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Frequency measurement of the 5S12(F = 3)−5D52(F = 5) two-photon transition in rubidium
1 January 1997
OPTICS
COMMUNICATIONS ELSEYIER
Optics Communications 133 ( 1997) 47 I-478
Full length article
Frequency measurement of the 5S,,,( F = 3) -5D,,,( F = 51 two-photon transition in rubidium D. Touahri a**, 0. Acef a, A. Clairon a, J.-J. Zondy a, R. Felder b, L. Hilico MU, B. de Beauvoir ‘, F. Biraben ‘, F. Nez ’ a Luboratoire
Primaire
du Temps et des Frhyuences
b Bureau ’ Luborutoire
lnternutional
Kustler Brossel. Ecole Normale 4. pluce Jussieu.
’ D&artement
(BNM-LPTF),
des Poids et Mesures Supdrieure,
Observuroire
de Paris. 61 Au. de I’Observutoire,
(BIPM). Puvillon de Breteuil, F-92312, Universith Pierre
Tour 12, EOI. C74. F-75252,
de Physique Chimie. University d’Evry val d’Essonne.
et Murk
S&res
Curie, Laboratoire
F-75014
Park.
France
Cedex, Fruncr ussocie’ uu CNRS (IRA 18.
Paris Cedex 05. France
Boulevard
des Coquibus.
F-91025,
Evry Cede-r, Frunce
Received 23 April 1996; accepted I1 July 1996
Abstract We have measured the frequencies of three diode lasers stabilized on the 5s ,,&F = 3)-5D,,,(F = 5) two-photon transition in rubidium at h = 778.1 nm, with an uncertainty of 1 kHz, using BNM-LPTP frequency synthesis chain starting from a CO,/OsO, reference laser at 10.3 km. We show that this frequency chain is able to reach the lo-‘” resolution level. After a discussion of the systematic effects that may shift the resonance, the transition frequency is found to be v = 385 285 142 378.280 + 2 kHz.
1. Introduction Progress toward the definition of highly accurate optical frequency standards in the visible and near-IR range is of fundamental importance in various applications. such as the Mise en Prarique of the definition of the Meter [l], high resolution spectroscopy of cold atoms or ions and precision measurement of fundamental constants. The Rydberg constant, determined from two-photon spectroscopy of hydrogen atom [2,3], is presently the most accurately known fundamental constant. The two-photon transition in
* Corresponding author. E-mail: [email protected]. ’ E-mail: [email protected]. 0030-4018/97/$17.00 PII SOO30-4018(96)0047
rubidium at 778.1 nm (385.3 THz) matches closely (A = 40 GHz) the 2S-8D two-photon transition frequency of natural hydrogen. To this extent it represents a more suitable reference than the 473.6 THz red He-Ne/I, standard [4] for the H-atom spectroscopy, all the better than its metrological performance in terms of stability and reproducibility is at least 20 times better [5]. Furthermore, the frequency of the 5S,,,-5D,,,z transition is only a few GHz away from the difference frequency between the red (He-Ne/I,l and mid-IR (He-Ne/CH, at 88.4 THz) standards. This coincidence was used for the first determination of its absolute frequency with an uncertainty of 5 kHz [6], mainly limited by the uncertainty on the red frequency standard. The frequency of the 5S, ,2( F =
Copyright 0 1997 Published by Elsevier Science B.V. All rights reserved. l-3
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3)-5D,,,(F = 5) was later on determined with an uncertainty of 6 kHz from that measurement using a Schottky diode to bridge the 45 GHz gap between the two fine structures [7]. Several laboratories world-wide are developing rubidium two-photon systems or use the neighbouring 780 nm Rb/D, saturated absorption line as a frequency reference. The 778.1 nm transition will provide an accurate reference for optical telecommunication network, through the frequency-doubling of 1.556 pm diode lasers. Last but not least, it can serve as a convenient secondary standard in simpler frequency chains, in conjunction with other IR optical standard (HeNe/CH, or COJOsO,), for the absolute frequency measurement of many ionic or molecular potential standards in the visible/near-IR range [8], such as the green iodine B-X line at 532 nm [9]. All these reasons motivated this work aimed at the absolute frequency determination, at the IO-l2 accuracy level, of this promising near-IR standard.
2. The two-photon system The three two-photon systems (Fig. 1) we have measured are very similar [5]. Two of them Ll and L2 are located in our laboratory (LPTF) and the third one (KB) in the Kastler-Brossel laboratory. The lat-
ECL Diode
Frequency
Anamorphic
, Prisms
I33 (1997) 471-478
ter is connected to the LPTF by two 3 km long optical fiber links. The rubidium vapour is enclosed in a fused silica sealed cell with Brewster window ends. A pressure of about 8 X IO-’ Torr is obtained by maintaining the temperature around 90°C. The cell as well as the detection apparatus are surrounded by a magnetic shield. A plano-concave Fabry-Perot cavity is constructed around the cell in order to probe the transition with a well defined Gaussian beam. The cavity length is 30 cm and the l/e2 waist radius is 420 pm. The loaded cavity finesses are of the order of 50. The Doppler-free two-photon hyperfine transition is probed with an extended-cavity AlGaAs laser diode (ECL). The diode injection current. is modulated at 70 kHz, producing a 600 kHz peak-to-peak modulation of the laser frequency, which is approximately equal to the measured two-photon transition linewidth [6]. To enhance the optical isolation of the diode, the laser frequency is 2 X 80 MHz shifted by an acousto-optic modulator (AOM) used in a double-pass configuration. The signal leaking out from the cavity is used to lock its length to the laser frequency, after demodulation. The transmitted power is compared to a reference level, which enables to stabilize the intracavity power by a second slow servo loop, controlling the diffraction efficiency of
Faraday isolator
LI ?J2 n
I
AOM
1
-_________________----------_--_
I________________I
Fig. 1. Schematic of the rubidium two-photon transition stabilized diode laser. L ,.*,) are matching lenses. L, is the fluorescence lens and PMT a photomultiplier tube. PZT is a piezo translator. AOM is an acousto-optic modulator.
collecting
D. Touahri et al. / Optics Communications
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r
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-4000
-
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-
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133 (1997) 471-478
\ ’ 2
.
’ 4
lntracavity
. 6
power
.
8
a
10
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Fig. 2. Light shift versus the intracavity optical power for Ll system. The integration time is 100 s per point. The standard deviation of the fit is 125 Hz. For the horizontal scale, I a.u. corresponds to about 7 mW.
the AOM. This system can be continuously tuned over 1 GHz. The well-resolved two-photon transitions are detected by monitoring the blue fluorescence (A = 420 nm) due to the radiative cascade 5D-6P-5S with a photomultiplier tube. The laser is frequency modulated and the fluorescence is phase sensitively detected at the first harmonic of the modulation in order to lock the laser frequency on the 5S,,,(F = 3)-5D,,,(F = 5) component of the *‘Rb two-photon transition. For Ll, with a total intracavity power of 35 mW, we detect a fluorescence photon flux of 5 X lO’/s. The light shifts of the systems were determined eight days after the measurement and found to be 8414, 7596 and 7300 Hz, corresponding to typical intracavity optical powers of 35 mW. The light shift versus the intracavity power is shown in Fig. 2. The intracavity power was controlled to within 0.2%, so the uncertainty on the light shift is due to the linear fit of Fig. 2 and is 130 Hz. The frequencies of Ll, L2 and KB are compared by counting the beat frequency between Ll and L2 or KB. These beatnotes have large signal-to-noise ratios (SNR) (> 60 dB in a 100 kHz bandwidth). The three two-photon set-ups have been periodically compared throughout a period of one year. The frequency stability, in terms of Allan variance, of these systems is about 4 X IO-’ 37-“’ per laser over 1000 s. Their repeatability is better than 300 Hz (lo) over one year. The reproducibility is better than 1200 Hz.
