- Email: [email protected]
Frequency stability of an optical frequency standard at 192.6 THz based on a two-photon transition of rubidium atoms
15 June 2002
Optics Communications 207 (2002) 233–242 www.elsevier.com/locate/optcom
Frequency stability of an optical frequency standard at 192.6 THz based on a two-photon transition of rubidium atoms M. Poulin a,*,1, C. Latrasse a,2, D. Touahri a,3, M. T^etu a a
Centre d’Optique, Photonique et Laser, D epartement de G enie Electrique et de G enie Informatique, Universit e Laval, Ste-Foy, Qc, Canada, G1K 7P4 Received 17 August 2001; accepted 6 March 2002
Abstract We have developed two frequency standards at 192.6 THz (1556.2 nm) based on a two-photon transition in rubidium at 385.2 THz (778.1 nm). These standards use a high power DFB laser at 1556.2 nm and second harmonic generation (SHG) in a periodically poled lithium niobate (PPLN) crystal. The linewidth of the DFB is reduced to the kHz level using optical feedback from a confocal cavity. The SH light is used to injection-lock a 778.1 nm laser diode which allows to observe the (5S1=2 , Fg ¼ 2 5D5=2 , Fe ¼ 4) two-photon transition in 87 Rb and lock the 1556.2 nm laser. Allan variance measurements between two identical standards show a beat stability of 2:5 1013 =s1=2 for observation times between 100 ms and 10 s and a level of 5:8 1014 for 100 s. Systematic effects shifting the locked frequency of the standards from that of the Rb transition are detailed and some experimental measurements are presented. Finally, absolute frequency measurements were performed at the INMS/CNRC in Ottawa allowing the determination of the absolute frequency of the standard to be 192 642 283 183:7 0:5 kHz. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Channel frequency allocation in wavelength division multiplexing (WDM) communication * Corresponding author. Tel.: +1-418-658-9500; fax: +1-418658-9595. E-mail address: [email protected] (M. Poulin). 1 Michel Poulin is now with TeraXion, 20-360 rue Franquet, Ste-Foy, Qc, Canada, G1P 4N3. 2 Christine Latrasse and Michel T^etu are now with DiCOS Technologies, 1000 route de l’Eglise, suite 400, Ste-Foy, Qc, Canada, G1V 3V9. 3 Driss Touahri is now with JDS Uniphase Corporation, 570 West Hunt Club Road, Nepean, On, Canada, K2G 5W8.
systems is presently based on a scale corresponding to multiples of 50 GHz. Trends for increased transmission capacity in long-haul systems and local area networks are directed towards extending the amplifiers spectral span and decreasing the channel spacing. Frequency control of the transmitters is essential and some devices, such as wavelength lockers, are already implemented in commercial products. Test instrumentation like wavemeters and optical spectrum analysers used for the characterization of these sources and other WDM components should also be calibrated with high precision frequency standards in the 1.55 lm band. Doppler-broadened lines in acetylene
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 3 5 4 - 8
234
M. Poulin et al. / Optics Communications 207 (2002) 233–242
(C2 H2 ) or hydrogen cyanide (HCN) are well suited for this purpose as they provide sub-GHz linewidth for frequency locking 1.55 lm lasers [1–4]. Also, with their different isotopes, these molecules offer many transitions across the 1510–1560 nm range. When a greater precision is required, saturated absorption in these gases can be used [4]. Such frequency standards present a frequency stability around 8 1012 =s1=2 up to an averaging time of 1000 s [5] and an absolute frequency uncertainty of 100 kHz [6]. Another possibility is the use of 5S–5D two-photon transitions in rubidium at 778.1 nm which offer even better metrological properties. These Doppler-free transitions can be observed through second harmonic generation of a 1556.2 nm laser [7–9]. They offer a theoretical linewidth as low as 150 kHz and an absolute frequency known to the kHz level [10,11]. In this paper, we discuss the realization of transportable standards at 1556.2 nm that inte-
grate a compact frequency doubler. Their metrological performances are presented and systematic effects that shift the frequency are evaluated.
2. Overview of the frequency standards A schematic view of these standards is shown in Fig. 1. As the two-photon lines exhibit a very narrow linewidth, we first reduce the nominal linewidth of the DFB laser (1 MHz) using weak optical feedback from a confocal cavity. The second harmonic signal of this laser is generated in a periodically poled lithium niobate crystal and used to injection-lock a powerful 778 nm laser in order to provide enough power for the observation of the two-photon transitions. The light from this laser is coupled into a plano-concave cavity containing a rubidium cell. A photomultiplier located on the side of the cell detects the fluorescence emitted by the atoms at resonance and allows to control the length
Fig. 1. Schematic diagram of compact 1556.2 nm frequency standard.
M. Poulin et al. / Optics Communications 207 (2002) 233–242
235
of the confocal cavity, therefore locking the DFB laser frequency to that of the 87 Rb ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ two-photon transition.
3. Linewidth reduction The 1556.2 nm laser source used is a MQW DFB laser emitting 70 mW. From a heterodyne measurement between two identical lasers, the free-running lineshape is found to be lorentzian with a 3-dB linewidth of about 1 MHz. Linewidth reduction is achieved using weak optical feedback from an off-axis confocal cavity [12]. A beamsplitter redirects 8% of the laser power towards the confocal cavity through a f ¼ 12:5 cm lens used for mode matching. The body of the cavity, made of super-invar, holds two spherical mirrors having a radius of curvature of 10 cm and a reflectivity greater than 99.5%. One of these mirrors (PZT-C1) is mounted on a PZT transducer to allow the control of the cavity length. The measured finesse of the untilted cavity is 470. A second PZTmounted mirror (M/) allows to adjust the distance between the DFB laser and the confocal cavity in order to control the phase of the feedback light. The linewidth reduction obtained with this technique has been investigated by recording the beat spectrum between two identical systems. In this particular measurement, the position of the phase mirror for each standard was manually adjusted so that the laser frequency was resonant with a transmission peak of the confocal cavity (no modulation on the laser). A typical spectrum is shown in Fig. 2. The solid line is a fit of the experimental data with a lorentzian to the power 3/2 [13] from which a 3-dB linewidth of about 2.8 kHz is deduced for each laser. Control of the path length between the DFB laser and the confocal cavity is required to maintain optimum phase of the feedback light for stable long-term operation. To this end, the laser frequency is modulated at 50 kHz through its injection current. The transmission signal of the confocal cavity, detected by a germanium photodetector, is demodulated using a lock-in amplifier to provide an error signal which is filtered and fed back to the PZT of the phase mirror M/. Control
Fig. 2. Optical beat spectrum between the 1556.2 nm DFB lasers submitted to optical feedback from a confocal cavity (resolution bandwidth: 1 kHz, video bandwidth: 300 Hz, sweep time: 5 s).
of the laser frequency over a few GHz is then possible by adjusting the confocal cavity length (through PZT-C1).
