Minimization of the temperature coefficientof resonance frequency shift in

the coherent population trapping clockKe Deng, Xuzong Chen, and Zhong Wang*

Institute of Quantum Electronics, School of Electronics Engineering & Computer Science,Peking University, Beijing 100871, China*Corresponding author: zw@pku.edu.cn

Received February 8, 2011; revised April 10, 2011; accepted April 10, 2011;posted April 11, 2011 (Doc. ID 142288); published May 4, 2011

We studied the relationship between the frequency shift of coherent population trapping resonance and the celltemperature of 85Rb. Results show that the temperature coefficient of the frequency shift can be reduced by buffergas pressure adjustment and light shift optimization. When the contribution of buffer gas collision to temperaturecoefficient of frequency shift is less than 0:3Hz=K, the contribution of light shift to the temperature coefficient offrequency shift becomes obvious. Under this cancelling effect, we can reduce the rate of total frequency shift to nearzero. © 2011 Optical Society of AmericaOCIS codes: 020.1670, 020.6580, 300.6260.

During the past few years, the chip scale atomic clock(CSAC) has attracted increasing attention in the fre-quency standard field [1,2]. CSAC is based on a nonlinearoptical phenomenon that has been called coherent popu-lation trapping (CPT) [3,4]. The CPT phenomenon occursin a Λ transition, when the frequency difference of twocoherent laser fields is close to the atomic hyperfine split-ting of the two ground states. The main advantage of theCPT atomic clock is its ability to miniaturize the physicalpackage and reduce power consumption.Because the CSAC is often placed in instruments sub-

ject to significant environmental variations, it is difficultto improve the temperature stability of the atom cell in itsphysical package. Because of collisions with buffer gasatoms, the energy levels of the alkali will shift as a func-tion of temperature. Therefore, the temperature drift hin-ders the long-term frequency stability of CSACs. In orderto improve the long-term stability of the CSAC and broad-en its application field, we must reduce the temperaturecoefficient of the frequency shift of CPT resonance. Inthis Letter, we will use “frequency shift rate” for the tem-perature coefficient of frequency shift. Previous methodshave been proposed and implemented for the reductionof the temperature sensitivity of CSACs [5].It is known that a mixture of different buffer gases can

be added to the atom cell to reduce the frequency shiftrate [6], as two different buffer gases can produce oppo-site frequency shift rates. In rubidium cells, Ar─Ne is agood choice because Ar produces negative shift rate andNe produces positive shift rate [7]. Generally, the fre-quency shift rate can be reduced from several Hz=K ortens of Hz=K to less than 1Hz=K through optimizationof the buffer gases’ pressure and ratio. In earlier work(see [8]) we noticed that the graph of frequency shift rateversus buffer gases’ ratio crossed the horizontal axis.Therefore, adjusting the buffer gases’ ratio should reducethe frequency shift rate to near zero. The minimum fre-quency shift rate in [8] is about 0:4Hz=K. With fine adjust-ment of the buffer gases’ ratio, we should be able toobtain better results. In this Letter we did further studyto minimize the frequency shift rate. We observed that

when the buffer gas collision shift rate is less than0:3Hz=K, the light shift rate and collision shift rate cancancel each other through the adjustment of pump laserintensity. Using this method we can reduce the total fre-quency shift rate to near zero.

In accordance with the results of [8], we constructed14 cells in which the ratio of Ne and Ar is about 1.25, tominimize the total shift rates. All cells have identical ex-terior dimensions—0:8 cm in length, 1 cm in diameter,and contain a mixture of natural rubidium (72% 85Rband 28% 87Rb) with buffer gases Ne and Ar. The ratioof Ne and Ar ranges from 1.15 to 1.35. The total pressureis 30mBar in seven cells and 40mBar in the other sevencells. We measured the CPT resonance frequency shift ofthese cells in the temperature range of 30 °C to 50 °C.

