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Physical Review A

Coherent population trapping in a Λ configuration coupled by magnetic dipole interactions

Huidong Kim, Hyok Sang Han, Tai Hyun Yoon, D. Cho

Published Mar 10, 2014• 7 citations
Publisher

Abstract

We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the $nP$ manifold via an optical transition on one of the spectroscopic $D$ lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.

DOI
10.1103/physreva.89.032507

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arXiv:1606.04375•Journal of Applied Physics•Jun 23, 2016•20 citations
We report our study on coherent population trapping (CPT) in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration coupled by magnetic dipole interactions. The \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We consider the coherent-population-trapping (CPT) phenomenon in a sodium atomic vapor. The experiment leading to the first observation of CPT is revisited with an improved experimental setup and a larger range of magnetic-field strengths. From the analysis of the ground-state hyperfine splitting as a function of the applied magnetic field, we conclude that we have observed the whole spectrum of dark resonances within the D1 line corresponding to the nonabsorbing coherent superposition of two Zeeman sublevels of two different components of the 32S1/2 level. This was not obvious a priori because the transition probabilities at high magnetic-field strengths, as applied in the experiment, have to be taken into account. The differences in the contrast of the various black lines are explained in terms of pumpings outside the interaction scheme preparing the nonabsorbing state. Possible applications of CPT in high magnetic fields are discussed.
There presented basic information on coherent population trapping (CPT) and related phenomenon of electromagnetically induced transparence, ‘dark’ and ‘bright’ (anomalous absorption) states is presented. Spectrum transformation is considered in probe field spectroscopy for Λ-scheme in various settings. The close relation is revealed between the effect of CPT in the manifold of magnetic sublevels and the phenomenon of optical pumping (optical orientation and optical alignment). CPT is shown to be generalized to the case of several transitions with a common upper level and with the corresponding number of light fields each being in quasiresonance with its ‘own’ transition.
The purpose of this communication is to summarize and compare the results obtained under the project "New all-optical systems and methods for magnetic and electromagnetic field measurement", financed by EC (contract G6RD-CT-2001-000642). The main aim of the project is investigation of the potential of different approaches based on the effect of Coherent Population Trapping (CPT) for magnetic field measurement. The investigated approaches are: (i) CPT prepared by coupling pairs of non-degenerate Zeeman sublevels belonging to the two ground-state hyperfine components of alkali atoms by means of polychromatic laser field; (ii) CPT prepared by coupling degenerate Zeeman sublevels belonging to a single ground-state hyperfine component of alkali atoms by means of single-frequency laser field of appropriate polarization at zero magnetic field (MF); and (iii) polychromatic laser field coupls pairs of non-degenerate Zeeman sublevels belonging to a single ground-state hyperfine level of alkali atoms.
We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted Y\mathsf{Y}Y configuration in an alkali-metal atom. It consists of a $\mathrm{\ensuremath{\Lambda}}$ formed by two Raman transitions between the ground hyperfine levels and the DDD transition, allowing RSC along two paths and formation of a CPT dark state. Using the state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $\mathrm{\ensuremath{\Lambda}}$ to make only the motional ground state a CPT dark state. We call this scheme motion-selective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a 87Rb^{87}\mathrm{Rb}87Rb atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss the application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.
Summary form only given. We have experimentally investigated the potential of narrow coherent population trapping resonances for precision applications like magnetometry or atomic frequency standards. CPT can be observed in /spl Lambda/ systems where two ground states are coupled to a common excited state by two near-resonant light fields. Effective formation of ground state coherences takes place when the frequency difference of the light fields precisely matches the ground state splitting. This process leads to reduced absorption in the medium (electromagnetically induced transparency) and thus reduced fluorescence intensity (dark resonance) at the optical resonance frequency. Extremely narrow dark resonances can be observed when the two light fields have fixed phase and frequency difference and time-of-flight broadening is suppressed by the use of a buffer gas, making this type of system a promising candidate for precision applications. The /spl Lambda/ systems under study here are the D/sub 2/ lines of Cs, /sup 87/Rb and /sup 85/Rb where the ground state hyperfine splittings are 9.2 GHz, 6.8 GHz, and 3.0 GHz, respectively. Thus in a magnetic field the CPT resonance splits into several Zeeman components whose frequency positions are determined by the Breit-Rabi formula.
Coherent population trapping (CPT) is extensively studied for future vapor cell clocks of high frequency stability. In the constructive polarization modulation CPT scheme, a bichromatic laser field with polarization and phase synchronously modulated is applied on an atomic medium. A high contrast CPT signal is observed in this so-called double-modulation configuration, due to the fact that the atomic population does not leak to the extreme Zeeman states, and that the two CPT dark states, which are produced successively by the alternate polarizations, add constructively. Here, we experimentally investigate CPT signal dynamics first in the usual configuration, a single circular polarization. The double-modulation scheme is then addressed in both cases: one pulse Rabi interaction and two pulses Ramsey interaction. The impact and the optimization of the experimental parameters involved in the time sequence are reviewed. We show that a simple seven-level model explains the experimental observations. The double-modulation scheme yields a high contrast similar to the one of other high contrast configurations like push-pull optical pumping or crossed linear polarization scheme, with a setup allowing a higher compactness. The constructive polarization modulation is attractive for atomic clock, atomic magnetometer, and high precision spectroscopy applications.