4. Second harmonic generation in a PPLN crystal In order to lock the DFB laser frequency at 192.6 THz to one of the two-photon transitions in rubidium at 385.2 THz, we use second harmonic generation in a periodically poled lithium niobate (PPLN) crystal. We poled a LiNbO3 sample having a length of 9.6 mm and a 19.2 lm grating period using an electric field [14]. The dependence of the SH power with respect to temperature and wavelength is shown in Fig. 3. Fitted sinc2 functions are indicated by solid lines. The FWHM of these curves are 9.7 °C and 1.3 nm, respectively, indicating that the sample is quasi-phase-matched over its entire length [15]. Optimal conversion efficiency is achieved using a f ¼ 3:5 cm lens. In that case, a SH power of 7.6 lW is obtained for 53.1 mW at 1556.2 nm incident on the crystal. Accounting for the Fresnel losses at the crystal facets, the internal conversion efficiency is 0.43%/W/cm which compares well with the theoretical value of 0.48%/W/cm for confocal focusing, calculated with an effective nonlinear
236
M. Poulin et al. / Optics Communications 207 (2002) 233–242
separated from the fundamental beam with a dichro€ıc beamsplitter. The transmitted beam at 1556.2 nm is the useful output for telecommunication applications. The reflected second harmonic signal is focused on the front facet of a 40 mW Fabry–Perot laser (SDL, model 5402-H1) through a single-stage 40-dB optical isolator equipped with a side escape port (Isowave, model I80-T5H). The locking bandwidth of the slave laser was measured using an analysis cavity and is on the order of 2.5 GHz. We measured the beat spectrum between the two 778.1 nm injection-locked slave lasers. A linewidth of about 5.5 kHz was obtained on a 5 s observation time. This is a sufficiently narrow linewidth to observe the two-photon transitions without broadening from the interrogation laser.
6. Two-photon spectroscopy and frequency-locking
Fig. 3. Variation of the second harmonic power as a function of: (a) the crystal temperature, and (b) fundamental wavelength. Solid lines represent fitted sinc2 functions.
coefficient deff ¼ ð2=pÞd33 at 1556 nm of )11.9 pm/ V [16]. When used in our frequency standard setup, the crystal is tilted with an angle of 5° to prevent unwanted feedback from its exit facet to the 778 nm laser. In these conditions, the sample is operated at 17 °C to generate the highest second harmonic power (7 lW).
5. Injection-locking of a 778.1 nm Fabry-Perot laser As the SH power generated in the PPLN crystal is too weak for direct observation of the twophoton transitions, it is used to injection-lock a more powerful 778 nm laser. The 7 lW SH beam is
The rubidium (isotopic 87 Rb at 98%) atoms are contained in an evacuated fused silica cell which is heated in a copper oven to about 90 °C using a twisted pair of resistive wires. The cold finger is maintained at about 83 °C. When the 778 nm laser is in resonance with the transition, the excited atoms return to the ground state through the radiative cascade 5D–6P–5S and emit blue fluorescence at 420 nm through the 6P–5S transition. An aspheric condenser and a Fresnel lens, located on the side of the cell, collect this fluorescence which is detected by a Hamamatsu R928 photomultiplier (PM). The PM is supplied with 800 V and its output is loaded with a 20 kX resistor. An interference filter centered at 420 nm and a colored glass filter are placed in the path of the fluorescence light to avoid noise from background light and 778 nm stray light. The Rb cell, the fluorescence collection optics and the photomultiplier are placed in a specially designed l-metal magnetic shield. The rubidium cell is further placed inside a plano-concave cavity that ensures perfect overlap of the two counter-propagating beams probing the rubidium atoms. This is necessary to avoid firstorder Doppler effect and to allow a good control of the beam geometry which affects the light shift.
M. Poulin et al. / Optics Communications 207 (2002) 233–242
Moreover, using this cavity, a sub-mW incident power is needed to observe the two-photon transitions and most of the slave laser power is thus available as a useful output. The cavity is formed by a PZT-mounted input plane mirror (PZT-C2) with a reflectivity of 96% and a 2-m radius concave mirror with a reflectivity of 99.5%, mounted on steel plates held by invar rods. The mirrors are separated by 30 cm, giving a free spectral range of 500 MHz and a beam waist in the cavity of 420 lm. The measured finesse of the cavity is 150 without the rubidium cell and 80 when the cell is inserted. An additional 65-dB isolator (Isowave, I-80U-2) is used to avoid direct reflections from this cavity into the slave laser. The optical power incident on the cavity can be controlled with a k/2 plate and a polarizing beam splitter arrangement. In order to maintain the laser and the cavity resonance frequencies in coincidence, we use a second lock-in amplifier to demodulate the transmitted signal at 778.1 nm, which is detected by a silicium photodetector. The error signal sent to a proportional-integrator loop filter is fed back to the PZT-C2 transducer, controlling the position of the input mirror of the cavity. By scanning the confocal cavity length using PZT-C1, we can sweep the laser frequency and observe the two-photon transitions. Fig. 4 shows the observed fluorescence profile corresponding to the Fg ¼ 2 to Fe ¼ 4; 3; 2; 1 transitions in 87 Rb. We use the strongest transition 5S1=2 , Fg ¼ 2 5D5=2 ,
237
Fig. 5. Fluorescence spectrum for the Fg ¼ 2 Fe ¼ 4 transition in 87 Rb and fit with a lorentzian profile.
Fe ¼ 4 to frequency-lock the 1556 nm DFB laser. Fig. 5 shows the corresponding profile with a 778 nm power of 0.5 mW incident on the cavity. In this case (as for Fig. 4), a minimal frequency excursion of 90 kHz p–p at 778 nm was used. A lorentzian profile having a full width at half maximum of 410 kHz (at 778 nm) was fitted to the fluorescence profile. The main contributions to this linewidth are the natural linewidth that can be evaluated to 300–390 kHz depending on the published values of the 5D level lifetime (205–266.2 ns [17–20]) and the transit time broadening (70 kHz) [21]. In order to lock the master laser frequency, we demodulate the PM signal using a third lock-in amplifier. The 1556.2 nm laser peak-to-peak frequency modulation excursion at 50 kHz is increased to about 150–200 kHz (0.7 times the FWHM of the line) to experimentally optimize the slope of the discrimination pattern. Fig. 6 presents the error signal when the modulation excursion is optimized for maximum amplitude and maximum center slope. The ratio of the slopes at resonance is 2, close to the one predicted by theory [22]. The error signal, filtered by a P-I circuit, is sent onto PZT-C1 controlling the confocal cavity length, therefore locking the DFB laser frequency to that of the two-photon transition.
7. Frequency stability measurements Fig. 4. Fluorescence spectrum for the Fg ¼ 2 Fe ¼ 4; 3; 2; 1 transition in 87 Rb.
The frequency stability of our standards is measured by recording the beat between two in-
238
M. Poulin et al. / Optics Communications 207 (2002) 233–242
these standards is the best ever reported, to our knowledge, in the 1.55 lm region. The repeatability of the frequency of the systems was evaluated to 200 Hz from the beat frequency, by locking and unlocking one system while the other remained locked.
