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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 18832–18838
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Repumping ground-state population in a coherently driven atomic resonance

Asif Sinay, Moshe Shuker, Ofer Firstenberg, Amnon Fisher, Amit Ben-Kish, and Jeff Steinhauer  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 18832-18838 (2010)
http://dx.doi.org/10.1364/OE.18.018832


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Abstract

We experimentally demonstrate an optical pumping technique to pump a dilute rubidium vapor into the mF = 0 ground states. The technique utilizes selection rules that forbid the excitation of the mF = 0 states by linearly-polarized light. A substantial increase in the transparency contrast of the coherent-population-trapping resonance used for frequency standards is demonstrated.

© 2010 OSA

1. Introduction

A well-studied technique to implement an all-optical atomic frequency standard utilizes a coherent population trapping (CPT) resonance [1

1. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005). [CrossRef]

,2

2. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996). [CrossRef]

] within the ground-state of an alkali atom. The clock transition is defined between two magnetically-insensitive mF = 0 levels of the ground state. The short-term frequency stability of the clock is determined by the width and the amplitude of the transparency resonance and by the accompanied noise. The amplitude of the CPT resonance is proportional to the atomic population within the clock transition, and hence it is desirable to increase the population fraction in the relevant mF = 0 states. At thermal equilibrium, the atoms are equally distributed among all possible ground-state sub-levels, and only a small fraction participates in the clock transition. Moreover, the common approach of using a circularly polarized light optically pumps most of the atoms into the highly polarized spin states [3

3. J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” PRA 67(6), 065801 (2003). [CrossRef]

], further reducing the population in the mF = 0 states. While this pumping is useful for end-state schemes, which utilize the absence of spin-exchange relaxation in highly polarized states [4

4. Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, in Proceedings of the 2003 IEEE Int. Freq. Control Symp. & PDA Exhibition Jointly with the 17th Euro. Freq. and Time Forum, 33 (2003).

,5

5. Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, “Intense, narrow atomic-clock resonances,” Phys. Rev. Lett. 92(11), 110801 (2004). [CrossRef] [PubMed]

], it is harmful to the mF = 0 CPT resonance.

Several techniques have been proposed to increase the CPT contrast by reducing the effect of pumping to highly polarized states. Most of these introduce an additional laser field, with the orthogonal circular polarization, that effectively pumps the atoms back to the central mF = 0 levels, while maintaining most of the CPT coherence. The destructive interference between the induced coherence of the two circular polarizations can be circumvented by temporarily alternating the left and right polarizations [6

6. Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, “Push-pull optical pumping of pure superposition states,” Phys. Rev. Lett. 93(16), 160802 (2004). [CrossRef] [PubMed]

]; by inducing an appropriate phase delay (lin⊥lin), either with co-propagating beams [7

7. T. Zanon, S. Tremine, S. Guerandel, E. De Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “Observation of Raman–Ramsey Fringes With Optical CPT Pulses,” IEEE Trans. Instrum. Meas. 54(2), 776–779 (2005). [CrossRef]

,8

8. M. Rosenbluh, V. Shah, S. Knappe, and J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]

] or with a counter-propagating configuration [9

9. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, “High-contrast dark resonances on the D1 line of alkali metals in the field of counterpropagating waves,” JETP Lett. 80(4), 236 (2004). [CrossRef]

,10

10. S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, “High-contrast dark resonance in σ+–σ- optical field,” Laser Phys. Lett. 1(10), 495–499 (2004). [CrossRef]

]; or utilizing the AC stark shift [11

11. M. Zhu, “High Contrast Signal in a Coherent Population Trapping Based Atomic Frequency Standard Application”, M. Zhu, in Proceedings of the 2003 IEEE International Frequency Control Symposium & PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 16 (2003).