The starting point for the frequency synthesis chain is the 0~0, reference frequency ( v = 29096274952 340 + 70 Hz) which is in quasi coincidence with the R(l2) CO, laser line. It is one of the most accurate frequencies in the 10 km range. We have two such frequency standards. One of them was measured against a caesium primary clock in 1983 [lo]. Both were compared to a Russian HeNe/CH, standard at 3.39 pm in 1986 Ill]. At this occasion, it was demonstrated that the agreement between two independent chains was at the lo-** level. Our standards have been successively improved, preserving the memory of their frequencies to within f70 Hz. These systems have a reproducibility of 3 parts in 1013 measured over 18 months. The relative stability of these oscillators is 1.4 X 10-‘3~-1/2 per laser over 300 s. We expect the frequency synthesis chain to translate this performance to the visible domain. two-photon transition in rubidThe 5S,,,-5D,,, ium is only 20 GHz away from the 13th harmonic of the R(42) ‘2C’602 line (v, = 29638880 152340 Hz). This R(42) CO, laser is phase-locked to the R(l2) CO, laser with a frequency offset of 540.605 200 GHz. A low phase noise 100 MHz quartz oscillator, weakly locked to a H-maser, is multiplied using a step recovery diode. The 113th harmonic, at 11.3 GHz, is filtered and mixed with a 90.409200 GHz klystron in a Schottky diode to phase-lock the klystron to the H-maser. The R(l2) reference and the R(42) CO, lasers are compared to the sixth harmonic of the klystron using a MIM diode. The beat note (25 dB SNR in a 100 kHz bandwidth) is used to phase-lock the R(421 CO, laser. This reference set-up remains locked for more than 12 hours. The uncertainty in the R(l2)/0sO, frequency is translated to the R(42) frequency, but the stability is slightly degraded: the IO- ’ ’ (1 sl relative stability of the 100 MHz quartz is translated to the sixth harmonic of the klystron. Its contribution to the R(42) laser relative stability is thus in the ratio 29.6 to 0.54, that is 2 X 10-13. The R(42) laser relative stability is then 2.5 X lo- I3 for 1 s integration time. Taking into account the 4 X 1O-‘3 relative stability of the two-photon systems, a quadratic sum leads
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to a 4.7 X lo- I3 expected value for the measurement stability for 1 s integration time.
4. Frequency synthesis and measurement chain Fig. 3 sketches the 29 THz (v,) to 385 THz (13 vR) frequency chain architecture, derived from the one implemented for the red He-Ne/I, frequency measurement [4]. The 13th harmonic is synthesized by a 29 THz up-conversion (SFG) of a diode laser at 842.9 nm (12~) [81. A 3:l frequency divider of the 842.9 nm diode laser is then implemented so as to translate the absolute frequency measurement in the 4uR range (A = 2.5287 pm): the near-IR laser frequency is down-converted to 8v, (A = 1.264 km> by difference-frequency generation (DFG) with a KCl:Li color-center laser (CCL) operating near 4~. The latter is simultaneously frequency-doubled (SHG) and the 3:l division is ful-
filled by monitoring the RF beatnotes between the two 8v, generated signals and a local oscillator (InGaAsP diode laser) at 8~~. Finally the CCL frequency is measured against the reference frequency using a fifth-order mixing in a metal-insulator-metal (MIM) W:Ni point-contact diode. The remaining 20 GHz gap between the 778.06 nm (13~~) transfer laser and the Rb (5%5D) frequency is bridged using a Schottky diode and a 10.08 GHz YIG oscillator phase-locked to a Cs clock. In its present status, this frequency chain is quasi-continuously tunable in the near-IR/visible spectrum [12]. 4.1. The transfer lasers The CCL operating at 2.528 km is frequencylocked on a ULE glass Fabry-Perot cavity to reduce its linewidth to less than 1 kHz [13]. The cavity frequency drift is of the order of 200 Hz/s. The available single-mode output power is I4 mW. The 1.264 pm InGaAsP diode laser is operated as an ECL, with a linewidth of 50-100 kHz. The available power of 3 mW, which is too low for efficient non-linear mixings, justifies its use as a local oscillator for the two beatnotes involved in the 3:l divider. The 842.9 nm laser is a high power (200 mW> AlGaAs diode laser injection-locked by a master ECL. The 778.06 nm (13~~) transfer oscillator is also an ECL. Both ECL’s are frequency-stabilized on the same temperature-controlled high finesse FabryPe’rot cavity to reduce their linewidths (< 1 kHz) and frequency drifts during the measurement ( < 250 Hz/s). 4.2. The non-linear mixings and beatnotes
Fig. 3. Frequency
synthesis and measurement
chain.
All the parametric mixings involved in the chain employ silver thiogallate crystals (AgGaS,) as the non-linear optical converter, because of its high non-linearity and its extended type-1 phase-matching capabilities over the entire optical spectrum [8,13]. All the reported beatnotes signal-to-noise ratio (SNR) were measured in a 100 kHz spectrum analyzer bandwidth. The color-center laser SHG and the 842.9 nm laser SFG are both critically phase-matched at B = 43” and yield respectively 5 nW at 8 V~ (from 13 mW of CCL) and 6 p,W at 13~~ (from 50 mW of
D. Touahri et al./Optics
Communications 133 (1997) 471-478
near-IR and 300 mW of CO, powers). The SNR of the corresponding beatnotes were 30 dB and 60 dB. The DFG process of the 3:l divider is temperaturetuned (T = - 10°C at the measurement wavelengths) non-critically phase-matched (NCPM) over the CCL tuning range, which spans over the fourth harmonic spectrum of CO, lasing lines. The beatnote between a fraction of the generated 8v, signal (80 nW>, and 1.5 mW of the InGaAsP laser, leads to a SNR of 40-45 dB. The SNR of the Schottky diode RF beatnote bridging the 20 GHz gap at the top end of the chain is about 35 dB [ 141. The beatnotes between Ll, L2 and KB have high enough SNR exceeding 50-60 dB. The most crucial beatnote detection was the MIM detection of the fourth harmonic of the reference laser because only 6 mW of CCL power is available at this stage (due to the losses experienced through the parametric mixing processes and to residual atmospheric water vapour absorption). The video response over a 1 Ma load resistor of the better MIM diode tried was 10 p.V/mW and 500 p.V/mW for the CCL and CO, radiation respeetively. However, the thermal instability of these diodes which occurred during the He-Ne/I, absolute frequency measurement [4] was not observed this time. The SNR of this beatnote ranged between 12 to 15 dB, depending on the quality of the contact point, but remained stable for hours for the best operating diode.
