom in the absence of external fields, the frequency value being 9 192 631 770.0000 Hz. The caesium frequency standard reproduces the frequency of this transition accurately to (1 - 2) x 10-l? The author is at the Institute of Spectroscopy, USSR Academy of Sciences, 142092 Moscow Region Troitrk. Received 8 April 1981.
0030-3992/81/040203-07 OPTICS AND LASER TECHNOLOGY.
AUGUST
1981
Such a source can serve, in principle, as the length and frequency standard at the same time. The optical frequency standard also allows a considerable reduction in frequency measuring time to a required precision, since the precision of measurement during the time interval is proportional to the frequency. A source of coherent radiation with a narrow spectral line, ie a gas laser, forms the basis for the optical quantum standard of frequency and wavelength. The frequency of such a laser is tuned (stabilized) by an automatic control system to the peak of a narrow reference line to a high precision. Like any frequency standard, the laser standard is characterized by the accuracy of reproduction of frequency and by the frequency stability. The latter means the degree to which the standard adheres to the chosen value of frequency during a given time. Usually it is characterized by the relative mean-square frequency shift from its average value Kduring the measuring time T. In determining the frequency stability it is necessary for the averaging time intervals r and frequency measurement T to be indicated. For a very short observation time the frequency stability depends on the spectral width of laser radiation. Methods of frequency
stabilization
of lasers
In frequency-stabilized lasers the following elements are common for all systems: a frequency discrimination (internal or external) which transforms the laser frequency shift to a time-varying error signal; a servo-system to detect and amplify this signal; and a controlling element tuning the laser frequency towards a decrease in error signal (Figs. 1 and 2). The long-term laser frequency stability in such a system is not better than the optical discriminator zero stability, and the response of the system to short frequency fluctuations depends on the transmission band of the servo-system. A controlling element regulates the laser frequency usually by varying the length of its cavity using a piezo effect, magnetic striction, electromagnetic effect or an electromechanical drive. Atomic and molecular resonances, in some cases the transmission maxima of an interferometer, are usually used as optical discriminators. The main requirements for the atomic or molecular reference spectral line are that its frequency must be stable and reproducible to at least the accuracy required of the optical quantum standard, and that the rela$02.000
1981 IPC Business Press 203
P
O”,
1
-2r
77
linear interaction between the laser light field and the moving atoms or molecules in a low pressure gas which gives rise to narrow resonances of saturated absorption and density of excited particles.) Figure 1 shows some widely used methods of laser frequency stabilization. In these schemes narrow saturation resonances are used as the reference line.
Fig. 1 Typical methods of laser frequency stabilization with narrow non-linear resonances. a - internal saturated absorbing cell giving standing light wave; b -external saturated absorbing cell giving quasi-running wave; c - saturated fluorescent call giving standing wave within(out) cavity. 1 -photodetector; 2 -frequency servo control; 3 -driving (PZT) element; 4 -optical isolator; 5 - semitransparent mirror; 6 - unidirectional element. 2r is the homogeneous line width Driving element
Absorbing
Amplifying cclI
Cdl
Laser frequency servo control systems operate on the usual principle of servo control systems, tuning the length of the cavity so that it corresponds to the top of the peak (dip) in the intensity-frequency curve. In practice it is possible for the zero of the fust derivative (Fig. 2) or the central zero of the third derivative of a narrow resonance to serve as a discriminator. Recording the error signal at the higher harmonics of the reference frequency makes it possible to reduce considerably the strong background of general change in radiation intensity which causes the frequency shift of the narrow resonance from its real position. This occurs particularly when the narrow resonance is far from the centre on the intensity profile slope. The total gain coefficient of the feedback loop depends on the value of frequency drift under free generation, the photodetector sensitivity, the discrimination curve gradient and the required degree of frequency stability. In practice it may be as high as 10’ . The servo system transmission band depends on the spectrum of suppressed frequency fluctuations of the laser. Frequency-stabilized
lasers
In the HeNe laser at 0.63 p with an iodine cell the amplification line coincides with some absorption lines in the electronic-vibrational spectrum of vapour-phase lz7 I2 and ‘29 I, to produce narrow resonances of output powersT6. At 0.1 Torr the power peak contrast constitutes 0.1% and the width varies from 3 to 5 MHz. The typical dimensions of the system are as follows: the laser cavity length is about 300 mm, the ’ 29I2 cell is 30 mm long and the beam diameter is 1 mm (Fig. 3). The required pressure of saturated iodine vapour is controlled by the temperature of the cell. The laser frequency stabilized with the central zero of the third derivative of narrow resonance can be 2 x lo-l2 with an average sample time T = 10 s (Fig. 4). The measured frequency reproducibility of the system is 5 x 10-l’ .7 The 3 He” Ne laser stabilized with the ith component of 12’12, with a wavelength in vacuum of 632 991.399 If: 0.0025 pm was recommended in 1973 by the Comite’ Consultatif pour la Ddftition du Mdtre as a secondary standard to be used in precision interferometric measurements.