Figure 1 shows a sketch of the experimental setup formeasuring the CPT resonance frequency shift at differenttemperatures for the 85Rb atom. In this experiment, thelaser injection current was modulated by an rf generatorwith full hyperfine frequency [9]. Thirty-three percentand 25% of the optical power were contained in thered and blue first sidebands, respectively, leaving 30%in the carrier. Then the carrier and the first red sideband

Fig. 1. Experimental setup for measuring the frequency shiftof CPT resonance.

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0146-9592/11/101740-03$15.00/0 © 2011 Optical Society of America

were used to excite CPT resonance. A 3mm laser beamwas collimated, then circularly polarized and attenuated.Light intensity was 100 μW=cm2 at the entrance to the va-por cell. The cell was temperature-controlled and magne-tically shielded. A small longitudinal magnetic field of10 μT was applied to lift the degeneracy of the Zeemanlevels. Using the first lock-in amplifier, the laser’s wave-length was locked on the 85Rb D1 line absorption spec-trum. The rf generator (model Agilent E8257D, AgilentTechnologies, USA) is frequency-modulated at 190Hz.The error signal generated by the second lock-in ampli-fier shows the difference between the CPT resonance fre-quency and the rf generator frequency. When we tune theerror signal to zero, the output frequency of the rf gen-erator becomes the CPT resonance frequency. The mea-surement was repeated for an atom cell at temperaturesbetween 30 °C and 50 °C, during which frequency shiftrates were obtained. Measurements were repeated forthe other 13 cells.The frequency shift rates of these cells mostly fall with-

in the range of −0:5Hz=K to 0:5Hz=K. Figure 2 shows aplot of the CPT resonance frequency shift as a function ofcell temperature for a special cell (cell 9). The frequencyshift measurement error is less than 0:3Hz. In this cell,the total pressure is 30mBar and the ratio of Ne to Aris 1.22. The collision shift rate of this cell is about0:15Hz=K. Cell 9 obtained the minimum rate amongthe 14 cells, around temperature 42 °C� 1 °C. We areinterested in this temperature point because the clockwould have its best short-term stability at a temperaturewithin the range of 41 °C to 43 °C if these cells wereused. It can be seen from Fig. 2 that the relationship be-tween frequency shift and temperature is not linear.From 28 °C to 35 °C, the frequency shift rate is positive.From 35 °C to 43 °C, the frequency shift rate is approxi-mately zero. When the temperature is above 43 °C, thefrequency shift rate is negative. For this special cell, atthe temperature operation point 42 °C, the frequencyshift rate is less than 0:1Hz=K, which means that if weuse this cell in a CPT clock, temperature instability of1K would lead to frequency instability in the 10−11 region.Furthermore, if we can keep the temperature within35 °C to 43 °C, the frequency shift will be less than0:1Hz, and frequency instability will be kept within the10−11 region.

Here we can give a qualitative explanation of the ex-perimental results. The measured total CPT resonancefrequency shift V tol can be given by [2]

V tol ¼ VB þ Vbg þ Vls: ð1Þ

Here, VB is the magnetic field shift; it is independent oftemperature. Vbg is the shift caused by collisions betweenthe buffer gases and the rubidium atoms. In low tempera-ture ranges (<20 °C) it can be given as Vbg ¼ P0½βþδðT − T0Þ�, where P0 is the buffer gas pressure, β isthe pressure shift coefficient, δ is the temperature coeffi-cient of the buffer gas, T is the temperature of the atomcell, and T0 is the reference temperature at which thecoefficient δ is measured.