5. The measurement
method
The frequency chain of Fig. 3 is not a phase-locked chain, so that a synchronized counting of the various beatnotes is required to cancel the frequency drifts of the transfer lasers. Furthermore, since some of the beatnotes cannot be directly counted due to their low SNR, tracking voltage-controlled oscillators (VCO) are phase-locked on those beatnotes. Additional synthesizers enable to down-convert the beat signals in the operating range (50-150 MHz) of the tracking VCO’s. The eight frequency counters we used were externally triggered and remote-controlled by a micro computer. Their synchronization is better than 0.5 ps, so that even if a beatnote drifts by 1 MHz/s, the counting error will be less than 1 Hz. The
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frequencies are counted during 1 s, with a dead time of 0.16 s. The two beatnotes between the two-photon systems, that between the two COJOsO, reference lasers, as well as the one comparing the frequency of the up-converted 13~, radiation to the 778.06 nm transfer laser were counted directly after appropriate filtering and amplifying. For the remaining beatnotes, which SNR were below the 50 dB range. tracking VCO’s with a loop bandwidth ranging from 30 to 300 kHz enabled them to be counted reliably [4]. The SNR of the beatnote produced by the MIM diode comparing the fourth harmonic of the R(42) CO, laser to the color center laser was very low ( 12 to 15 dB). In addition, this beat note was slightly frequency modulated (10 kHz peak-to-peak at a 2.2 kHz rate>. We have checked that it is possible to reliably track such a beatnote by simulating it with a frequency-modulated synthesizer. Between 9 and 12 dB of SNR, counting errors are observed, which strongly depend on the tracking loop bandwidth. So long as the SNR exceeds 12 dB in a 100 kHz bandwidth, the phase-tracked signal is counted without any error for a large range of loop bandwidths. The first time we ran the experiment, the SNR of that beatnote was only about 10 dB in a 100 kHz bandwidth. Though we noticed a posteriori that the mean value of the corresponding measured frequency was only 280 Hz smaller than that we obtained with measurement series performed with a larger SNR, the related standard deviation was however two or three times greater. The high frequency part of the chain, from the 842.9 nm diode laser to the three DL/Rb systems, as well as the CO, lasers were extremely stable and able to run for several hours without any miss-locking of the feedback loops. Several MIM diodes have detected the beatnote between the CO, laser and the CCL, and the one that gave the 12 to 15 dB SNR survived for more than six hours. On the other hand, the CCL and to a lesser extent the InCaAsP diode displayed frequent mode-hopping, resulting in the switching-off of the corresponding tracking oscillators and limiting the integration time of the experiment. This behaviour may have several origins. Actually, in order to get 14 mW at 2.52 pm, the CCL was strongly pumped by 3.7 W of a Krf laser and was operating close to a multimode regime. Optical
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feedback from the MIM. diode as well as intracavity water vapour absorption may have increased the laser instability. Over more than 4 hours, the experiment has produced 2348 measurements of the two-photon transition frequency, in small time series ranging from 17 to 502 seconds.
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n
6. Results and discussion The three two-photon systems frequencies have been measured simultaneously. Fig. 4 shows the histogram of the 2348 1 second measurements together with its Gaussian fit curve, for the Ll synthesised frequency. Similar curves are obtained for L2 and KB. The relative standard deviation of the results is 4.5 X IO-l3 for Ll and slightly larger for L2 and KB. Fig. 5 shows the square root of the Allan variance of the Ll synthesized frequency for the sequence of 502 successive measurements. The stabilities of the three measurements are quite similar, 4.6 X 10-‘3r-‘/2, 7.7 X 10-‘3r-/2 and 4 X 10-‘3r7-‘/2 for Ll, L2 and KB respectively. Those values are in good agreement with the expected 4.7 X lo-l3 stability for 1 s integration time. We have also plotted the relative stability between two two-photon systems deduced from the Ll/KB beatnote, as well as the relative stability between the two CO,/OsO, reference lasers: one can conclude that the measurement uncertainty is mainly limited by the
n.
A
Fig. 5. Allan standard deviation of the measured value of Ll (circles) deduced from the continuous set of 502 data, and relative stability of the two-photon systems Ll and KB (triangles). The relative stability of the two reference standards CO, /OsO, is also plotted (squares). The full line shows the r- “* dependence of the stabilities.
present intrinsic Rb/DL stability. The frequency synthesis chain does not add significant noise contribution to the measurement, at the lo-l3 level. The chain is able to reach at least lo-l3 in resolution. The two-photon transition frequency has to be corrected for the light (or power) shift which depends linearly on the intracavity optical power. This effect was measured for each two-photon system a few days after the experiment. The average frequencies of Ll, L2 and KB, extrapolated to zero power, are indicated in Table 1 for the 5S,d2(F = 3)5D,,,(F = 5) hyperfine component of ‘Rb. Note that during the experiment, KB was unlocked for a few minutes, so the KB value is averaged only over 1492 points. L 1 and KB are found to be very close to each other (within the repeatability of the systems), while L2 differs from Ll by about 1100 Hz, that is
Table 1 Absolute frequency values of Ll, L2 and KB two-photon set-ups, extrapolated to zero optical power, but not corrected from the second order Doppler effect. ‘The uncertainty is 1 kHz. RSD is the relative standard deviation of the sample of measurements (Hz)
Fig. 4. Histogram of the 2348 measurement of Lt. and its Gaussian tit. The mean value is 385285 142369.190 kHz and the standard deviation is 170 Hz.