8. Systematic effects
Fig. 6. Error signal obtained with excursion set for maximum amplitude and maximum center slope.
dependent systems. Both are locked to the same transition and one of them is shifted by 100 MHz using an acousto-optic modulator (AOM). The timebase of the frequency counter was synchronized on the synthesizer used to drive the AOM. Fig. 7 presents the Allan standard deviation of the beat note relative to the optical frequency. A slope of about 2:5 1013 =s1=2 is obtained for averaging times between 0.1 and 10 s. The best stability is 5:8 1014 for 100 s. For greater averaging times, a degradation of the stability is observed. This is mainly attributed to light shift variations induced by changes in the optical power probing the rubidium transition. Improvement of the long-term stability could be obtained by implementing a servo-loop to stabilize the intracavity power [23]. However, the frequency stability of
Fig. 7. Allan standard deviation of the beat frequency between the 1556.2 nm frequency standards, relative to the optical frequency.
Due to some systematic effects, the frequency of the standards is not exactly half that of the Rb transition. From the absolute measurement of the frequency of our standards and the evaluation of these systematic shifts, the determination of the unperturbed two-photon transition frequency is possible. These systematic effects are investigated below. 8.1. Light shift Theoretical calculation of the light shift gives a shift of +0.7346 P =S for the ground state 5S1=2 and +0.0370 P =S for the excited state 5D5=2 where P is the optical power in Watt and S the light beam surface area in m2 [21,24]. Therefore, considering a gaussian beam having a waist of 420 lm and applying a shaping factor of 2/3, the two-photon transition theoretical light shift is )420 Hz/mW at 778 nm. Experimentally, the light shift was measured by recording the beat frequency between the two systems against the optical power probing the transition [23]. As a direct measurement of the intra-cavity optical power is impossible, we plot the beat frequency against the silicium photodetector voltages V1;2 for each system. Fig. 8 shows the beat frequency as the optical power of system #1 is varied for different values of system #2 intracavity power. The same measurements were repeated after reversing the role of the two systems. Extrapolation of the fitted straight lines to zero power allowed to plot the data presented on Fig. 9. The slope for system #1 is then )11.7 Hz/mV (at 1556 nm). The relation between the photodetector voltage and the intra-cavity power can be obtained indirectly. The 778 nm cavity enhancement factor is about 15 using the equation Cð1 R1 ÞTf
M. Poulin et al. / Optics Communications 207 (2002) 233–242
239
The reproductibility of the systems can be evaluated from these light shift measurements. If the systems were perfectly identical, the two curves on Fig. 9 should cross at zero on the frequency axis. The sets of measurements presented in Fig. 9 were repeated four times and allowed us to estimate the reproductibility of the systems to 400 Hz (at 1556.2 nm). 8.2. Relativistic shift
Fig. 8. Light shift variation against Si detector voltage V1 (proportionnal to intra-cavity power) for system #1, for different values of the detector voltage V2 on system #2.
A relativistic treatment of the two-photon transition shows that the transition frequency m0 is shifted by an amount proportional to m0 VA2 =2c2 , where VA is the speed of the atom [24]. Considering a gas of rubidium atoms at thermodynamic equilibrium at a given temperature, the speed of the atoms follows a Boltzman distribution leading to a corresponding relativistic shift distribution. It can be shown that the two-photon transition will be shifted by an amount equal to the mass center of this relativistic shift distribution. For a temperature of 90 0:2 °C, we obtain a shift of 223:1 0:2 Hz (with respect to the 385 THz frequency). 8.3. Collisions
Fig. 9. Light shift variation against intra-cavity power for system #1 (resp. #2) with system #2 (resp. #1) intra-cavity power extrapolated to zero.
pffiffiffiffiffiffiffiffiffiffiffi ðF 2 =p2 R1 Rm Þ, where C is the coupling factor, R1 is the reflectivity of the input mirror, Tf is the facet transmission of the rubidium cell, F is the cavity finesse and Rm is the equivalent reflectivity of the Rb cell-output mirror ensemble. The coupling factor is experimentally measured to be C ¼ 57%. Considering the calibration of the photodetector voltage against the incident power to be 276 mV/ mW, we obtain an experimental light shift slope of )428 Hz/mW at 778 nm which compares very well with the theoretical value. Under standard conditions, the light shift is about )2.8 kHz (i.e., intracavity power of 6.5 mW).
Theoretical shifts due to collisions between rubidium atoms can be evaluated from the measurements performed by Stoicheff and Weinberger [25] for two-photon transitions from 5S1=2 to nS or nD ðn ¼ 10–70Þ. Extending these measurements for the 5S1=2 5D5=2 transition, we obtain a shift of 970 90 Hz (relative to the 385 THz frequency) for a pressure of 8.7 mPa (83 0:2 °C). However, this value appears to be overestimated considering recent measurements by Hilico et al. [23]. Collisions can also occur between Rb atoms and residual gas present in the cell. Let us consider the presence of argon which is often released by ionic diffusion pumps. From previous results published on ð5S–7DÞ two-photon transitions in Rb [26], we can evaluate the Rb–Ar collisional shift to be 0:397 109 Hz cm3 for the ð5S–5DÞ two-photon transitions. In the extreme case where the Ar relative pressure would be equal to that of rubidium, the corresponding shift would be )703 Hz.