v. Frequency,
Y i
Fig. 2 Schematic and principle means of output power peak
of laser frequency
stabilization
by
tive width of the reference line does not exceed the required values of stability by more than IO2 to IO4 times (this condition depends on the quality of the servo system). Spectral absorption lines with the reproducibility and stability at their centres of from 10”’ to lo-l3 exist at many quantum transitions of atoms and molecules, the initial and final levels of which are very weakly disturbed by external fields and gaseous inter-particle collisions. Narrow reference lines with their relative width of about 10” to 1Ode can be produced on any long-lived transitions by ehminating the Doppler broadening. (This arises due to non-
In a HeNe laser at 3.39 Mm with a methane cell the output power peak in absorption saturation of the component F,(2) of vibrational-rotational transition P(7) of the u3 methane band was used as the reference for frequency stabilization.* The importarit feature of the component F2 (2) here is that there is a magnetic hyperfine transition structure formed mainly of three strong components of different intensity with frequency intervals between the adjacent components of 11.4 and 14.2 kHz.9 The influence of the light field in the cavity and the pressure of methane in the cell on the position of narrow resonance can be reduced substantially by using resonances with their half-width r of the order of the hyperfine splitting value A for frequency stabilization and by applying the radiation frequency modulation with frequency f - A and a small modulation index (91).
OPTICS AND LASER TECHNOLOGY
. AUGUST
1981
End plate
Plasma tube and carrier
Steel hall Quartz absorption
Adjustment screw
Retainer screw
Piezoelectric translator Rubber compression ring
Inva: rod
Mirror‘carrier
Plasma t&e carriage
Thermoelectric coder
Silicone oil filled aluminium cup
Fig. 3
Design of
HeNe laser (A = 633
nm) with “‘12
absorbing cell6
the COs /CO2 system are as follows: cavity is 1 m long, the length of the intra-cavity fluorescent cell is between 50 and 100 mm, the COZ pressure in the cavity is 2 x 10T2 Torr and the beam diameter is 10 mm. To increase the fluorescence signal a highly sensitive, cooled (Ge :Cu ,4 K) large area photodetector (up to 20 x 20 mm) is used.