System
Frequency
Ll L2 KB
385 285 142377.600 385 285 142378.730 385 285 142 377.820
&Hz)
RSD 4.4x 10-13 6.8X lo-l3 3.7x lo-l3
D. Towhri
et al./Optics
Communications
3 x IO-I2in relative value. The repeatability of the
systems (300 Hz day to day) and the uncertainty of 70 Hz on the COJOsO, reference laser multiplied by 13 add quadratically to give a 1000 Hz uncertainty in the oscillation frequency of each system. Compared to the present value of the 5S,,,(F= 3)-5D,,,( F = 5), the one given in Ref. [7] is smaller by 4.4 kHz (Y = 385 285 142 373.6 + 6 kHz). However, given the uncertainty of 46 kHz, which was mainly limited by the 473 THz He-Ne/I, uncertainty [6], these two independent determinations are found to be in good agreement and comforts a posteriori the actual recommended value found for the red standard after its re-measurement using the BNM-LPTF’s chain in 1992 [1,4]. It is rather difficult to infer the *‘Rb 5S,,,(F = 3)-5D,,,(F = 5) two-photon transition frequency precisely from the oscillation frequencies of Ll, L2 and KB. Let us analyze the possible systematic errors. The Rb(nD)/Rb(SS) collision induced shifts of the two-photon transitions frequencies have been studied for large values of the principal quantum number ( 10 5 n I 70) [ 15,161. The shifts are proportional to the atomic density and vary with the effective principal quantum number as n *2.4.The extrapolation of those results to the 5S-5D transition (n’ = 3.7) with a pressure of 8 X lo-’ Torr gives a frequency shift of - 1200 Hz. This value is overestimated since by increasing the rubidium pressure by a factor 2 or 3, we have not observed frequency shifts due to Rb-Rb collisions larger than the repeatability of the systems (300 Hz). The Rb cells have been carefully filled using ultra vacuum techniques. The residual gas pressure, measured on a test cell, just after sealing is of the order of 2 X IO-* Torr, and has been shown to increase by about lo-’ per week. Even though the cells are three years old, we can think that the residual gas pressure is less than low4 Torr. Since rubidium acts as a getter, the pollution of the cell is probably mainly due to rare gases, and particularly to argon. Rb-Ar collision-induced resonance shifts studied for principal quantum number between 7 and 35 [ 171 vary as n* 3. The extrapolation to n’ = 3.7, assuming an Ar residual pressure of 1O-4 Torr in our experimental conditions gives a - 600 Hz shift of the two-photon transition frequency. Those two values are only an order of
133 (1997) 471-478
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magnitude, but should explain the discrepancy of 1130 Hz between Ll and L2. The light shifts are measured to within 20 Hz. The mode-matching of the counter-propagating beams in the cavity ensures that the first order Doppler effect is completely suppressed. The second order Doppler effect shifts the resonance by 230 Hz, assuming a temperature of 90°C. The magnetic shield secures a magnetic field of less than 1 mG, and no systematic error is expected since the polarisation is linear. We have checked that the electronic gains of the various feedback loops have no effect on the oscillation frequencies of the two-photon systems so long as the lock-in amplifiers were not saturated. The shifts due to the offsets at the output of the lock-in amplifiers can be controlled to be less than 70 Hz. The modulation of the diode lasers injection current induces a small modulation in their output power, but because of the feedback loop locking the cavity length to the laser frequency, the intracavity power which excites the two-photon transition is no longer modulated. The transition frequency we have measured is blue shifted by the adjacent two-photon transitions (F = 3 to F = 1,2, 3 or 4). Assuming that the lines have Lorentzian lineshapes with 600 kHz FWHM, we estimate this shift to be less than 30 Hz. The frequency may also be shifted by the Doppler background due to the absorption of two copropagating photons. Since the Doppler width is of the order of 320 MHz, the blue expected shift is less than 10 mHz. The value of the frequency of the *‘Rb 5S,,,,(F = 3)-5D,,,( F = 5) two-photon transition, calculated as the mean value of Ll , L2 and KB oscillation frequencies extrapolated to zero optical power and compensated for the second order Doppler effect, is 385285 142378.280 + 2 kHz (5.2 X 10-‘2). The 2 kHz of uncertainty (1 u) includes the uncertainty of the CO,/OsO, reference laser, the reproducibility of the two-photon systems and all the uncertainties affecting the systematic effects. Their quadratic sum is rounded to 2 kHz. 7. Conclusion This experiment has shown that our frequency synthesis chain is able to reach the lo-l3 resolution level in the visible domain for 40 s integration time.
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However, it appears that its operation could be much easier and the integration time much longer if the comparison of the CO, laser with the color center laser (CCL) was more reliable. We are thus working on the optical frequency quadrupling of the CO, laser using a doubly resonant external cavity enhancement [ 131 to produce a few mW of 5 pm and a few nanowatts of 2.5 ym radiation. This will allow us to run the CCL at a lower power level where it is much more stable. The value of the oscillation frequency of KB is in daily use at the Kastler-Brossel laboratory to determine various transition frequencies in hydrogen. The knowledge of the frequency of the Rb systems is mainly limited by the uncertainty on the frequency of the reference CO,/OsO4 laser. A new measurement of this reference frequency against a hydrogen maser clock is scheduled in the near future. Because of the present high level of stability and reproducibility of our secondary IR standards (3 X lo-l3 over the past 18 months), the expected results will be directly translated to Rb/DL systems. We have measured the “Rb 5S,,,(F = 3)5D,,,(F = 5) two-photon transition with an uncertainty of 2 kHz that is 5.2 X lo-‘* in relative value. The repeatability of our systems is much better, at the lo-‘* level, and the relative stability of the measurement for 1 s integration time is 5 X 10-13. The reproducibility is 1.2 kHz (3 X lo-‘*). These results motivate the improvement of the metrological performance of our systems, and in particular the analysis of the systematic effects in the rubidium cells, such as the role of the collisions with the residual gases. Together with the recently measured frequency of the 3P,-‘S0 intercombination line of atomic calcium at A = 657 nm [18], the rubidium two-photon transition provides the second most accurate frequency marker in the vis/near-IR range at the lo-‘* accuracy level. Because the set-up is compact and transportable, it should replace advantageously the popular He-Ne/I, standard. Acknowledgements
This work is a part of the scientific development program of the Bureau National de MCtrologie (BNM, Paris). We are grateful to Y. Millerioux (BNM-INM, Paris) who initiated the realization of
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the two-photon systems and started their metrological studies. The authors are indebted to B. Cagnac for stimulating discussions about Doppler-free twophoton spectroscopy and for his care in the fiber link installation. We are also grateful to P. Goy (Kastler Brossel Laboratory, Paris) who gave us the 10 GHz YIG oscillator and to J. Landreau (CNET, Bagneux, France) for their AR coatings service on the InGaAsP diode laser. Thanks are due to the electronic department staff of the BNM-LPTF for their help during the past three years, and to A.H. Gerard and P. Aynie for their contribution in mechanics servicing. This work was partially supported by the Direction des Etudes et Recherches. References [ll T.J. Quinn, Metrologia 30 (1994) 523. [2] F. Nez, M.D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, Y. Millerioux and P. de Natale, Europhys. Lett. 24 (1993) 635. [3] M. Weitz, A. Huber, F. Schmidt-Kaller, D. Leibfried and T.W. H%nsch, Phys. Rev. Lett. 72 (1994) 328. [4] 0. Acef. J.J. Zondy, M. Abed, D.G. Rovera, A.H. Gerard, A. Clairon. Ph. Laurent, Y. Millerioux and P. Juncar. Optics Comm. 97 (1993)29. [5] Y. Millerioux, D. Touahri, L. Hilico, A Clairon, R. Felder, F. Biraben and B de Beauvoir, Optics Comm. IO8 (1994) 91. [6] F. Nez, F. Biraben, R. Felder and Y. Millerioux, Optics Comm. 102 (1993) 432. [7] R. Felder, D. Touahri, 0. Acef, L. Hilico, J.J. Zondy, A. Clairon, B. de Beauvoir. F. Biraben, F. Nez, L. Julien and Y. Millerioux, Proc. SPIE 2378 (1995) 52. 181 D. Touahri, 0. Acef and J.J. Zondy, Optics Lett. 21 (1996) 213. [9] P.A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J.L. Hall and S. Waltman, IEEE Trans. Inst. Meas. 44 (1995) 151. [lo] A. Clairon, B. Dahmani, A. Filimon and J. Rutman, IEEE Trans. Inst. Meas. IM 34 (1985) 265. [I 11 A. Clairon, B. Dahmani, 0. Acef. M. Granveaud, Y.S. Domnin, S.B. Pouchkine, V.M. Tatarenkov and R. Felder, Metrologia 25 ( 1988) 9. [I21 J.J. Zondy, M. Abed and A. Clairon, J. Opt. Sot. Am. B I1 ( 1994) 2004. 1131 D. Touahri, J.J. Zondy and 0. Acef, OSA Trends in Optics and Photonics Series, Vol. 1. eds. S.A. Payne and C.R. Pollock (OSA, Washington DC, 1996) p. 164. [I41 0. Acef, F. Nez and G.D. Rovera, Optics Lett. 19 (1994) 1275. 1151 B.P. Stoicheff 733.