]. An alternative approach utilizes the four m F = ±1 Zeeman states, instead of the m F = 0, using a symmetric configuration of left and right circular polarization (lin||lin) [12

12. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, “On the Unique Possibility of Significantly Increasing the Contrast of Dark Resonances on the D1 Line of 87Rb,” JETP Lett. 82(7), 398–403 (2005). [CrossRef]

,13

13. E. E. Mikhailov, T. Horrom, N. Belcher, and I. Novikova, “Performance of a prototype atomic clock based on lin||lin coherent population trapping resonances in Rb atomic vapor”, arXiv:0910.5881 (2009).

].

Here we experimentally demonstrate a technique to improve the CPT contrast, by pumping the atoms to the m F = 0 levels with a π-polarized beam (Figs. 1a
Fig. 1 (Color online) Energy levels diagram for the CPT clock in 87Rb D1 line. The green bars are an illustration of the expected population distribution. (a) Without the repump beam: the σ+-beam create the CPT resonance while pumping the population towards the end state (mF = 2). (b) With the modulated repump beam: the π transitions (F = 1, mF = 0) → (F' = 1, mF = 0) and (F = 2, mF = 0) → (F' = 2, mF = 0) are forbidden, and thus the repump beam repumps the population to the m F= 0 states. (c) The effective states and allowed transitions in the numerical model are marked: the CPT states (1, 2, and 3), the 'trap state' (4), the 'π-excited state' (5), and the 'off-resonance pumping states' (6 and 7). The dashed arrows represent the off-resonant π-excitations.
and 1b). The technique, theoretically suggested by Kazakov et al. [14

14. G. Kazakov, I. Mazets, Yu. Rozhdestvensky, G. Mileti, J. Delporte, and B. Matisov, “High-contrast dark resonance on D2-line of 87Rb in a vapor cell with different directions of the pump-probe waves,” Eur. Phys. J. D 35(3), 445–448 (2005). [CrossRef]

], exploits the forbidden optical transitions (F = 1, mF = 0) → (F' = 1, mF = 0) and (F = 2, mF = 0) → (F' = 2, mF = 0), which have a vanishing dipole matrix elements [15

15. D. A. Steck, Rubidium 87 D Line Data, Theoretical Division (T-8), MS B285 Los Alamos National Laboratory Los Alamos, NM 87545 25 September 2001 (revision 1.6, 14 October 2003).

]. Using a modulated π-polarized pumping beam, all ground levels except the two m F = 0 are repumped, leading to increased population in the clock transition (depopulation optical pumping [16

16. W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972). [CrossRef]

]). We further investigate additional effects of the repump beam, such as broadening and off-resonance pumping. In section 2, we describe a theoretical model for CPT in a multi-level atom, incorporating the four optical modes and all the relevant atomic levels. In addition to the CPT process, the model describes population pumping to the end state, ground-state depolarization, and re-pumping of population to the mF = 0 levels. In section 3, we describe the experimental setup. In section 4, we detail the experimental results showing the predicted increase in contrast, due to the repump beam, along with a broadening of the CPT line. Finally, we conclude our work in section 5 and discuss the results.

2. Model system

The full 16-level structure of the D1 transition of 87Rb is depicted in Fig. 1a. The common model for CPT with σ+ light, describing CPT in the mF = 0 resonance, reduces the atomic structure to a 3-level Λ-system. These levels represent the two ground 'clock states', (F = 1, mF = 0) and (F = 2, mF = 0), and one excited state, e.g., (F' = 2, mF = 1). These are denoted as |1〉, |2〉, and |3〉, respectively, and are coupled by two σ+-polarized electromagnetic fields. However, in order to allow for more elaborated processes, such as optical pumping, a more detailed model is required. Our model includes four additional states as illustrated in Fig. 1c. To account for the ground-state depopulation and for the σ+ optical pumping, we represent the mF ≠ 0 states in the ground manifold by the effective state |4〉, denoted as the 'trap state'. To incorporate the re-pumping action of the modulated repump beam, we represent the mF ≠ 0 states in the excited levels by the effective state |5〉, denoted as the 'π-excited state'. State |4〉 is coupled to state |5〉 by a π-polarized electromagnetic field. To account for off-resonance pumping of the repump beam, as explained later, we represent the excited mF = 0 states, (F' = 1, mF = 0) and (F' = 2, mF = 0), by two effective states, |6〉 and |7〉, denoted as the 'off-resonance pumping states'. Due to selection rules for the π-polarization, state |1〉 is decoupled from state |6〉, and state |2〉 is decoupled from state |7〉. Therefore, in our model, the π-polarized fields off-resonantly couple states |1〉 to |7〉 and |2〉 to |6〉. The excited states, |3〉, |5〉, |6〉, and |7〉, may spontaneously decay to all the lower levels in accordance with selection rules, and the ground states, |1〉, |2〉, and |4〉, exhibit standard population transfer and decoherence.