I IO
-3
I -2
IO
I
I
I
I
10-l
IO0
IO
100
1000
Sample time (5) Fig. 4
Frequency stability nm as a function
at h = 633
(Allan variance plots) of HeNe 12’12 of sample time6
laser
Such an idea has been used experimentally’0 in a system with long absorbing (3 m) and amplifying (2 m) cells where the parameters of saturation are matched by increasing the beam diameter of the CI-L, cell up to 10 mm. With the CH,J pressure in the region of 10-j Torr, the output power peak comes to several milliwatts with a width of 30 to 50 kHz and a contrast above 50%. At present the HeNe laser with a CH, cell enables the highest values of frequency reproducibility to be obtained with long-term stability (Table 1):
In the CO2 laser with an external, non-linear absorption cell the narrow resonances of saturated absorption within the Doppler line of some vibrational-rotational transitions of the v3 band in heavy, highly symmetrical molecules such as SF, and 0~0~ can be used as a reference frequency. For a typical CO2 /SF6 or CO2 /Os04 system, the CO2 laser output power required for absorption saturation is about 0.1 W the absorbing gas pressure is 10m3 to 10m2 Torr, the external cell length is 1 to 3 m, the beam diameter is several centimetres, the intensity ratio of saturating and probing waves is about 1O:l and the width of probe wave transmission resonances is about 100 kHz. For the CO2 laser, frequency stabilized with the central zero of the third derivative of narrow resonance of SF6, the long-term frequency stability
The CO* laser with a COs saturated cell fluorescing at 4.3 pm” has an important advantage in practice. This is that there is the possibility of generating sufficient power at more than 100 vibrational-rotational lines of the P and R branches of both bands (at 9.6 and 10.6 pm) over a frequency range from 27 to 33 THz. By non-linear mixing of the frequencies of two stabilized COs lasers it is also possible to produce several thousand harmonic frequencies over a range from 0.025 to 100 THz. Typical dimensions of Table 1. 1.
Frequency stability of HeNeKH4
The stability of such a laser has been improved12 by using an external CO2 absorbing cell, a 4.3 pm fluorescence collector cooled by nitrogen and a better detector. All these measures have given an increase in the signal-to-noise ratio of two orders of magnitude and a frequency stability of the two independent lasers, each 1.5 m long, of about o/2% N 6 x 10-r’/ 2;‘) where 7 denotes the averaging time. With r varying from 20 to 30 s the frequency stability was about 10-12, and the authors hope that this can be increased tenfold with further technical modifications. It must be added that the use of a sealed CO2 laser and CO2 absorbing cells with other isotopic molecules (I3 Cl6 02, I3 Ci802) enables the number of lines in the infra-red range with a highly stable frequency to be increased considerably.r2
laser systems10
Averaging time, 7 (s)
lo-3
lo-2
10-l
loo
10
100
2.
Measurement, T (min)
30
30
30
120
120
120
3.
Average differency of frequencies of two lasers (Hz)
-
-
-
3
2
-
FraFtional standard* deviation per laser u/2 av
6 x lo-l2
3 x lo-l2
5 x IO-l3
IO-l3
3 x lo-l4
5 x lo-l5
4.
~Fteproducibilitv
of frequency
during 30 independent
OPTICS AND LASER TECHNOLOGY.
measurements
AUGUST
1981
was 3.5 x 16-14
205
attained on the P(18) line of COZ was the maximum for CO2 lasers (better than 10”2)13~14. The expected values of frequency stability and reproducibility for the CO2 /Os04 system are higher smce the vibrational-rotational spectrum of monoisotopic Os04 molecules with even-numbered isotopes of OS has no hyperfme nuclear structure. Lasers with very narrow frequency-stable output
spectral
For more accurate fixing of the laser frequency to the molecular reference line, the signal-to-noise ratio of the servo-system should be increased by narrowing its transmission band. The ultimate transmission band of the servosystem is governed by fast laser frequency fluctuations, ie its short-term frequency stability. The minimum spectral width of laser radiation due to spontaneous emission is given by
-6
-8 -
-loiY -12
Au min
=
8rlhvAv2,/P,
(1)
1 -10
-8
-6
I -4
‘I
I -2
0
w -w
c
I
I
I
I
I
2
4
6
8
IO
J 12
b
rb
where Au, is the cavity line half-width at frequency v and P is the laser output power. A greater contribution to frequency instability is made by the fluctuations of lowfrequency spatial modes excited by the thermal fluctuations in the material of the laser cavity. Their relative average value is