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Optics Communications 133 ( 1997) 47 I-478
Full length article
Frequency measurement of the 5S,,,( F = 3) -5D,,,( F = 51 two-photon transition in rubidium D. Touahri a**, 0. Acef a, A. Clairon a, J.-J. Zondy a, R. Felder b, L. Hilico MU, B. de Beauvoir ‘, F. Biraben ‘, F. Nez ’ a Luboratoire
Primaire
du Temps et des Frhyuences
b Bureau ’ Luborutoire
lnternutional
Kustler Brossel. Ecole Normale 4. pluce Jussieu.
’ D&artement
(BNM-LPTF),
des Poids et Mesures Supdrieure,
Observuroire
de Paris. 61 Au. de I’Observutoire,
(BIPM). Puvillon de Breteuil, F-92312, Universith Pierre
Tour 12, EOI. C74. F-75252,
de Physique Chimie. University d’Evry val d’Essonne.
et Murk
S&res
Curie, Laboratoire
F-75014
Park.
France
Cedex, Fruncr ussocie’ uu CNRS (IRA 18.
Paris Cedex 05. France
Boulevard
des Coquibus.
F-91025,
Evry Cede-r, Frunce
Received 23 April 1996; accepted I1 July 1996
Abstract We have measured the frequencies of three diode lasers stabilized on the 5s ,,&F = 3)-5D,,,(F = 5) two-photon transition in rubidium at h = 778.1 nm, with an uncertainty of 1 kHz, using BNM-LPTP frequency synthesis chain starting from a CO,/OsO, reference laser at 10.3 km. We show that this frequency chain is able to reach the lo-‘” resolution level. After a discussion of the systematic effects that may shift the resonance, the transition frequency is found to be v = 385 285 142 378.280 + 2 kHz.
1. Introduction Progress toward the definition of highly accurate optical frequency standards in the visible and near-IR range is of fundamental importance in various applications. such as the Mise en Prarique of the definition of the Meter [l], high resolution spectroscopy of cold atoms or ions and precision measurement of fundamental constants. The Rydberg constant, determined from two-photon spectroscopy of hydrogen atom [2,3], is presently the most accurately known fundamental constant. The two-photon transition in
* Corresponding author. E-mail: [email protected]. ’ E-mail: [email protected]. 0030-4018/97/$17.00 PII SOO30-4018(96)0047
rubidium at 778.1 nm (385.3 THz) matches closely (A = 40 GHz) the 2S-8D two-photon transition frequency of natural hydrogen. To this extent it represents a more suitable reference than the 473.6 THz red He-Ne/I, standard [4] for the H-atom spectroscopy, all the better than its metrological performance in terms of stability and reproducibility is at least 20 times better [5]. Furthermore, the frequency of the 5S,,,-5D,,,z transition is only a few GHz away from the difference frequency between the red (He-Ne/I,l and mid-IR (He-Ne/CH, at 88.4 THz) standards. This coincidence was used for the first determination of its absolute frequency with an uncertainty of 5 kHz [6], mainly limited by the uncertainty on the red frequency standard. The frequency of the 5S, ,2( F =
Copyright 0 1997 Published by Elsevier Science B.V. All rights reserved. l-3
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3)-5D,,,(F = 5) was later on determined with an uncertainty of 6 kHz from that measurement using a Schottky diode to bridge the 45 GHz gap between the two fine structures [7]. Several laboratories world-wide are developing rubidium two-photon systems or use the neighbouring 780 nm Rb/D, saturated absorption line as a frequency reference. The 778.1 nm transition will provide an accurate reference for optical telecommunication network, through the frequency-doubling of 1.556 pm diode lasers. Last but not least, it can serve as a convenient secondary standard in simpler frequency chains, in conjunction with other IR optical standard (HeNe/CH, or COJOsO,), for the absolute frequency measurement of many ionic or molecular potential standards in the visible/near-IR range [8], such as the green iodine B-X line at 532 nm [9]. All these reasons motivated this work aimed at the absolute frequency determination, at the IO-l2 accuracy level, of this promising near-IR standard.
2. The two-photon system The three two-photon systems (Fig. 1) we have measured are very similar [5]. Two of them Ll and L2 are located in our laboratory (LPTF) and the third one (KB) in the Kastler-Brossel laboratory. The lat-
ECL Diode
Frequency
Anamorphic
, Prisms
I33 (1997) 471-478
ter is connected to the LPTF by two 3 km long optical fiber links. The rubidium vapour is enclosed in a fused silica sealed cell with Brewster window ends. A pressure of about 8 X IO-’ Torr is obtained by maintaining the temperature around 90°C. The cell as well as the detection apparatus are surrounded by a magnetic shield. A plano-concave Fabry-Perot cavity is constructed around the cell in order to probe the transition with a well defined Gaussian beam. The cavity length is 30 cm and the l/e2 waist radius is 420 pm. The loaded cavity finesses are of the order of 50. The Doppler-free two-photon hyperfine transition is probed with an extended-cavity AlGaAs laser diode (ECL). The diode injection current. is modulated at 70 kHz, producing a 600 kHz peak-to-peak modulation of the laser frequency, which is approximately equal to the measured two-photon transition linewidth [6]. To enhance the optical isolation of the diode, the laser frequency is 2 X 80 MHz shifted by an acousto-optic modulator (AOM) used in a double-pass configuration. The signal leaking out from the cavity is used to lock its length to the laser frequency, after demodulation. The transmitted power is compared to a reference level, which enables to stabilize the intracavity power by a second slow servo loop, controlling the diffraction efficiency of
Faraday isolator
LI ?J2 n
I
AOM
1
-_________________----------_--_
I________________I
Fig. 1. Schematic of the rubidium two-photon transition stabilized diode laser. L ,.*,) are matching lenses. L, is the fluorescence lens and PMT a photomultiplier tube. PZT is a piezo translator. AOM is an acousto-optic modulator.
collecting
D. Touahri et al. / Optics Communications
D>~.
r
‘\.
‘l
-zoooE z f E 5
-4000
-
-6000
-
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-
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.
.
.
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.-
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133 (1997) 471-478
\ ’ 2
.
’ 4
lntracavity
. 6
power
.
8
a
10
(CLtJ.)
Fig. 2. Light shift versus the intracavity optical power for Ll system. The integration time is 100 s per point. The standard deviation of the fit is 125 Hz. For the horizontal scale, I a.u. corresponds to about 7 mW.
the AOM. This system can be continuously tuned over 1 GHz. The well-resolved two-photon transitions are detected by monitoring the blue fluorescence (A = 420 nm) due to the radiative cascade 5D-6P-5S with a photomultiplier tube. The laser is frequency modulated and the fluorescence is phase sensitively detected at the first harmonic of the modulation in order to lock the laser frequency on the 5S,,,(F = 3)-5D,,,(F = 5) component of the *‘Rb two-photon transition. For Ll, with a total intracavity power of 35 mW, we detect a fluorescence photon flux of 5 X lO’/s. The light shifts of the systems were determined eight days after the measurement and found to be 8414, 7596 and 7300 Hz, corresponding to typical intracavity optical powers of 35 mW. The light shift versus the intracavity power is shown in Fig. 2. The intracavity power was controlled to within 0.2%, so the uncertainty on the light shift is due to the linear fit of Fig. 2 and is 130 Hz. The frequencies of Ll, L2 and KB are compared by counting the beat frequency between Ll and L2 or KB. These beatnotes have large signal-to-noise ratios (SNR) (> 60 dB in a 100 kHz bandwidth). The three two-photon set-ups have been periodically compared throughout a period of one year. The frequency stability, in terms of Allan variance, of these systems is about 4 X IO-’ 37-“’ per laser over 1000 s. Their repeatability is better than 300 Hz (lo) over one year. The reproducibility is better than 1200 Hz.