240
M. Poulin et al. / Optics Communications 207 (2002) 233–242
8.4. Black-body radiation Black-body radiation shifts were calculated by Farley and Wing [27] for hydrogen and different alkali atoms including rubidium at 300 K. These calculations can be extrapolated to a temperature of 90 0:2 °C considering a T 4 dependence and give a shift of )6 Hz for the 5S1=2 level and )389.5 Hz for the 5D5=2 level leading to a shift of 191:8 2:4 Hz for the 5S1=2 5D5=2 two-photon transitions (at 385 THz). 8.5. Neighbouring transitions We evaluate theoretically the influence of the transitions ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 3; 2; 1Þ neighbouring the strongest transition used to lock the frequency of our standard. The shift due to the lorentzian profiles of the neighbouring transitions is found to be +275 mHz (at 385 THz), while the shift due to their gaussian pedestals amounts to +2.4 mHz (at 385 THz). 8.6. Electronic shifts The offsets at the output of the lock-in amplifiers used to lock the 778 nm cavity and the confocal cavity can influence the locked frequency of our standards. We first varied the offset at the output of the lock-in amplifier generating the error signal for the confocal cavity of the first system while keeping the second system unchanged. We obtained a linear change of the locked frequency with a slope of )87.9 Hz/mV (at 192.6 THz) which agrees well with the one that can be calculated from the slope of the error signal. The same measurement was done for the lock-in amplifier used to lock the cavity surrounding the rubidium cell. A linear change with a slope of +7.8 Hz/mV was observed for the locked frequency. In practice, we can set the offsets at the output of these two lock-in amplifiers to 0:1 and 1:5 mV which correspond respectively to a shift of 9 and 12 Hz at 192.6 THz. We also checked for possible errors related to drifts in the integrator stage of the loop filter used to lock the confocal cavity to the rubidium transition. The drift was experimentally measured,
under open-loop conditions, at the output of the integrator and evaluated to 78 mV/s. This corresponds to an offset of 67 lV at its input, from which we can evaluate a frequency shift of 6 Hz for our frequency standard, considering the slope previously measured ()87.9 Hz/mV). 8.7. Effect due to the excursion of the frequency modulation To check for shifts induced by modulation distortion or rubidium transition asymmetry, the amplitude of the frequency modulation excursion was varied from half to twice the optimum value (i.e., 150–200 kHz at 192.6 THz). No frequency shift could be detected within the repeatability of the measurements. 8.8. Amplitude modulation The direct modulation of the laser current used to produce the frequency modulation required for synchronous detection also produces some residual amplitude modulation. This one can be transferred to the slave laser and induce a frequency shift of the locked laser. However, as the cell is placed inside a build-up cavity whose length is controlled using a synchronous detection scheme, the intra-cavity light is not modulated at 50 kHz [23]. In fact, the locking point of the build-up cavity sets in such a way as to cancel any amplitude fluctuation at 50 kHz. 8.9. Summary Table 1 summarizes the values for the different systematic shifts. Table 1 Summary of the systematic frequency shifts Effect
Shift at 778 nm
Light shift Relativistic shift Rb–Rb collisions Ar–Rb collisions Black-body radiation Neighbouring transitions Electronics
2:81 0:02 kHz 223:1 0:2 Hz 970 90 Hz )703 Hz 191:8 2:4 Hz < 1 Hz 50 Hz
M. Poulin et al. / Optics Communications 207 (2002) 233–242
9. Absolute frequency measurement The two frequency standards were moved to the Institute for National Measurements Standards at the National Research Council in Ottawa, Canada for an absolute frequency determination of the ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ transition in 87 Rb [11]. Using a Cs-linked frequency chain, the absolute frequency of system #1 under standard operating conditions (intra-cavity power of 6.5 mW, cold finger temperature of 83 °C and cell body temperature of 90 °C) was measured to be 192 642 283 183:7 0:5 kHz. In order to obtain the frequency of the two-photon transition, the Comite international des poids et measures (CIPM) has recommended that only the light shift and relativistic shift be applied for the correction. The other effects are taken into account in the overall uncertainty and their contribution amounts to 1.2 kHz. Taking into account the previously evaluated systematic effects and the uncertainty related to the absolute measurement, the Rb transition frequency was determined to be 385 284 566 370:4 2 kHz.
10. Conclusion Two independent frequency standards at 192.6 THz (1556.2 nm) using the two-photon transition ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ of 87 Rb have been built and characterized. They present a frequency stability of 2:5 1013 s1=2 for averaging times between 0.1 and 10 s, which is the best ever reported at 1.55 lm. A detailed study of systematic effects shifting the locked frequency from that of the unperturbed Rb transititon is presented. The absolute frequency of system #1 under standard operating conditions is 192 642 283 183:7 0:5 kHz. These standards presently provide two absolute frequency outputs at 192.6 and 385.2 THz. These could be optically summed to provide a third reference at 577.8 THz in the visible region.
Acknowledgements We acknowledge Dr. John Bernard, Alan Madej, Louis Marmet and Klaus Siemsen for their
241
contribution to the measurement of the absolute frequency. We thank Dr. B. Villeneuve and M. Svilans, from Nortel Networks, Ottawa, Canada, for providing the high power DFB lasers. We are grateful to Carl Paquet, Sylvain Der^ ome, Martin Lapointe and Dr. Christine Tremblay from INO, and to Dr. Pierre Mathieu from DREV for their participation in the development of the PPLN crystals. We also take this opportunity to thank Mr. Yvon Chalifour for the design and machining of many mechanical parts of these setups. Finally, we acknowledge EXFO Electro-Optical Engineering and NSERC for their financial support through a NSERC/NRC grant.
References [1] F. Bertinetto, P. Gambini, R. Lano, M. Puleo, SPIE 1837 (1992) 154. [2] C. Latrasse, M. Breton, M. T^etu, N. Cyr, R. Roberge, B. Villeneuve, Opt. Lett. 19 (1994) 1885. [3] H. Sasada, K. Yamada, Appl. Opt. 29 (1990) 3535. [4] M. de Labachelerie, K. Nakagawa, Y. Awaji, M. Ohtsu, Opt. Lett. 20 (1995) 572. [5] A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamagushi, M. Kourogi, K. Imai, B. Widiyatomoko, IEEE Trans. Instrum. Meas. 48 (1999) 563. [6] K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, J. Opt. Soc. Am. B 13 (1996) 2708. [7] M. Zhu, R.W. Standridge, Opt. Lett. 22 (1997) 730. [8] M. Poulin, C. Latrasse, N. Cyr, M. T^etu, Photon. Technol. Lett. 9 (1997) 1631. [9] A. Danielli, P. Rusian, A. Arie, M.H. Chou, M.M. Fejer, Opt. Lett. 25 (2000) 905. [10] D. Touahri, O. Acef, A. Clairon, J.J. Zondy, R. Felder, L. Hillico, B. de Beauvoir, F. Biraben, F. Nez, Opt. Commun. 133 (1997) 471. [11] J.E. Bernard, A.A. Madej, K.J. Siemsen, L. Marmet, C. Latrasse, D. Touahri, M. Poulin, M. Allard, M. T^etu, Opt. Commun. 173 (2000) 357. [12] B. Dahmani, L. Hollberg, R. Drullinger, Opt. Lett. 12 (1987) 876. [13] P. Laurent, A. Clairon, C. Breant, IEEE J. Quantum Electron. 25 (1989) 1131. [14] L.E. Myers, G.D. Miller, R.C. Eckardt, M.M. Fejer, R.L. Byer, W.R. Bosenberg, Opt. Lett. 20 (1995) 52. [15] M.M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer, IEEE J. Quantum Electron. 28 (1992) 2631. [16] I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, R. Ito, J. Opt. Soc. Am. B 14 (1997) 2268. [17] O.S. Heavens, J. Opt. Soc. Am. 51 (1961) 1058. [18] C. Tai, W. Happer, R. Gupta, Phys. Rev. A 12 (1975) 736.
242
M. Poulin et al. / Optics Communications 207 (2002) 233–242
[19] A. Lindg ard, S.E. Nielsen, Atomic Data and Nuclear Data Tables 19 (1977) 606. [20] J. Marek, P. M€ unster, J. Phys. B 13 (1980) 1731. [21] F. Biraben, M. Bassini, B. Cagnac, Le J. Phys. 40 (1979) 445. [22] H. Wahlquist, J. Chem. Phys. 35 (1961) 1708. [23] L. Hilico, R. Felder, D. Touahri, O. Acef, A. Clairon, F. Biraben, Eur. Phys. J. AP 4 (1998) 219.
[24] B. Cagnac, G. Grynberg, F. Biraben, Le J. Phys. 34 (1973) 845. [25] B.P. Stoicheff, E. Weinberger, Phys. Rev. Lett. 44 (1980) 733. [26] K.H. Weber, K. Niemax, Z. Phys. A – Atoms and Nuclei 307 (1982) 13. [27] J.W. Farley, W.H. Wing, Phys. Rev. A 23 (1981) 2397.