CL L
Fig. 6 Dependence of the oscillation frequency w of a gas laser with non-linear absorption on the cavity frequency shift around the centre of the absorption line ~b. 2rb is the homogeneous idth of absorbing w6 line andqb is the non-linear frequency PUlhTg faCtOr
” lo-l4 to lo-‘5,
where i-is the temperature, V is the volume of the bars in the cavity and Y is Young’s modulus. The main contribution to the frequency instability of laser systems is made by technical effects. The use of the various methods makes it possible to narrow the spectral width of laser radiation lines, for short times (lOa to 10”s) to several Hz @v/v 2 lo-rO/lo~s). It is possible to produce an extremely narrow radiation spectrum in frequency-stabilized lasers in which technically introduced frequency fluctuations are eliminated by all
1
possible means. l5 In experiments by V. Chebotayev the frequency beating signal of the two independent frequencystabilized HeNe/CH, lasers was recorded with a characteristic beat frequency of just several Hz, conditioned by a frequency difference of the lasers. The spectral width of the beat signal was only 0.4 Hz (!). Figure 5 shows the beat signal spectrum of two independently stabilized lasers of this type. Its width is again about 0.4 Hz. Thus, a laser with its frequency stabilized to a narrow resonance of nonlinear absorption in CH4 is the most monochromatic oscillator of electromagnetic radiation at present available The requirement of simultaneous high short- and longterm frequency stability can be met with the use of combined systems of frequency servo control having the advantages of frequency reproduction by an atomic (molecular) reference line, and the high sensitivity and short-term frequency stability of a Fabry-Perot interferometer. The modulation frequency and transmission band of the loop consisting of a laser and an interferometer must be relatively high (up to 10’ Hz), and the loop including both optical discriminators and compensating for slow, thermal frequency drifts of the Fabry-Perot interferometer has a narrow band of 0.1 to 1 Hz. In another version, the interferometer resonance frequency is stabilized by an additional frequency controlled laser, for example a 3.39 pm HeNe laser with a methane cell. High short-term laser frequency stability can also be attained by tuning its beat signal frequency to another laser, the frequency of which is stabilized to a high accuracy using a wide band servo loop. The gain of the servo system may be as high as lob’, and the band width several MHz. Such laser heterodynes, without frequency modulation of radiation, form the basis for most measurement methods (comparison) of the laser frequency and its stability.
1 Fig. 5 Sp trum of beats of two independently CH4 lasers”
206
stabilized
HeNe/
To eliminate fast laser frequency fluctuations it is potentially very effective to use the frequency self-stabilization effect, particularly in combination with a narrow-band loop of frequency servo tuning with an atomic or molecular reference line.lb This effect manifests itself by a non-linear distortion of a laser frequency w with an internal absorbing cell to the centre of an absorption line ab. The degree of
OPTICS AND LASER TECHNOLOGY.
AUGUST
1981
distortion depends (Fig. 6) on the slopes of the curve W-U,, =(w, -c+,)(l +Q,)~ at thepointw=Wb. With considerable self-stabilization (qb 5 lo), frequency hysteresis can be observed. Furthermore, absolute frequency self-stabilization is possible when, regardless of the variation of the cavity frequency w, , laser action appears at longitudinal modes such that its frequency lies completely within the homogeneous width 2I’ near the centre of the absorption line. The frequency self-stabilization time coincides with the transient time of laser field amplitude in the cavity and may be as small as IO-’ - 10e6 s. Methods of laser wavelength
measurement