The starting point for the frequency synthesis chain is the 0~0, reference frequency ( v = 29096274952 340 + 70 Hz) which is in quasi coincidence with the R(l2) CO, laser line. It is one of the most accurate frequencies in the 10 km range. We have two such frequency standards. One of them was measured against a caesium primary clock in 1983 [lo]. Both were compared to a Russian HeNe/CH, standard at 3.39 pm in 1986 Ill]. At this occasion, it was demonstrated that the agreement between two independent chains was at the lo-** level. Our standards have been successively improved, preserving the memory of their frequencies to within f70 Hz. These systems have a reproducibility of 3 parts in 1013 measured over 18 months. The relative stability of these oscillators is 1.4 X 10-‘3~-1/2 per laser over 300 s. We expect the frequency synthesis chain to translate this performance to the visible domain. two-photon transition in rubidThe 5S,,,-5D,,, ium is only 20 GHz away from the 13th harmonic of the R(42) ‘2C’602 line (v, = 29638880 152340 Hz). This R(42) CO, laser is phase-locked to the R(l2) CO, laser with a frequency offset of 540.605 200 GHz. A low phase noise 100 MHz quartz oscillator, weakly locked to a H-maser, is multiplied using a step recovery diode. The 113th harmonic, at 11.3 GHz, is filtered and mixed with a 90.409200 GHz klystron in a Schottky diode to phase-lock the klystron to the H-maser. The R(l2) reference and the R(42) CO, lasers are compared to the sixth harmonic of the klystron using a MIM diode. The beat note (25 dB SNR in a 100 kHz bandwidth) is used to phase-lock the R(421 CO, laser. This reference set-up remains locked for more than 12 hours. The uncertainty in the R(l2)/0sO, frequency is translated to the R(42) frequency, but the stability is slightly degraded: the IO- ’ ’ (1 sl relative stability of the 100 MHz quartz is translated to the sixth harmonic of the klystron. Its contribution to the R(42) laser relative stability is thus in the ratio 29.6 to 0.54, that is 2 X 10-13. The R(42) laser relative stability is then 2.5 X lo- I3 for 1 s integration time. Taking into account the 4 X 1O-‘3 relative stability of the two-photon systems, a quadratic sum leads
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to a 4.7 X lo- I3 expected value for the measurement stability for 1 s integration time.
4. Frequency synthesis and measurement chain Fig. 3 sketches the 29 THz (v,) to 385 THz (13 vR) frequency chain architecture, derived from the one implemented for the red He-Ne/I, frequency measurement [4]. The 13th harmonic is synthesized by a 29 THz up-conversion (SFG) of a diode laser at 842.9 nm (12~) [81. A 3:l frequency divider of the 842.9 nm diode laser is then implemented so as to translate the absolute frequency measurement in the 4uR range (A = 2.5287 pm): the near-IR laser frequency is down-converted to 8v, (A = 1.264 km> by difference-frequency generation (DFG) with a KCl:Li color-center laser (CCL) operating near 4~. The latter is simultaneously frequency-doubled (SHG) and the 3:l division is ful-
filled by monitoring the RF beatnotes between the two 8v, generated signals and a local oscillator (InGaAsP diode laser) at 8~~. Finally the CCL frequency is measured against the reference frequency using a fifth-order mixing in a metal-insulator-metal (MIM) W:Ni point-contact diode. The remaining 20 GHz gap between the 778.06 nm (13~~) transfer laser and the Rb (5%5D) frequency is bridged using a Schottky diode and a 10.08 GHz YIG oscillator phase-locked to a Cs clock. In its present status, this frequency chain is quasi-continuously tunable in the near-IR/visible spectrum [12]. 4.1. The transfer lasers The CCL operating at 2.528 km is frequencylocked on a ULE glass Fabry-Perot cavity to reduce its linewidth to less than 1 kHz [13]. The cavity frequency drift is of the order of 200 Hz/s. The available single-mode output power is I4 mW. The 1.264 pm InGaAsP diode laser is operated as an ECL, with a linewidth of 50-100 kHz. The available power of 3 mW, which is too low for efficient non-linear mixings, justifies its use as a local oscillator for the two beatnotes involved in the 3:l divider. The 842.9 nm laser is a high power (200 mW> AlGaAs diode laser injection-locked by a master ECL. The 778.06 nm (13~~) transfer oscillator is also an ECL. Both ECL’s are frequency-stabilized on the same temperature-controlled high finesse FabryPe’rot cavity to reduce their linewidths (< 1 kHz) and frequency drifts during the measurement ( < 250 Hz/s). 4.2. The non-linear mixings and beatnotes
Fig. 3. Frequency
synthesis and measurement
chain.
All the parametric mixings involved in the chain employ silver thiogallate crystals (AgGaS,) as the non-linear optical converter, because of its high non-linearity and its extended type-1 phase-matching capabilities over the entire optical spectrum [8,13]. All the reported beatnotes signal-to-noise ratio (SNR) were measured in a 100 kHz spectrum analyzer bandwidth. The color-center laser SHG and the 842.9 nm laser SFG are both critically phase-matched at B = 43” and yield respectively 5 nW at 8 V~ (from 13 mW of CCL) and 6 p,W at 13~~ (from 50 mW of
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near-IR and 300 mW of CO, powers). The SNR of the corresponding beatnotes were 30 dB and 60 dB. The DFG process of the 3:l divider is temperaturetuned (T = - 10°C at the measurement wavelengths) non-critically phase-matched (NCPM) over the CCL tuning range, which spans over the fourth harmonic spectrum of CO, lasing lines. The beatnote between a fraction of the generated 8v, signal (80 nW>, and 1.5 mW of the InGaAsP laser, leads to a SNR of 40-45 dB. The SNR of the Schottky diode RF beatnote bridging the 20 GHz gap at the top end of the chain is about 35 dB [ 141. The beatnotes between Ll, L2 and KB have high enough SNR exceeding 50-60 dB. The most crucial beatnote detection was the MIM detection of the fourth harmonic of the reference laser because only 6 mW of CCL power is available at this stage (due to the losses experienced through the parametric mixing processes and to residual atmospheric water vapour absorption). The video response over a 1 Ma load resistor of the better MIM diode tried was 10 p.V/mW and 500 p.V/mW for the CCL and CO, radiation respeetively. However, the thermal instability of these diodes which occurred during the He-Ne/I, absolute frequency measurement [4] was not observed this time. The SNR of this beatnote ranged between 12 to 15 dB, depending on the quality of the contact point, but remained stable for hours for the best operating diode.