The light shift, Vls, is proportional to the light intensity.It can be given by V ls ¼ DIopt, where D is the light inten-sity coefficient and Iopt is the incident light intensity. InCSACs, all of the sidebands create light shift [9], and wetake into account the total effect in our analysis; there-fore D is dependent on the modulation depth of the pumplaser. For an optically thin cell, light intensity can be seenas a constant in the cell. However, for a thick sample,light intensity is not homogeneous in the cell due tothe light absorption. Iopt should be the average of lightintensity in the cell, which can be given by Iopt ¼RIðzÞdz=L, where L is the length of the cell. We assume

that Iopt ¼ ðIL þ I0Þ=2. Here, I0 is the light intensity at thecell entrance (z ¼ 0); IL is the light intensity at the end ofthe cell (z ¼ L). We define absorption percentage asp ¼ 1 − IL=I0, p is dependent on atom vapor densityand I0. Considering that the atom vapor density has anear exponential relationship with temperature in therange of 40 °C to 50 °C, the light intensity can be givenas Iopt ¼ I0ð1 − p=2Þ ¼ I0f1 − κ · exp½aðT −T0Þ�=2g, wherea is a quantity related to the absorption percentage and κis the absorption percentage at temperature T0.

If we specially consider the relationship between totalfrequency shift and the atom cell temperature, the totalfrequency shift equation can be written as:

V tol ¼ δP0ðT − T0Þ −κ2DI0eaðT−T0Þ þ C: ð2Þ

Here, C includes all terms independent of temperature.When the contribution of the buffer gas collision to fre-quency shift rate is large, for example, several Hz=K ortens of Hz=K, the contribution of light shift to frequencyshift rate can be ignored. When the collision shift rate isless than 0:3Hz=K, the light shift rate becomes compar-able, and cannot be ignored. In Fig. 2, the positivefrequency shift rate below 35 °C is dominated by the buf-fer gas collision. The negative frequency shift rate above43 °C is mainly influenced by the light shift. In the tem-perature range of 40 °C to 43 °C, the two effects canceleach other, and the total frequency shift rate is approxi-mately zero.

Data from another cell concurred with the above ana-lyses. We measured frequency shift for cell 6 under a dif-ferent light intensity from temperature 40 °C to 50 °C.Cell 6 has an Ne–Ar ratio of 1.28, and the total buffergas pressure is 40mBar. For this cell, the collisionshift rate is about 0:2Hz=K. We are not interested in

Fig. 2. Frequency shift of CPT resonance as a function of celltemperature for cell 9.

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temperature ranges below 40 °C, because the CPT reso-nance signal-to-noise ratio is not good enough in thisrange. The results are plotted in Fig. 3, which shows acomparison of frequency shift between 50 μW=cm2 and100 μW=cm2. It can be seen that the two curves have a si-milar behavior. From 40 °C to 43 °C, the frequency shiftrate is close to zero, and above 43 °C, the frequency shiftrate is negative. The solid lines in Fig. 3 were fitted toEq. (2). With light intensity I0 ¼ 100 μW=cm2, T0 ¼ 40 °C,P0 ¼ 40mBar, and κ ¼ 0:1, the fitting parameterswere δ¼0:011Hz=ð°C�mBarÞ, D ¼ 0:537Hz=ðμW=cm2Þ,a ¼ 0:1455=°C, andC ¼ 225Hz. HereC increases linearlywith buffer gas pressure, and increasing the modulationdepth of the pump laser leads to a reduction of D.It can be seen from Fig. 3 that the frequency shift rate is

influenced by both light intensity and temperature. Wecan adjust the frequency shift rate by adjusting light in-tensity and choosing a suitable operating temperature.The experimental results show that the frequency wasreduced by 4:5Hz when the temperature increased from40 °C to 50 °C for light intensity of 100 μW=cm2, while thefrequency was reduced by 3Hz for light intensity of50 μW=cm2. Thus, a light intensity increase of 50 μW=cm2

causes a 1:5Hz light shift reduction, because the collisionshift and magnetic field shift are the same for differentlight intensities. This means that the average light shiftrate in this temperature range is roughly −0:15Hz=Kfor a light intensity of 50 μW=cm2.The light shift rate is proportional to the light intensity,