To measure (compare) the wavelengths of two different etalon lasers it is possible in some cases to measure the orders of interference of light from one type of laser heterodyne in the cavity, the length of which is tuned on transmission resonance to the frequency of a laser heterodyne of another type. The orders of interference are counted by scanning the frequency fo the first laser heterodyne relative to the reference laser and by measuring their difference in frequency. The use of laser heterodynes with etalon lasers not only allows elimination of the effect of stabilized lasers but also makes it possible to overcome the problem of scanning the interferometer length. To reduce the effect of different phase shifts during beam reflection the measurements must be carried out in series with two interferometers of different length. The measurement accuracy of wavelength is determined by the signal-to-noise ratio. With prolonged observation it may beashighas lO+ and at ordinary observation durations (about 1 s) it is 10”. A more important restriction on the reproducibility is caused by the diffraction of a light wave with a limited diameter. To obtain a reproducibility of 10” it is necessary for the divergence of light beam to be around lOa rad. To obtain this value for a Gaussian beam with diameter 20, the condition 20~5 104Xln must be satisfied. For the wavelength A = 0.63 m the beam diameter should be 20~ >” 2 mm and for h = 10.4 w 20~ 5 30 mm. An increase m beam diameter appears to be of low efficiency since it becomes difficult to align the optics. It can pay for itself only in unique metrological set-ups. Because of the wide use of tunable lasers with narrow radiation lines in spectroscopy, several reasonably simple laboratory wavemeters have recently been devebped for laser radiation over the range from 1 to 10 MHz, ie AX z IO” IO-‘. They all are based on a comparison between the wavelength measured and that of stabilized NeNe& laser.‘*-** The use of an array of photodiodes (usually 1 024 elements) makes is possible to record the interference pattern electronically and thereby to automate completely the data
AUGUST
1981
photodiode orray
:
‘02as
Beam exponding
4
Fig. 7
Absolute measurements of wavelength in stabilized lasers are consistent with interferometric comparison to the wavelength of the krypton standard. In this arrangement the light beam from the laser is made to coincide with that from a s6Kr lamp and is passed through a linearly frequencyscanned Fabry-Perot or Michelson interferometer. The interferometer resonances are simultaneously recorded from each source and compared. The measurement accuracy of laser wavelength depends mainly on the accuracy of the krypton standard and the lenarity of interferometer frequency scanning. The scanning linearity can be improved by servo control tuning of the interferometer length by means of the additional laser heterodyne, the frequency of which is scanned slowly relative to the frequency of the etalon laser.
OPTICS AND LASER TECHNOLOGY.
Linear
t-20
collimator
seconds of arc
Fizeau wavemeter
of laser radiation*’
processing. Figure 7 shows schematically a laser wavemeter with a Fizeau interferometer. *I The instrument consists of an optical system for the laser beam, a collimator widening the light beam, a simple Fizeau interferometer, a linear array of 1 024 photodiode elements, electronics for signal processing and a microcomputer for calculation and digital display of wavelength values. The wavelengths measured by the instrument are in the range 0.4 to 1 .l pm; the measurement accuracy is about 3 x lo-‘. The wavemeter can operate with continuous or pulsed operation and is fairly simple as far as its optics and mechanics are concerned. Recently commercial wavemeters have come into the market with accuracies of about 10”. These can be suitable for routine operation with tunable lasers. The WA-20 type wavemeter produced by Burleigh Instruments23 is an example. It is designed to measure continuous radiation wavelengths accurately to 10 d in the region 0.4 to 4.0 pm. The measurement time is 1.6 s and the result can be seen on an illuminated indicator display. Similar parameters of wavelneters can be obtained not only for continuous but also for pulsed radiation. For example, the French firm Sopra SA23 have introduced a wavemeter with an accuracy of about 10d in the range 0.3 to 1 .O pm for pulsed and continuous laser radiation. Commercial wavemetres with a higher accuracy for precision metrological measurement on the basis of a reference HeNe/I, laser are expected to be
develaped . Methods of laser frequency
measurement