5. The measurement
method
The frequency chain of Fig. 3 is not a phase-locked chain, so that a synchronized counting of the various beatnotes is required to cancel the frequency drifts of the transfer lasers. Furthermore, since some of the beatnotes cannot be directly counted due to their low SNR, tracking voltage-controlled oscillators (VCO) are phase-locked on those beatnotes. Additional synthesizers enable to down-convert the beat signals in the operating range (50-150 MHz) of the tracking VCO’s. The eight frequency counters we used were externally triggered and remote-controlled by a micro computer. Their synchronization is better than 0.5 ps, so that even if a beatnote drifts by 1 MHz/s, the counting error will be less than 1 Hz. The
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frequencies are counted during 1 s, with a dead time of 0.16 s. The two beatnotes between the two-photon systems, that between the two COJOsO, reference lasers, as well as the one comparing the frequency of the up-converted 13~, radiation to the 778.06 nm transfer laser were counted directly after appropriate filtering and amplifying. For the remaining beatnotes, which SNR were below the 50 dB range. tracking VCO’s with a loop bandwidth ranging from 30 to 300 kHz enabled them to be counted reliably [4]. The SNR of the beatnote produced by the MIM diode comparing the fourth harmonic of the R(42) CO, laser to the color center laser was very low ( 12 to 15 dB). In addition, this beat note was slightly frequency modulated (10 kHz peak-to-peak at a 2.2 kHz rate>. We have checked that it is possible to reliably track such a beatnote by simulating it with a frequency-modulated synthesizer. Between 9 and 12 dB of SNR, counting errors are observed, which strongly depend on the tracking loop bandwidth. So long as the SNR exceeds 12 dB in a 100 kHz bandwidth, the phase-tracked signal is counted without any error for a large range of loop bandwidths. The first time we ran the experiment, the SNR of that beatnote was only about 10 dB in a 100 kHz bandwidth. Though we noticed a posteriori that the mean value of the corresponding measured frequency was only 280 Hz smaller than that we obtained with measurement series performed with a larger SNR, the related standard deviation was however two or three times greater. The high frequency part of the chain, from the 842.9 nm diode laser to the three DL/Rb systems, as well as the CO, lasers were extremely stable and able to run for several hours without any miss-locking of the feedback loops. Several MIM diodes have detected the beatnote between the CO, laser and the CCL, and the one that gave the 12 to 15 dB SNR survived for more than six hours. On the other hand, the CCL and to a lesser extent the InCaAsP diode displayed frequent mode-hopping, resulting in the switching-off of the corresponding tracking oscillators and limiting the integration time of the experiment. This behaviour may have several origins. Actually, in order to get 14 mW at 2.52 pm, the CCL was strongly pumped by 3.7 W of a Krf laser and was operating close to a multimode regime. Optical
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feedback from the MIM. diode as well as intracavity water vapour absorption may have increased the laser instability. Over more than 4 hours, the experiment has produced 2348 measurements of the two-photon transition frequency, in small time series ranging from 17 to 502 seconds.
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n
6. Results and discussion The three two-photon systems frequencies have been measured simultaneously. Fig. 4 shows the histogram of the 2348 1 second measurements together with its Gaussian fit curve, for the Ll synthesised frequency. Similar curves are obtained for L2 and KB. The relative standard deviation of the results is 4.5 X IO-l3 for Ll and slightly larger for L2 and KB. Fig. 5 shows the square root of the Allan variance of the Ll synthesized frequency for the sequence of 502 successive measurements. The stabilities of the three measurements are quite similar, 4.6 X 10-‘3r-‘/2, 7.7 X 10-‘3r-/2 and 4 X 10-‘3r7-‘/2 for Ll, L2 and KB respectively. Those values are in good agreement with the expected 4.7 X lo-l3 stability for 1 s integration time. We have also plotted the relative stability between two two-photon systems deduced from the Ll/KB beatnote, as well as the relative stability between the two CO,/OsO, reference lasers: one can conclude that the measurement uncertainty is mainly limited by the
n.
A
Fig. 5. Allan standard deviation of the measured value of Ll (circles) deduced from the continuous set of 502 data, and relative stability of the two-photon systems Ll and KB (triangles). The relative stability of the two reference standards CO, /OsO, is also plotted (squares). The full line shows the r- “* dependence of the stabilities.
present intrinsic Rb/DL stability. The frequency synthesis chain does not add significant noise contribution to the measurement, at the lo-l3 level. The chain is able to reach at least lo-l3 in resolution. The two-photon transition frequency has to be corrected for the light (or power) shift which depends linearly on the intracavity optical power. This effect was measured for each two-photon system a few days after the experiment. The average frequencies of Ll, L2 and KB, extrapolated to zero power, are indicated in Table 1 for the 5S,d2(F = 3)5D,,,(F = 5) hyperfine component of ‘Rb. Note that during the experiment, KB was unlocked for a few minutes, so the KB value is averaged only over 1492 points. L 1 and KB are found to be very close to each other (within the repeatability of the systems), while L2 differs from Ll by about 1100 Hz, that is
Table 1 Absolute frequency values of Ll, L2 and KB two-photon set-ups, extrapolated to zero optical power, but not corrected from the second order Doppler effect. ‘The uncertainty is 1 kHz. RSD is the relative standard deviation of the sample of measurements (Hz)
Fig. 4. Histogram of the 2348 measurement of Lt. and its Gaussian tit. The mean value is 385285 142369.190 kHz and the standard deviation is 170 Hz.