The model Hamiltonian is given by
H=i=17ωi|ii|{i,j}[Ωijei(ωiωj+Δij)t|ij|+H.c.],
(1)
where ωi are the energies of the states, and Ωij are the Rabi frequencies for each of the relevant transitions ji. Δij are the individual one-photon detunings, and we set Δij=0 for transitions 1→3, 2→3, and 4→5, and Δij≠0 for 1→7 and 2→6. The steady-state solution of the system, in terms of a density operator, is obtained numerically by solving the Master equation (d/dt)ρ=[H,ρ]/(i)+Lρ, yielding the absorption coefficients for the various fields and the population distribution in the ground state [17

17. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, “Atom-Photon Interactions: Basic Processes and Applications”, 1998.

]. The non-Hamiltonian decay processes are introduced using the Lindblad formalism, with
Lρ=mγm(CmρCm+12ρCm+Cm12Cm+Cmρ),
(2)
where Cm are the Lindblad operators, and γm are the associated decay rates. Depolarization (population transfer) and decoherence within the ground state are described, respectively, by Lindblad operators of the form C dep.=|i〉〈j| [with (j=1,2,4)→(i=1,2,4)] and C gound .dec.=|i〉〈i| [with (i=1,2,4)]. Spontaneous emission is described by C spon.=|i〉〈j| [with (j=3,5,6,7)→(i=1,2,4), except the forbidden transitions (7→2) and (6→1)]. Decoherence of the optical transitions, taking into account the homogenous pressure-broadening due to the buffer gas, is incorporated with C opt.dec.=|i〉〈i| [with (i=3,5,6,7)].

The cell temperature and thus the atomic density were constant in all experiments and have been determined from absorption measurements. Some of the dipole matrix-elements and the decay rates in the model are effective parameters and thus required calibration. In practice, we have set them according to relevant known values of the 16-level system [18

18. M. Shuker, O. Firstenberg, Y. Sagi, A. Ben-kish, N. Davidson, and A. Ron, “Ramsey-like measurement of the decoherence rate between Zeeman sublevels,” Phys. Rev. A 78(6), 063818 (2008). [CrossRef]

], and only used the Rabi frequency of the repump beam as a fit parameter. Also, we have calibrated an effective frequency detuning for the off-resonant π-transitions from the relevant experiments, as detailed below.

3. Experimental setup

The experimental setup is depicted in Fig. 2
Fig. 2 Experimental setup. Left: VCSEL – vertical cavity surface emitting laser; PBS – polarizing beam-splitter; QWP – ¼-wave plate (Not shown: three sets of Helmholtz coils within the magnetic shield). Right: The cross-shaped glass vapor cell with Indium-Tin-Oxide (ITO) heaters pressed against its four facets.
(left). A vertical-cavity surface-emitting laser diode (VCSEL) is stabilized to the D1 transition of 87Rb (~795 nm). The VCSEL is current-modulated at 3.417 GHz, and the –1, +1 sidebands are tuned to the F = 2 → F' = 2, F = 1 → F' = 2 transitions, respectively (CPT-VCSEL in Fig. 2). The polarization is set to right-circular by a polarizing beam-splitter and a quarter-wave plate. The beam passes through a cross-shaped vapor cell along the z-direction, and the transmitted intensity is measured with a photo-diode. A second VCSEL (repump-VCSEL) is current modulated at ~3 GHz, and its –1, +1 sidebands are tuned to the F = 2 → F' = 2, F = 1 → F' = 1 transitions, respectively. The repump-VCSEL is set to linear polarization parallel to the z-direction (π-polarization), and passes the vapor cell in perpendicular to the CPT beam. The intensity of both beams is controlled by neutral-density filters.