Laser frequency measurement is based on multiplying laser frequency microwave oscillators, known with a high accuracy, up to laser radiation frequencies and on their subsequent comparison by frequency mixing. To realize this process a set of frequency-stabilized sub-milllmetre and infra-red lasers must be used as well as non&near elements (mixers), inertia-less up to optical frequencies. The chain of synthesis of the frequency of optical-range lasers has been described.24*25 In this chain laser radiation of an unknown frequency (VL) serves as the reference oscillator signal in heterodyne detection of the weak signal of the high-harmonic klystron radiation (nv,) and of other lasers (IQ, mv,), the frequencies of which (v, , vI, v,) are measured initially. The radio frequency signal passing through the diode mixer can be expressed as vd = VL - (Iv, f mv, + nv,,) where 1, m, n are the numbers of frequency harmonics. Absolute measurement (synthesis) of frequencies is accomplished in several steps. The first step of the frequency synthesis is to measure the frequency of the standard lines R(10) at 9.33 cun and R(30) at 10.18 lun of the stabilized CO2 laser (narrow resonance of fluorescence in CO2
207
serves as a reference frequency). In the second stage the frequencies of the standard lines serve as a basis from which to measure the frequencies of the rest of the COZ laser lines. Third, frequency-stabilized CO? lasers are used to measure the frequency of the absorption line P(7) of methane to which a HeNe 3.39 pm laser is stabilized. Fourth, HeNe and COa lasers are used for frequency synthesis and measurement in the near infra-red range. The frequencies of HCN, DCN, Ha 0 and Dz 0 lasers are measured using silicon point-contact diodes. The highest frequency measured is about 3 THz. To detect infra-red frequencies up to 200 THz25 point-contact metal oxidediodes can be used. The design of such diodes is a pointed (up to 100 pm) thin (several microns) tungsten wire antenna which is in mechanical contact with a nickel plate. This contact is realized through a thin oxide fh several angstroms thick which serves a a barrier in quantum-mechanical electron tunelhng. The laser radiation is focused onto the wire antenna directly at the point of contact, and the microwave signal from the klystron is also fed to this contact. The best stability of characteristics over the entire cycle of frequency measurement can be ensued using another diode design in which the point contacts with the infra-red antenna are printed on a sapphire sub-stratum photolithographicall.26 Absolute measurement of laser frequency is being developed in two directions. First, the high-frequency limit of absolute frequency measurement is increasing continuously. In the very first experiments in 1967 the 890 GHz radiation frequency of a HCN laser2’ was measured and ten years later it has become possible to measure the 260 THz frequency of radiation at the 1 .15 pm wavelength of a aeNe laser and the absolute frequencies of certain spectral lines of 12’12 in the visible range at nearly 520 THz.~* The accuracy of such measurements of absolute frequency varies between lo+ and 10-lo in accordance with the measurement accuracy of sub-millimetre laser frequencies. The second direction of progress is connected with an increase of frequency measurement accuracy. The following scheme29 for transfer of standard frequencies from the caesium frequency standard to the optical spectral region has been realized: Cs standard & HCN (337 m) -% COa/Os04
(10.53 m)
& Dz 0 (84 pm) -+
% CO2 (10.18 pm) -+
(3)
-% HeNe/CH4 (3.39 run) The measurement accuracy of the HeNe/CH4 laser frequency was 1O-1o and for the CO,/OsO,, laser 3 x lo-” . Such an increase in accuracy has been made possible by using a more rational structure for frequency synthesis with the introduction of D2 0 and CO2 /Os04 lasers. This allows the order of frequency multiplication to be decreased while increasing the signal-to-noise ratio in frequency conversion. The sub-milhmetre laser frequency was stabilized through phase locking by the Cs standard of microwave frequency. In this case the first three oscillators in the chain of frequency synthesis have frequency values defined to an accuracy of 10-13. With the use of the eighth harmonic of the D2 0 laser it is now possible to determine the COZ /OsOd laser frequency with the same accuracy. In the work of reference 29 the frequency measurement accuracy (3 x lo-“) was governed only by the frequency instability of the CO2 / 0~0~ laser itself. This value is expected to be increased in
208
future up to lo-l3 with the possibility a fairly high frequency stability.