System
Frequency
Ll L2 KB
385 285 142377.600 385 285 142378.730 385 285 142 377.820
&Hz)
RSD 4.4x 10-13 6.8X lo-l3 3.7x lo-l3
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3 x IO-I2in relative value. The repeatability of the
systems (300 Hz day to day) and the uncertainty of 70 Hz on the COJOsO, reference laser multiplied by 13 add quadratically to give a 1000 Hz uncertainty in the oscillation frequency of each system. Compared to the present value of the 5S,,,(F= 3)-5D,,,( F = 5), the one given in Ref. [7] is smaller by 4.4 kHz (Y = 385 285 142 373.6 + 6 kHz). However, given the uncertainty of 46 kHz, which was mainly limited by the 473 THz He-Ne/I, uncertainty [6], these two independent determinations are found to be in good agreement and comforts a posteriori the actual recommended value found for the red standard after its re-measurement using the BNM-LPTF’s chain in 1992 [1,4]. It is rather difficult to infer the *‘Rb 5S,,,(F = 3)-5D,,,(F = 5) two-photon transition frequency precisely from the oscillation frequencies of Ll, L2 and KB. Let us analyze the possible systematic errors. The Rb(nD)/Rb(SS) collision induced shifts of the two-photon transitions frequencies have been studied for large values of the principal quantum number ( 10 5 n I 70) [ 15,161. The shifts are proportional to the atomic density and vary with the effective principal quantum number as n *2.4.The extrapolation of those results to the 5S-5D transition (n’ = 3.7) with a pressure of 8 X lo-’ Torr gives a frequency shift of - 1200 Hz. This value is overestimated since by increasing the rubidium pressure by a factor 2 or 3, we have not observed frequency shifts due to Rb-Rb collisions larger than the repeatability of the systems (300 Hz). The Rb cells have been carefully filled using ultra vacuum techniques. The residual gas pressure, measured on a test cell, just after sealing is of the order of 2 X IO-* Torr, and has been shown to increase by about lo-’ per week. Even though the cells are three years old, we can think that the residual gas pressure is less than low4 Torr. Since rubidium acts as a getter, the pollution of the cell is probably mainly due to rare gases, and particularly to argon. Rb-Ar collision-induced resonance shifts studied for principal quantum number between 7 and 35 [ 171 vary as n* 3. The extrapolation to n’ = 3.7, assuming an Ar residual pressure of 1O-4 Torr in our experimental conditions gives a - 600 Hz shift of the two-photon transition frequency. Those two values are only an order of
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magnitude, but should explain the discrepancy of 1130 Hz between Ll and L2. The light shifts are measured to within 20 Hz. The mode-matching of the counter-propagating beams in the cavity ensures that the first order Doppler effect is completely suppressed. The second order Doppler effect shifts the resonance by 230 Hz, assuming a temperature of 90°C. The magnetic shield secures a magnetic field of less than 1 mG, and no systematic error is expected since the polarisation is linear. We have checked that the electronic gains of the various feedback loops have no effect on the oscillation frequencies of the two-photon systems so long as the lock-in amplifiers were not saturated. The shifts due to the offsets at the output of the lock-in amplifiers can be controlled to be less than 70 Hz. The modulation of the diode lasers injection current induces a small modulation in their output power, but because of the feedback loop locking the cavity length to the laser frequency, the intracavity power which excites the two-photon transition is no longer modulated. The transition frequency we have measured is blue shifted by the adjacent two-photon transitions (F = 3 to F = 1,2, 3 or 4). Assuming that the lines have Lorentzian lineshapes with 600 kHz FWHM, we estimate this shift to be less than 30 Hz. The frequency may also be shifted by the Doppler background due to the absorption of two copropagating photons. Since the Doppler width is of the order of 320 MHz, the blue expected shift is less than 10 mHz. The value of the frequency of the *‘Rb 5S,,,,(F = 3)-5D,,,( F = 5) two-photon transition, calculated as the mean value of Ll , L2 and KB oscillation frequencies extrapolated to zero optical power and compensated for the second order Doppler effect, is 385285 142378.280 + 2 kHz (5.2 X 10-‘2). The 2 kHz of uncertainty (1 u) includes the uncertainty of the CO,/OsO, reference laser, the reproducibility of the two-photon systems and all the uncertainties affecting the systematic effects. Their quadratic sum is rounded to 2 kHz. 7. Conclusion This experiment has shown that our frequency synthesis chain is able to reach the lo-l3 resolution level in the visible domain for 40 s integration time.
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However, it appears that its operation could be much easier and the integration time much longer if the comparison of the CO, laser with the color center laser (CCL) was more reliable. We are thus working on the optical frequency quadrupling of the CO, laser using a doubly resonant external cavity enhancement [ 131 to produce a few mW of 5 pm and a few nanowatts of 2.5 ym radiation. This will allow us to run the CCL at a lower power level where it is much more stable. The value of the oscillation frequency of KB is in daily use at the Kastler-Brossel laboratory to determine various transition frequencies in hydrogen. The knowledge of the frequency of the Rb systems is mainly limited by the uncertainty on the frequency of the reference CO,/OsO4 laser. A new measurement of this reference frequency against a hydrogen maser clock is scheduled in the near future. Because of the present high level of stability and reproducibility of our secondary IR standards (3 X lo-l3 over the past 18 months), the expected results will be directly translated to Rb/DL systems. We have measured the “Rb 5S,,,(F = 3)5D,,,(F = 5) two-photon transition with an uncertainty of 2 kHz that is 5.2 X lo-‘* in relative value. The repeatability of our systems is much better, at the lo-‘* level, and the relative stability of the measurement for 1 s integration time is 5 X 10-13. The reproducibility is 1.2 kHz (3 X lo-‘*). These results motivate the improvement of the metrological performance of our systems, and in particular the analysis of the systematic effects in the rubidium cells, such as the role of the collisions with the residual gases. Together with the recently measured frequency of the 3P,-‘S0 intercombination line of atomic calcium at A = 657 nm [18], the rubidium two-photon transition provides the second most accurate frequency marker in the vis/near-IR range at the lo-‘* accuracy level. Because the set-up is compact and transportable, it should replace advantageously the popular He-Ne/I, standard. Acknowledgements
This work is a part of the scientific development program of the Bureau National de MCtrologie (BNM, Paris). We are grateful to Y. Millerioux (BNM-INM, Paris) who initiated the realization of
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the two-photon systems and started their metrological studies. The authors are indebted to B. Cagnac for stimulating discussions about Doppler-free twophoton spectroscopy and for his care in the fiber link installation. We are also grateful to P. Goy (Kastler Brossel Laboratory, Paris) who gave us the 10 GHz YIG oscillator and to J. Landreau (CNET, Bagneux, France) for their AR coatings service on the InGaAsP diode laser. Thanks are due to the electronic department staff of the BNM-LPTF for their help during the past three years, and to A.H. Gerard and P. Aynie for their contribution in mechanics servicing. This work was partially supported by the Direction des Etudes et Recherches. References [ll T.J. Quinn, Metrologia 30 (1994) 523. [2] F. Nez, M.D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, Y. Millerioux and P. de Natale, Europhys. Lett. 24 (1993) 635. [3] M. Weitz, A. Huber, F. Schmidt-Kaller, D. Leibfried and T.W. H%nsch, Phys. Rev. Lett. 72 (1994) 328. [4] 0. Acef. J.J. Zondy, M. Abed, D.G. Rovera, A.H. Gerard, A. Clairon. Ph. Laurent, Y. Millerioux and P. Juncar. Optics Comm. 97 (1993)29. [5] Y. Millerioux, D. Touahri, L. Hilico, A Clairon, R. Felder, F. Biraben and B de Beauvoir, Optics Comm. IO8 (1994) 91. [6] F. Nez, F. Biraben, R. Felder and Y. Millerioux, Optics Comm. 102 (1993) 432. [7] R. Felder, D. Touahri, 0. Acef, L. Hilico, J.J. Zondy, A. Clairon, B. de Beauvoir. F. Biraben, F. Nez, L. Julien and Y. Millerioux, Proc. SPIE 2378 (1995) 52. 181 D. Touahri, 0. Acef and J.J. Zondy, Optics Lett. 21 (1996) 213. [9] P.A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J.L. Hall and S. Waltman, IEEE Trans. Inst. Meas. 44 (1995) 151. [lo] A. Clairon, B. Dahmani, A. Filimon and J. Rutman, IEEE Trans. Inst. Meas. IM 34 (1985) 265. [I 11 A. Clairon, B. Dahmani, 0. Acef. M. Granveaud, Y.S. Domnin, S.B. Pouchkine, V.M. Tatarenkov and R. Felder, Metrologia 25 ( 1988) 9. [I21 J.J. Zondy, M. Abed and A. Clairon, J. Opt. Sot. Am. B I1 ( 1994) 2004. 1131 D. Touahri, J.J. Zondy and 0. Acef, OSA Trends in Optics and Photonics Series, Vol. 1. eds. S.A. Payne and C.R. Pollock (OSA, Washington DC, 1996) p. 164. [I41 0. Acef, F. Nez and G.D. Rovera, Optics Lett. 19 (1994) 1275. 1151 B.P. Stoicheff 733.
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