The cross-shaped vapor cell (Fig. 2, right) contains isotopically pure 87Rb and 10 Torr of nitrogen buffer gas. The dimensions of the cell are 18 mm length, along the z-direction, and 6 mm diameter. Due to technical limitations, the overlap of the repump beam along the optical path of the CPT beam is limited to 6 mm. Therefore, only one third of the path within the cell is directly repumped (see Fig. 2). The temperature of the cell is controlled using electrical heaters (glass with ITO coating), setting the rubidium vapor density to n = 7x1010atoms/cc. The resulting small-signal transparency is about 40%, providing the optimal conditions for a CPT clock [19

19. S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74(3), 217–222 (2002). [CrossRef]

]. A four-layered magnetic shield is used to isolate the cell from the earth magnetic field. Three sets of Helmholtz coils are used to set a small magnetic field, Bz = 20mG, along the z-direction, and to eliminate the residual magnetic field in the perpendicular plane. The CPT spectrum is obtained by shutting-down the electrical heaters and scanning the frequency of the RF oscillator, which modulates the CPT-VCSEL current, around the CPT clock-transition. The scanning rate is sufficiently slow, so that the steady-state spectrum is obtained.

4. Results

We study the CPT spectrum of our experimental system while applying the repump beam. For five different CPT-VCSEL intensities, we vary the repump-VCSEL intensity and measure the CPT resonance. Each CPT line is fitted to a Voigt profile, and its full width at half maximum (FWHM) and contrast (the ratio between the CPT resonance amplitude and its background) are inferred. Figure 3
Fig. 3 (Color online) The CPT contrast (left) and FWHM (right) as a function of the repump-VCSEL intensity at different CPT-VCSEL intensities (* Black 1440µW/cm2, x Blue 4320µW/cm2, ◊ Red 5760µW/cm2, + Orange 8640µW/cm2, ○ Brown 12960µW/cm2). The lines are our model's results.
(left) depicts the measured CPT contrast of the spectrum versus the repump-VCSEL intensities for the five different CPT-VCSEL intensities.

When the intensity of the CPT-VCSEL is weak, the pumping to high mF states is small, and the positive effect of the repump is negligible, as shown by the black curve. As the intensity of the CPT-VCSEL is increased, a larger fraction of the atoms is pumped to higher mF states, and the repump beam is more effective, bringing back more atoms to the mF = 0 state and increasing the CPT contrast, as shown by the red curve. The effectiveness of the repump beam depends also on its intensity. Obviously at low intensities, the repump effect is small, and it increases with the intensity. However at larger intensities, the improvement in the contrast diminishes, and eventually the contrast begins to drop. This is attributed mostly to the off-resonant pumping from the mF=0 states, as predicted by our numerical model, and possibly also to small imperfections in the polarization of the repump beam. The solid lines in Fig. 3 are the results of our numerical model, showing a good agreement with the experimental results. Figure 3 (right) depicts the measured CPT linewidth (FWHM) versus the repump-VCSEL intensity at five different CPT-VCSEL intensities. The CPT lines broaden with the laser intensity due to power broadening.

A second set of measurements was devoted to verifying the effectiveness of the repump, by studying the CPT spectrum without applying the repump beam. Figure 4
Fig. 4 (Color online) The CPT contrast (circles) and the CPT FWHM (asterisks) without the repump beam (black) and with the repump beam (red). For each intensity of the CPT beam, the maximal contrast, obtained by scanning the repump-beam intensity, is shown. The solid lines are model results.
depicts the measured properties of the CPT spectrum at various laser intensities. The CPT linewidth increases linearly with the laser intensity due to power broadening. The CPT contrast initially increases with the laser intensity, but then decreases as the population is pumped out of the clock transition into the high mF states [3

3. J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” PRA 67(6), 065801 (2003). [CrossRef]

], in good agreement with our numerical model. This phenomenon poses a fundamental limit on the maximal contrast that can be obtained in this CPT apparatus and limits the possible accuracy of CPT based frequency standards.