Optics Communications 207 (2002) 233–242 www.elsevier.com/locate/optcom
Frequency stability of an optical frequency standard at 192.6 THz based on a two-photon transition of rubidium atoms M. Poulin a,*,1, C. Latrasse a,2, D. Touahri a,3, M. T^etu a a
Centre d’Optique, Photonique et Laser, D epartement de G enie Electrique et de G enie Informatique, Universit e Laval, Ste-Foy, Qc, Canada, G1K 7P4 Received 17 August 2001; accepted 6 March 2002
Abstract We have developed two frequency standards at 192.6 THz (1556.2 nm) based on a two-photon transition in rubidium at 385.2 THz (778.1 nm). These standards use a high power DFB laser at 1556.2 nm and second harmonic generation (SHG) in a periodically poled lithium niobate (PPLN) crystal. The linewidth of the DFB is reduced to the kHz level using optical feedback from a confocal cavity. The SH light is used to injection-lock a 778.1 nm laser diode which allows to observe the (5S1=2 , Fg ¼ 2 5D5=2 , Fe ¼ 4) two-photon transition in 87 Rb and lock the 1556.2 nm laser. Allan variance measurements between two identical standards show a beat stability of 2:5 1013 =s1=2 for observation times between 100 ms and 10 s and a level of 5:8 1014 for 100 s. Systematic effects shifting the locked frequency of the standards from that of the Rb transition are detailed and some experimental measurements are presented. Finally, absolute frequency measurements were performed at the INMS/CNRC in Ottawa allowing the determination of the absolute frequency of the standard to be 192 642 283 183:7 0:5 kHz. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Channel frequency allocation in wavelength division multiplexing (WDM) communication * Corresponding author. Tel.: +1-418-658-9500; fax: +1-418658-9595. E-mail address: [email protected] (M. Poulin). 1 Michel Poulin is now with TeraXion, 20-360 rue Franquet, Ste-Foy, Qc, Canada, G1P 4N3. 2 Christine Latrasse and Michel T^etu are now with DiCOS Technologies, 1000 route de l’Eglise, suite 400, Ste-Foy, Qc, Canada, G1V 3V9. 3 Driss Touahri is now with JDS Uniphase Corporation, 570 West Hunt Club Road, Nepean, On, Canada, K2G 5W8.
systems is presently based on a scale corresponding to multiples of 50 GHz. Trends for increased transmission capacity in long-haul systems and local area networks are directed towards extending the amplifiers spectral span and decreasing the channel spacing. Frequency control of the transmitters is essential and some devices, such as wavelength lockers, are already implemented in commercial products. Test instrumentation like wavemeters and optical spectrum analysers used for the characterization of these sources and other WDM components should also be calibrated with high precision frequency standards in the 1.55 lm band. Doppler-broadened lines in acetylene
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 3 5 4 - 8
234
M. Poulin et al. / Optics Communications 207 (2002) 233–242
(C2 H2 ) or hydrogen cyanide (HCN) are well suited for this purpose as they provide sub-GHz linewidth for frequency locking 1.55 lm lasers [1–4]. Also, with their different isotopes, these molecules offer many transitions across the 1510–1560 nm range. When a greater precision is required, saturated absorption in these gases can be used [4]. Such frequency standards present a frequency stability around 8 1012 =s1=2 up to an averaging time of 1000 s [5] and an absolute frequency uncertainty of 100 kHz [6]. Another possibility is the use of 5S–5D two-photon transitions in rubidium at 778.1 nm which offer even better metrological properties. These Doppler-free transitions can be observed through second harmonic generation of a 1556.2 nm laser [7–9]. They offer a theoretical linewidth as low as 150 kHz and an absolute frequency known to the kHz level [10,11]. In this paper, we discuss the realization of transportable standards at 1556.2 nm that inte-
grate a compact frequency doubler. Their metrological performances are presented and systematic effects that shift the frequency are evaluated.
2. Overview of the frequency standards A schematic view of these standards is shown in Fig. 1. As the two-photon lines exhibit a very narrow linewidth, we first reduce the nominal linewidth of the DFB laser (1 MHz) using weak optical feedback from a confocal cavity. The second harmonic signal of this laser is generated in a periodically poled lithium niobate crystal and used to injection-lock a powerful 778 nm laser in order to provide enough power for the observation of the two-photon transitions. The light from this laser is coupled into a plano-concave cavity containing a rubidium cell. A photomultiplier located on the side of the cell detects the fluorescence emitted by the atoms at resonance and allows to control the length
Fig. 1. Schematic diagram of compact 1556.2 nm frequency standard.
M. Poulin et al. / Optics Communications 207 (2002) 233–242
235
of the confocal cavity, therefore locking the DFB laser frequency to that of the 87 Rb ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ two-photon transition.
3. Linewidth reduction The 1556.2 nm laser source used is a MQW DFB laser emitting 70 mW. From a heterodyne measurement between two identical lasers, the free-running lineshape is found to be lorentzian with a 3-dB linewidth of about 1 MHz. Linewidth reduction is achieved using weak optical feedback from an off-axis confocal cavity [12]. A beamsplitter redirects 8% of the laser power towards the confocal cavity through a f ¼ 12:5 cm lens used for mode matching. The body of the cavity, made of super-invar, holds two spherical mirrors having a radius of curvature of 10 cm and a reflectivity greater than 99.5%. One of these mirrors (PZT-C1) is mounted on a PZT transducer to allow the control of the cavity length. The measured finesse of the untilted cavity is 470. A second PZTmounted mirror (M/) allows to adjust the distance between the DFB laser and the confocal cavity in order to control the phase of the feedback light. The linewidth reduction obtained with this technique has been investigated by recording the beat spectrum between two identical systems. In this particular measurement, the position of the phase mirror for each standard was manually adjusted so that the laser frequency was resonant with a transmission peak of the confocal cavity (no modulation on the laser). A typical spectrum is shown in Fig. 2. The solid line is a fit of the experimental data with a lorentzian to the power 3/2 [13] from which a 3-dB linewidth of about 2.8 kHz is deduced for each laser. Control of the path length between the DFB laser and the confocal cavity is required to maintain optimum phase of the feedback light for stable long-term operation. To this end, the laser frequency is modulated at 50 kHz through its injection current. The transmission signal of the confocal cavity, detected by a germanium photodetector, is demodulated using a lock-in amplifier to provide an error signal which is filtered and fed back to the PZT of the phase mirror M/. Control
Fig. 2. Optical beat spectrum between the 1556.2 nm DFB lasers submitted to optical feedback from a confocal cavity (resolution bandwidth: 1 kHz, video bandwidth: 300 Hz, sweep time: 5 s).
of the laser frequency over a few GHz is then possible by adjusting the confocal cavity length (through PZT-C1).