which can be seen from Eq. (2). The light intensity usual-ly has an operation range in the clock, i.e., from50 μW=cm2 to 100 μW=cm2, which means that the lightshift rate can be tuned from −0:15Hz=K to −0:3Hz=Kthrough adjustments in light intensity. To make the cellin the clock work at a low frequency shift rate, first wecan adjust the buffer gases’ pressure and ratio to makethe collision shift rate positive; the collision shift rate va-lue is from 0:15Hz=K to 0:3Hz=K at best. The total buffergas pressure should be from 20 to 80mBar when the sizeof the cell is as mentioned above. Then we can choose anoptimal light intensity and use the light shift rate to can-

cel out the collision shift rate, which allows us to reducethe total frequency shift rate to near zero. This methodhas a significant advantage, because precisely controllingthe buffer gas pressure is difficult in the cell fabricationprocess, while adjusting light intensity is relatively sim-ple. Furthermore, due to diffusion and leakage of the buf-fer gas in the cell, maintaining the buffer gas at a constantpressure is challenging for the miniaturized cell. Whenthe collision shift rate changes after a long-term use,we can adjust the light shift rate through light intensityto compensate for the variation in collision shift rate.Thus we extend the age of a cell.

In CSACs, millimeter cells were used at higher tem-peratures, with higher buffer gas pressures than the largecells in our experiment. The millimeter cell is an opticallythick sample at its operating temperature, and light ab-sorption also has a near exponential relationship with re-spect to temperature in a small temperature range.Therefore, Eq. (2) should equally apply to millimetercells, and our method could be applied to CSACs.

In conclusion, we have demonstrated that by optimiz-ing buffer gas pressure and light intensity it is possible tosubstantially reduce the frequency shift rate of CPT reso-nance. When the collision shift rate is less than 0:3Hz=K,with adjustments in light intensity, the collision shift rateand light shift rate can cancel each other, allowing thetotal frequency shift rate to be minimized to near zero.Reducing the temperature sensitivity is crucial for long-term stability of CSACs. This method not only enhancesthe commercial feasibility of CSACs by improving theirreliability, especially when used in harsh environmentalconditions, it also relaxes the requirement for the accu-racy of the buffer gas pressure. In addition, the methodcould be applied to other microwave clocks where thelight shift and collision shift produce opposite tempera-ture coefficients.

This work was supported by the National NaturalScience Foundation of China (NSFC) under grant11074012. The authors thank Xin Wang for help withthe English language.

References

1. Y.-Y. Jau, A. B. Post, N.N.Kuzma, A.M.Braun,M. V. Romalis,and W. Happer, Phys. Rev. Lett. 92, 110801 (2004).

2. J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345(1998).

3. J. Vanier, Appl. Phys. B 81, 421 (2005).4. E. Arimondo and G. Orriols, Lett. Nuovo Cimento 17,

333 (1976).5. D. Miletic, P. Dziuban, R. Boudot, M. Hasegawa, R. K.

Chutani, G. Mileti, V. Giordano, and C. Gorecki, Electron.Lett. 46, 1069 (2010).

6. J. Vanier and C. Audoin, The Quantum Physics of AtomicFrequency Standards (Hilger, 1989).

7. B. Bean and R. Lambert, Phys. Rev. A 13, 492 (1976).8. K. Deng, T. Guo, D. W. He, X. Y. Liu, D. Z. Guo, X. Z. Chen,

and Z. Wang, Appl. Phys. Lett. 92, 211104 (2008).9. K. Deng, T. Guo, J. Su, D. Z. Guo, X. Y. Liu, L. Liu, X. Z. Chen,

and Z. Wang, Phys. Lett. A 373, 1130 (2009).

Fig. 3. Frequency shift of CPT resonance as a function of celltemperature for cell 6 under different light intensity. Squares,50 μW=cm2; triangles, 100 μW=cm2.

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