The maximal increase in contrast achieved using the repump beam, for different CPT-VCSEL intensities, is also plotted in Fig. 4 (along with the associated FWHM). It is important to note that, due to technical limitations in the current apparatus, the repump beam is applied to only one third of the length of the cell, limiting the effectiveness of the repumping method.

To obtain the best frequency stability, it is important to maximize the contrast and to minimize the linewidth [1

1. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005). [CrossRef]

]. Therefore, in order to use this optical pumping technique to substantially improve the short-term frequency stability, it is necessary to pump the atoms without increasing the CPT linewidth due to power broadening. One option is to time-alternate the repump beam, and to perform the CPT measurement when the repump beam is off. Another possibility is to apply the repump beam in the vicinity of the CPT beam, but with minimal spatial overlap. In the latter case, the repumping effect will be obtained utilizing the diffusion of atoms in the cell [20

20. I. Novikova, Y. Xiao, D. F. Phillips, and R. L. Walsworth, “EIT and diffusion of atomic coherence,” J. Mod. Opt. 52(16), 2381–2390 (2005). [CrossRef]

].

The contrast observed at the optimum operating point of the system is ~6.1% using the repump beam, instead of 5% without the repump beam. For an arrangement of maximal spatial overlap of the two beams, our numerical model predicts a contrast of about 20%, demonstrating an improvement of a factor of 4.

5. Conclusion

We have demonstrated an optical pumping technique to increase the contrast of CPT-based frequency standards utilizing two additional optical modes (a modulated repump beam). The improvement of the CPT contrast was studied for a wide range of CPT and repump beams intensities. A major drawback of this pumping method is the power broadening of the CPT resonance associated with the repump beam. This limitation may be prevented by turning off the repump beam just before making the measurements or by applying them in the near vicinity of the CPT beam, with minimal spatial overlap. We estimate that by using an optimal setup, the contrast may be improved by up to a factor of four.

Acknowledgements

We thank Yoav Erlich, Igal Levi and Kosta Kogan for technical support. This work is partially supported by the fund for encouragement of research in the Technion and by the DDRND.

References and links

1.

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005). [CrossRef]

2.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996). [CrossRef]

3.

J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” PRA 67(6), 065801 (2003). [CrossRef]

4.

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, in Proceedings of the 2003 IEEE Int. Freq. Control Symp. & PDA Exhibition Jointly with the 17th Euro. Freq. and Time Forum, 33 (2003).

5.

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, “Intense, narrow atomic-clock resonances,” Phys. Rev. Lett. 92(11), 110801 (2004). [CrossRef] [PubMed]

6.

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, “Push-pull optical pumping of pure superposition states,” Phys. Rev. Lett. 93(16), 160802 (2004). [CrossRef] [PubMed]

7.

T. Zanon, S. Tremine, S. Guerandel, E. De Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “Observation of Raman–Ramsey Fringes With Optical CPT Pulses,” IEEE Trans. Instrum. Meas. 54(2), 776–779 (2005). [CrossRef]

8.

M. Rosenbluh, V. Shah, S. Knappe, and J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]

9.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, “High-contrast dark resonances on the D1 line of alkali metals in the field of counterpropagating waves,” JETP Lett. 80(4), 236 (2004). [CrossRef]

10.

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, “High-contrast dark resonance in σ+–σ- optical field,” Laser Phys. Lett. 1(10), 495–499 (2004). [CrossRef]

11.

M. Zhu, “High Contrast Signal in a Coherent Population Trapping Based Atomic Frequency Standard Application”, M. Zhu, in Proceedings of the 2003 IEEE International Frequency Control Symposium & PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 16 (2003).