4. Second harmonic generation in a PPLN crystal In order to lock the DFB laser frequency at 192.6 THz to one of the two-photon transitions in rubidium at 385.2 THz, we use second harmonic generation in a periodically poled lithium niobate (PPLN) crystal. We poled a LiNbO3 sample having a length of 9.6 mm and a 19.2 lm grating period using an electric field [14]. The dependence of the SH power with respect to temperature and wavelength is shown in Fig. 3. Fitted sinc2 functions are indicated by solid lines. The FWHM of these curves are 9.7 °C and 1.3 nm, respectively, indicating that the sample is quasi-phase-matched over its entire length [15]. Optimal conversion efficiency is achieved using a f ¼ 3:5 cm lens. In that case, a SH power of 7.6 lW is obtained for 53.1 mW at 1556.2 nm incident on the crystal. Accounting for the Fresnel losses at the crystal facets, the internal conversion efficiency is 0.43%/W/cm which compares well with the theoretical value of 0.48%/W/cm for confocal focusing, calculated with an effective nonlinear
236
M. Poulin et al. / Optics Communications 207 (2002) 233–242
separated from the fundamental beam with a dichro€ıc beamsplitter. The transmitted beam at 1556.2 nm is the useful output for telecommunication applications. The reflected second harmonic signal is focused on the front facet of a 40 mW Fabry–Perot laser (SDL, model 5402-H1) through a single-stage 40-dB optical isolator equipped with a side escape port (Isowave, model I80-T5H). The locking bandwidth of the slave laser was measured using an analysis cavity and is on the order of 2.5 GHz. We measured the beat spectrum between the two 778.1 nm injection-locked slave lasers. A linewidth of about 5.5 kHz was obtained on a 5 s observation time. This is a sufficiently narrow linewidth to observe the two-photon transitions without broadening from the interrogation laser.
6. Two-photon spectroscopy and frequency-locking
Fig. 3. Variation of the second harmonic power as a function of: (a) the crystal temperature, and (b) fundamental wavelength. Solid lines represent fitted sinc2 functions.
coefficient deff ¼ ð2=pÞd33 at 1556 nm of )11.9 pm/ V [16]. When used in our frequency standard setup, the crystal is tilted with an angle of 5° to prevent unwanted feedback from its exit facet to the 778 nm laser. In these conditions, the sample is operated at 17 °C to generate the highest second harmonic power (7 lW).
5. Injection-locking of a 778.1 nm Fabry-Perot laser As the SH power generated in the PPLN crystal is too weak for direct observation of the twophoton transitions, it is used to injection-lock a more powerful 778 nm laser. The 7 lW SH beam is
The rubidium (isotopic 87 Rb at 98%) atoms are contained in an evacuated fused silica cell which is heated in a copper oven to about 90 °C using a twisted pair of resistive wires. The cold finger is maintained at about 83 °C. When the 778 nm laser is in resonance with the transition, the excited atoms return to the ground state through the radiative cascade 5D–6P–5S and emit blue fluorescence at 420 nm through the 6P–5S transition. An aspheric condenser and a Fresnel lens, located on the side of the cell, collect this fluorescence which is detected by a Hamamatsu R928 photomultiplier (PM). The PM is supplied with 800 V and its output is loaded with a 20 kX resistor. An interference filter centered at 420 nm and a colored glass filter are placed in the path of the fluorescence light to avoid noise from background light and 778 nm stray light. The Rb cell, the fluorescence collection optics and the photomultiplier are placed in a specially designed l-metal magnetic shield. The rubidium cell is further placed inside a plano-concave cavity that ensures perfect overlap of the two counter-propagating beams probing the rubidium atoms. This is necessary to avoid firstorder Doppler effect and to allow a good control of the beam geometry which affects the light shift.
M. Poulin et al. / Optics Communications 207 (2002) 233–242
Moreover, using this cavity, a sub-mW incident power is needed to observe the two-photon transitions and most of the slave laser power is thus available as a useful output. The cavity is formed by a PZT-mounted input plane mirror (PZT-C2) with a reflectivity of 96% and a 2-m radius concave mirror with a reflectivity of 99.5%, mounted on steel plates held by invar rods. The mirrors are separated by 30 cm, giving a free spectral range of 500 MHz and a beam waist in the cavity of 420 lm. The measured finesse of the cavity is 150 without the rubidium cell and 80 when the cell is inserted. An additional 65-dB isolator (Isowave, I-80U-2) is used to avoid direct reflections from this cavity into the slave laser. The optical power incident on the cavity can be controlled with a k/2 plate and a polarizing beam splitter arrangement. In order to maintain the laser and the cavity resonance frequencies in coincidence, we use a second lock-in amplifier to demodulate the transmitted signal at 778.1 nm, which is detected by a silicium photodetector. The error signal sent to a proportional-integrator loop filter is fed back to the PZT-C2 transducer, controlling the position of the input mirror of the cavity. By scanning the confocal cavity length using PZT-C1, we can sweep the laser frequency and observe the two-photon transitions. Fig. 4 shows the observed fluorescence profile corresponding to the Fg ¼ 2 to Fe ¼ 4; 3; 2; 1 transitions in 87 Rb. We use the strongest transition 5S1=2 , Fg ¼ 2 5D5=2 ,
237
Fig. 5. Fluorescence spectrum for the Fg ¼ 2 Fe ¼ 4 transition in 87 Rb and fit with a lorentzian profile.
Fe ¼ 4 to frequency-lock the 1556 nm DFB laser. Fig. 5 shows the corresponding profile with a 778 nm power of 0.5 mW incident on the cavity. In this case (as for Fig. 4), a minimal frequency excursion of 90 kHz p–p at 778 nm was used. A lorentzian profile having a full width at half maximum of 410 kHz (at 778 nm) was fitted to the fluorescence profile. The main contributions to this linewidth are the natural linewidth that can be evaluated to 300–390 kHz depending on the published values of the 5D level lifetime (205–266.2 ns [17–20]) and the transit time broadening (70 kHz) [21]. In order to lock the master laser frequency, we demodulate the PM signal using a third lock-in amplifier. The 1556.2 nm laser peak-to-peak frequency modulation excursion at 50 kHz is increased to about 150–200 kHz (0.7 times the FWHM of the line) to experimentally optimize the slope of the discrimination pattern. Fig. 6 presents the error signal when the modulation excursion is optimized for maximum amplitude and maximum center slope. The ratio of the slopes at resonance is 2, close to the one predicted by theory [22]. The error signal, filtered by a P-I circuit, is sent onto PZT-C1 controlling the confocal cavity length, therefore locking the DFB laser frequency to that of the two-photon transition.
7. Frequency stability measurements Fig. 4. Fluorescence spectrum for the Fg ¼ 2 Fe ¼ 4; 3; 2; 1 transition in 87 Rb.
The frequency stability of our standards is measured by recording the beat between two in-
238
M. Poulin et al. / Optics Communications 207 (2002) 233–242
these standards is the best ever reported, to our knowledge, in the 1.55 lm region. The repeatability of the frequency of the systems was evaluated to 200 Hz from the beat frequency, by locking and unlocking one system while the other remained locked.