of using a laser with
Conclusion and prospects In the past ten years the methods of laser Doppler-free spectroscopy have resulted in considerable progress in optical quantum metrology of length and frequency. Measurements of wavelength accurate to 1Om8are quite possible now, not only in metrological but also in physical laboratories. They are based on the use of a highly frequency-stabilized HeNe/ I2 laser as reference. In combination with methods of nonlinear spectroscopy, without Doppler broadening of the quantum transitions of the hydrogen atom, the Rydberg constant has been determined more accurately. It has become possible to carry out absolute measurements of light oscillation frequency with an accuracy of better than lo+. On the basis of independent measurements of light wavelength and frequency, the light velocity in vacuum has been also measured to a higher accuracy. The values obtained for the Rydberg constant and light velocity are given in Table 2. The possibility of absolute measurement of light frequency and precise measurement of light velocity have opened the way for the creation of a joint standard for time and length instead of two independent standards based on the spectral lines of the 133Cs and 86Kr atoms. This is one of the primary goals of optical quantum metrology where the latest advances in laser spectroscopy are used. It is now possible to carry out absolute measurement of frequencies in the infrared range accurate to 10-l’ on the basis that the CO, laser and the frequency of molecular vibration transitions can be measured with the same accuracy. We can hope for further increasing accuracy up to lOA using individual metrological laser set-ups. This offers considerable scope for comparison between the frequencies of atomic and molecular transitions, ie between the atomic and molecular time scalesT9 Such experiments based on the advances in laser spectroscopy are of fundamental importance for quantum metrology Some fundamental problems of quantum metrology, such as how to achieve frequency stability and reproducibility much better than 10 13 , stimulate the development of methods to produce very narrow optical resonances. It is difficult to overcome the barrier 6v/v Z lo-l3 1lo-l4 principally because of broadening and shift of the frequency of spectral lines, including narrow non-linear resonances, due to the second-order Doppler effect Table 2. Values of physical constants obtained with the use of frequency-stabilized lasers
Constants
Relative measurement accuracy
Value
Light velocity in vacuum,24,25 c (m s-1 ) 299 792 456.2 + 1 .l
k3.5 x lo*
Rydberg constant= R km-‘)
+3x
Note:
In 1973 the Comiti
recommended (k/c
109 737.31476
the following
+ 0.00032
Consultatif
pour la Dhfinition
10-e du M’etre
value: c = 299 792 458 m s-1
= f 4 x 10-Y.
OPTICS AND LASER TECHNOLOGY
. AUGUST
1981
6V __=__= V
V2
-
2
4.6 x lo-r4 T
2c2 The numerical value here is given for the atomic mass A = 200, T is the temperature of particles in gas. One of the main possibilities for elimination of this effect is based on particle cooling to temperature below several K. Deep cooling of ions by laser radiation has been demonstrated3’ and some schemes have been put forward3’ for using highquality (Q = 1O-l3 /l 0-14) spectral lines of cooled ions in a trap to establish an optical frequency standard. Finally, among interesting applications of laser frequency standards we should point out the possibility of measurement of small displacements and creation of gravitational wave detectors by this technique. Indeed, the measurements of the laser oscillation phase or frequency at small displacements of the mirror can be performed with the use of narrow optical resonances and highly frequency-stabilized lasers. Published recently33 are results of the first successful experiments of this kind in which the relative sensitivity of length measurement was AL/L E 10-16. The experiments were carried out with a HeNe laser at X = 3.39 pm. The nonlinear resonances in methane were 50 kHz in width and low3 W in intensity. One of the mirrors of the laser cavity was fed with a periodic perturbation. The absolute sensitivity of measurements with L = 500 cm was as high as 6 x 10” A. The minimum detectable deviation in cavity length depends on the photon noise of laser radiation. In case of a narrow non-linear resonance with width 2r the detectable displacement AL,,,i, is determined from the expression33
3 4 5 6 7 8 9 10 11 12 13 14 15
16
17 18 19 20 21 22 23 24 25
AL min 26
where v,,, = c/U, is the mode spacing, k, is the narrow resonance contrast in the laser output power PO, Af is the band width measurement. As compared to the method of Michelson interferometry, the use of a laser stabilized by a narrow resonance allows an increase in sensitivity by factor v,/I’ E 103. The estimation of ALmh under the experimental conditions33 gives A.L,h N lo-l6 cm Hz-“‘. The real sensitivity is about two orders worse because of technical fluctuations.
24 (1974)
29
Hacker, L.O., Javan, A. et aZAppZ Phys Lett 10 (1967) 147 Jennings, D.A., Petersen, F.R., Evenson, K.M. in Laser sepctroscopy IV’ edited by H. Walther, K.W. Rothe Optical Sciences 21 (Springer-Verlag. 1979) 39 Domnin, YS., Kosheliaevs&i, NJ. et al pis’ma Zh Eksp
30
Goldsmith, J.G.M.,Web& E.W., Jansch~T.W. Phys Rev Lett
27 28
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41 (1978)
31 32
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