12.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, “On the Unique Possibility of Significantly Increasing the Contrast of Dark Resonances on the D1 Line of 87Rb,” JETP Lett. 82(7), 398–403 (2005). [CrossRef]

13.

E. E. Mikhailov, T. Horrom, N. Belcher, and I. Novikova, “Performance of a prototype atomic clock based on lin||lin coherent population trapping resonances in Rb atomic vapor”, arXiv:0910.5881 (2009).

14.

G. Kazakov, I. Mazets, Yu. Rozhdestvensky, G. Mileti, J. Delporte, and B. Matisov, “High-contrast dark resonance on D2-line of 87Rb in a vapor cell with different directions of the pump-probe waves,” Eur. Phys. J. D 35(3), 445–448 (2005). [CrossRef]

15.

D. A. Steck, Rubidium 87 D Line Data, Theoretical Division (T-8), MS B285 Los Alamos National Laboratory Los Alamos, NM 87545 25 September 2001 (revision 1.6, 14 October 2003).

16.

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972). [CrossRef]

17.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, “Atom-Photon Interactions: Basic Processes and Applications”, 1998.

18.

M. Shuker, O. Firstenberg, Y. Sagi, A. Ben-kish, N. Davidson, and A. Ron, “Ramsey-like measurement of the decoherence rate between Zeeman sublevels,” Phys. Rev. A 78(6), 063818 (2008). [CrossRef]

19.

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74(3), 217–222 (2002). [CrossRef]

20.

I. Novikova, Y. Xiao, D. F. Phillips, and R. L. Walsworth, “EIT and diffusion of atomic coherence,” J. Mod. Opt. 52(16), 2381–2390 (2005). [CrossRef]

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: April 27, 2010
Revised Manuscript: June 19, 2010
Manuscript Accepted: June 24, 2010
Published: August 19, 2010

Citation
Asif Sinay, Moshe Shuker, Ofer Firstenberg, Amnon Fisher, Amit Ben-Kish, and Jeff Steinhauer, "Repumping ground-state population in a coherently driven atomic resonance," Opt. Express 18, 18832-18838 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18832


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References

  1. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005). [CrossRef]
  2. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996). [CrossRef]
  3. J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” PRA 67(6), 065801 (2003). [CrossRef]
  4. Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, in Proceedings of the 2003 IEEE Int. Freq. Control Symp. & PDA Exhibition Jointly with the 17th Euro. Freq. and Time Forum, 33 (2003).
  5. Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, “Intense, narrow atomic-clock resonances,” Phys. Rev. Lett. 92(11), 110801 (2004). [CrossRef] [PubMed]
  6. Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, “Push-pull optical pumping of pure superposition states,” Phys. Rev. Lett. 93(16), 160802 (2004). [CrossRef] [PubMed]
  7. T. Zanon, S. Tremine, S. Guerandel, E. De Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “Observation of Raman–Ramsey Fringes With Optical CPT Pulses,” IEEE Trans. Instrum. Meas. 54(2), 776–779 (2005). [CrossRef]
  8. M. Rosenbluh, V. Shah, S. Knappe, and J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]
  9. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, “High-contrast dark resonances on the D1 line of alkali metals in the field of counterpropagating waves,” JETP Lett. 80(4), 236 (2004). [CrossRef]
  10. S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, “High-contrast dark resonance in σ+–σ- optical field,” Laser Phys. Lett. 1(10), 495–499 (2004). [CrossRef]
  11. M. Zhu, “High Contrast Signal in a Coherent Population Trapping Based Atomic Frequency Standard Application,” in Proceedings of the 2003 IEEE International Frequency Control Symposium & PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 16 (2003).
  12. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, “On the Unique Possibility of Significantly Increasing the Contrast of Dark Resonances on the D1 Line of 87Rb,” JETP Lett. 82(7), 398–403 (2005). [CrossRef]
  13. E. E. Mikhailov, T. Horrom, N. Belcher, and I. Novikova, “Performance of a prototype atomic clock based on lin||lin coherent population trapping resonances in Rb atomic vapor,” arXiv:0910.5881 (2009).
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