8. Systematic effects
Fig. 6. Error signal obtained with excursion set for maximum amplitude and maximum center slope.
dependent systems. Both are locked to the same transition and one of them is shifted by 100 MHz using an acousto-optic modulator (AOM). The timebase of the frequency counter was synchronized on the synthesizer used to drive the AOM. Fig. 7 presents the Allan standard deviation of the beat note relative to the optical frequency. A slope of about 2:5 1013 =s1=2 is obtained for averaging times between 0.1 and 10 s. The best stability is 5:8 1014 for 100 s. For greater averaging times, a degradation of the stability is observed. This is mainly attributed to light shift variations induced by changes in the optical power probing the rubidium transition. Improvement of the long-term stability could be obtained by implementing a servo-loop to stabilize the intracavity power [23]. However, the frequency stability of
Fig. 7. Allan standard deviation of the beat frequency between the 1556.2 nm frequency standards, relative to the optical frequency.
Due to some systematic effects, the frequency of the standards is not exactly half that of the Rb transition. From the absolute measurement of the frequency of our standards and the evaluation of these systematic shifts, the determination of the unperturbed two-photon transition frequency is possible. These systematic effects are investigated below. 8.1. Light shift Theoretical calculation of the light shift gives a shift of +0.7346 P =S for the ground state 5S1=2 and +0.0370 P =S for the excited state 5D5=2 where P is the optical power in Watt and S the light beam surface area in m2 [21,24]. Therefore, considering a gaussian beam having a waist of 420 lm and applying a shaping factor of 2/3, the two-photon transition theoretical light shift is )420 Hz/mW at 778 nm. Experimentally, the light shift was measured by recording the beat frequency between the two systems against the optical power probing the transition [23]. As a direct measurement of the intra-cavity optical power is impossible, we plot the beat frequency against the silicium photodetector voltages V1;2 for each system. Fig. 8 shows the beat frequency as the optical power of system #1 is varied for different values of system #2 intracavity power. The same measurements were repeated after reversing the role of the two systems. Extrapolation of the fitted straight lines to zero power allowed to plot the data presented on Fig. 9. The slope for system #1 is then )11.7 Hz/mV (at 1556 nm). The relation between the photodetector voltage and the intra-cavity power can be obtained indirectly. The 778 nm cavity enhancement factor is about 15 using the equation Cð1 R1 ÞTf
M. Poulin et al. / Optics Communications 207 (2002) 233–242
239
The reproductibility of the systems can be evaluated from these light shift measurements. If the systems were perfectly identical, the two curves on Fig. 9 should cross at zero on the frequency axis. The sets of measurements presented in Fig. 9 were repeated four times and allowed us to estimate the reproductibility of the systems to 400 Hz (at 1556.2 nm). 8.2. Relativistic shift
Fig. 8. Light shift variation against Si detector voltage V1 (proportionnal to intra-cavity power) for system #1, for different values of the detector voltage V2 on system #2.
A relativistic treatment of the two-photon transition shows that the transition frequency m0 is shifted by an amount proportional to m0 VA2 =2c2 , where VA is the speed of the atom [24]. Considering a gas of rubidium atoms at thermodynamic equilibrium at a given temperature, the speed of the atoms follows a Boltzman distribution leading to a corresponding relativistic shift distribution. It can be shown that the two-photon transition will be shifted by an amount equal to the mass center of this relativistic shift distribution. For a temperature of 90 0:2 °C, we obtain a shift of 223:1 0:2 Hz (with respect to the 385 THz frequency). 8.3. Collisions
Fig. 9. Light shift variation against intra-cavity power for system #1 (resp. #2) with system #2 (resp. #1) intra-cavity power extrapolated to zero.
pffiffiffiffiffiffiffiffiffiffiffi ðF 2 =p2 R1 Rm Þ, where C is the coupling factor, R1 is the reflectivity of the input mirror, Tf is the facet transmission of the rubidium cell, F is the cavity finesse and Rm is the equivalent reflectivity of the Rb cell-output mirror ensemble. The coupling factor is experimentally measured to be C ¼ 57%. Considering the calibration of the photodetector voltage against the incident power to be 276 mV/ mW, we obtain an experimental light shift slope of )428 Hz/mW at 778 nm which compares very well with the theoretical value. Under standard conditions, the light shift is about )2.8 kHz (i.e., intracavity power of 6.5 mW).
Theoretical shifts due to collisions between rubidium atoms can be evaluated from the measurements performed by Stoicheff and Weinberger [25] for two-photon transitions from 5S1=2 to nS or nD ðn ¼ 10–70Þ. Extending these measurements for the 5S1=2 5D5=2 transition, we obtain a shift of 970 90 Hz (relative to the 385 THz frequency) for a pressure of 8.7 mPa (83 0:2 °C). However, this value appears to be overestimated considering recent measurements by Hilico et al. [23]. Collisions can also occur between Rb atoms and residual gas present in the cell. Let us consider the presence of argon which is often released by ionic diffusion pumps. From previous results published on ð5S–7DÞ two-photon transitions in Rb [26], we can evaluate the Rb–Ar collisional shift to be 0:397 109 Hz cm3 for the ð5S–5DÞ two-photon transitions. In the extreme case where the Ar relative pressure would be equal to that of rubidium, the corresponding shift would be )703 Hz.
240
M. Poulin et al. / Optics Communications 207 (2002) 233–242
8.4. Black-body radiation Black-body radiation shifts were calculated by Farley and Wing [27] for hydrogen and different alkali atoms including rubidium at 300 K. These calculations can be extrapolated to a temperature of 90 0:2 °C considering a T 4 dependence and give a shift of )6 Hz for the 5S1=2 level and )389.5 Hz for the 5D5=2 level leading to a shift of 191:8 2:4 Hz for the 5S1=2 5D5=2 two-photon transitions (at 385 THz). 8.5. Neighbouring transitions We evaluate theoretically the influence of the transitions ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 3; 2; 1Þ neighbouring the strongest transition used to lock the frequency of our standard. The shift due to the lorentzian profiles of the neighbouring transitions is found to be +275 mHz (at 385 THz), while the shift due to their gaussian pedestals amounts to +2.4 mHz (at 385 THz). 8.6. Electronic shifts The offsets at the output of the lock-in amplifiers used to lock the 778 nm cavity and the confocal cavity can influence the locked frequency of our standards. We first varied the offset at the output of the lock-in amplifier generating the error signal for the confocal cavity of the first system while keeping the second system unchanged. We obtained a linear change of the locked frequency with a slope of )87.9 Hz/mV (at 192.6 THz) which agrees well with the one that can be calculated from the slope of the error signal. The same measurement was done for the lock-in amplifier used to lock the cavity surrounding the rubidium cell. A linear change with a slope of +7.8 Hz/mV was observed for the locked frequency. In practice, we can set the offsets at the output of these two lock-in amplifiers to 0:1 and 1:5 mV which correspond respectively to a shift of 9 and 12 Hz at 192.6 THz. We also checked for possible errors related to drifts in the integrator stage of the loop filter used to lock the confocal cavity to the rubidium transition. The drift was experimentally measured,
under open-loop conditions, at the output of the integrator and evaluated to 78 mV/s. This corresponds to an offset of 67 lV at its input, from which we can evaluate a frequency shift of 6 Hz for our frequency standard, considering the slope previously measured ()87.9 Hz/mV). 8.7. Effect due to the excursion of the frequency modulation To check for shifts induced by modulation distortion or rubidium transition asymmetry, the amplitude of the frequency modulation excursion was varied from half to twice the optimum value (i.e., 150–200 kHz at 192.6 THz). No frequency shift could be detected within the repeatability of the measurements. 8.8. Amplitude modulation The direct modulation of the laser current used to produce the frequency modulation required for synchronous detection also produces some residual amplitude modulation. This one can be transferred to the slave laser and induce a frequency shift of the locked laser. However, as the cell is placed inside a build-up cavity whose length is controlled using a synchronous detection scheme, the intra-cavity light is not modulated at 50 kHz [23]. In fact, the locking point of the build-up cavity sets in such a way as to cancel any amplitude fluctuation at 50 kHz. 8.9. Summary Table 1 summarizes the values for the different systematic shifts. Table 1 Summary of the systematic frequency shifts Effect
Shift at 778 nm
Light shift Relativistic shift Rb–Rb collisions Ar–Rb collisions Black-body radiation Neighbouring transitions Electronics
2:81 0:02 kHz 223:1 0:2 Hz 970 90 Hz )703 Hz 191:8 2:4 Hz < 1 Hz 50 Hz
M. Poulin et al. / Optics Communications 207 (2002) 233–242
9. Absolute frequency measurement The two frequency standards were moved to the Institute for National Measurements Standards at the National Research Council in Ottawa, Canada for an absolute frequency determination of the ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ transition in 87 Rb [11]. Using a Cs-linked frequency chain, the absolute frequency of system #1 under standard operating conditions (intra-cavity power of 6.5 mW, cold finger temperature of 83 °C and cell body temperature of 90 °C) was measured to be 192 642 283 183:7 0:5 kHz. In order to obtain the frequency of the two-photon transition, the Comite international des poids et measures (CIPM) has recommended that only the light shift and relativistic shift be applied for the correction. The other effects are taken into account in the overall uncertainty and their contribution amounts to 1.2 kHz. Taking into account the previously evaluated systematic effects and the uncertainty related to the absolute measurement, the Rb transition frequency was determined to be 385 284 566 370:4 2 kHz.
10. Conclusion Two independent frequency standards at 192.6 THz (1556.2 nm) using the two-photon transition ð5S1=2 ; Fg ¼ 2 5D5=2 ; Fe ¼ 4Þ of 87 Rb have been built and characterized. They present a frequency stability of 2:5 1013 s1=2 for averaging times between 0.1 and 10 s, which is the best ever reported at 1.55 lm. A detailed study of systematic effects shifting the locked frequency from that of the unperturbed Rb transititon is presented. The absolute frequency of system #1 under standard operating conditions is 192 642 283 183:7 0:5 kHz. These standards presently provide two absolute frequency outputs at 192.6 and 385.2 THz. These could be optically summed to provide a third reference at 577.8 THz in the visible region.
Acknowledgements We acknowledge Dr. John Bernard, Alan Madej, Louis Marmet and Klaus Siemsen for their
241
contribution to the measurement of the absolute frequency. We thank Dr. B. Villeneuve and M. Svilans, from Nortel Networks, Ottawa, Canada, for providing the high power DFB lasers. We are grateful to Carl Paquet, Sylvain Der^ ome, Martin Lapointe and Dr. Christine Tremblay from INO, and to Dr. Pierre Mathieu from DREV for their participation in the development of the PPLN crystals. We also take this opportunity to thank Mr. Yvon Chalifour for the design and machining of many mechanical parts of these setups. Finally, we acknowledge EXFO Electro-Optical Engineering and NSERC for their financial support through a NSERC/NRC grant.
References [1] F. Bertinetto, P. Gambini, R. Lano, M. Puleo, SPIE 1837 (1992) 154. [2] C. Latrasse, M. Breton, M. T^etu, N. Cyr, R. Roberge, B. Villeneuve, Opt. Lett. 19 (1994) 1885. [3] H. Sasada, K. Yamada, Appl. Opt. 29 (1990) 3535. [4] M. de Labachelerie, K. Nakagawa, Y. Awaji, M. Ohtsu, Opt. Lett. 20 (1995) 572. [5] A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamagushi, M. Kourogi, K. Imai, B. Widiyatomoko, IEEE Trans. Instrum. Meas. 48 (1999) 563. [6] K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, J. Opt. Soc. Am. B 13 (1996) 2708. [7] M. Zhu, R.W. Standridge, Opt. Lett. 22 (1997) 730. [8] M. Poulin, C. Latrasse, N. Cyr, M. T^etu, Photon. Technol. Lett. 9 (1997) 1631. [9] A. Danielli, P. Rusian, A. Arie, M.H. Chou, M.M. Fejer, Opt. Lett. 25 (2000) 905. [10] D. Touahri, O. Acef, A. Clairon, J.J. Zondy, R. Felder, L. Hillico, B. de Beauvoir, F. Biraben, F. Nez, Opt. Commun. 133 (1997) 471. [11] J.E. Bernard, A.A. Madej, K.J. Siemsen, L. Marmet, C. Latrasse, D. Touahri, M. Poulin, M. Allard, M. T^etu, Opt. Commun. 173 (2000) 357. [12] B. Dahmani, L. Hollberg, R. Drullinger, Opt. Lett. 12 (1987) 876. [13] P. Laurent, A. Clairon, C. Breant, IEEE J. Quantum Electron. 25 (1989) 1131. [14] L.E. Myers, G.D. Miller, R.C. Eckardt, M.M. Fejer, R.L. Byer, W.R. Bosenberg, Opt. Lett. 20 (1995) 52. [15] M.M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer, IEEE J. Quantum Electron. 28 (1992) 2631. [16] I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, R. Ito, J. Opt. Soc. Am. B 14 (1997) 2268. [17] O.S. Heavens, J. Opt. Soc. Am. 51 (1961) 1058. [18] C. Tai, W. Happer, R. Gupta, Phys. Rev. A 12 (1975) 736.
242
M. Poulin et al. / Optics Communications 207 (2002) 233–242
[19] A. Lindg ard, S.E. Nielsen, Atomic Data and Nuclear Data Tables 19 (1977) 606. [20] J. Marek, P. M€ unster, J. Phys. B 13 (1980) 1731. [21] F. Biraben, M. Bassini, B. Cagnac, Le J. Phys. 40 (1979) 445. [22] H. Wahlquist, J. Chem. Phys. 35 (1961) 1708. [23] L. Hilico, R. Felder, D. Touahri, O. Acef, A. Clairon, F. Biraben, Eur. Phys. J. AP 4 (1998) 219.
[24] B. Cagnac, G. Grynberg, F. Biraben, Le J. Phys. 34 (1973) 845. [25] B.P. Stoicheff, E. Weinberger, Phys. Rev. Lett. 44 (1980) 733. [26] K.H. Weber, K. Niemax, Z. Phys. A – Atoms and Nuclei 307 (1982) 13. [27] J.W. Farley, W.H. Wing, Phys. Rev. A 23 (1981) 2397.