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Europhysics Letters (EPL)

Depopulation and repopulation pumping in coherent population trapping

Ferruccio Renzoni, E. Arimondo

Published Jun 15, 1999• 14 citations
Publisher

Abstract

The role of the depopulation and repopulation pumping mechanisms in coherent population trapping (CPT) is discussed. The case of open F g → F e transitions resonant with polarized laser light of different polarizations is examined. The efficiency of the preparation of the atomic population into the dark state is studied both for exact Raman resonance and for small Raman detuning. Dependences of the CPT-preparation on the laser polarization are described.

DOI
10.1209/epl/i1999-00324-1

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The role of the depopulation and repopulation pumping mechanisms in coherent population trapping (CPT) is discussed. The case of open F g → F e transitions resonant with polarized laser light of different polarizations is examined. The efficiency of the preparation of the atomic population into the dark state is studied both for exact Raman resonance and for small Raman detuning. Dependences of the CPT-preparation on the laser polarization are described.
Coherent population trapping (CPT) with losses towards off-resonant levels is analyzed on the basis of the coupled/noncoupled states. We derive that at a long interaction time the noncoupled state is depopulated at a rate that is decreasing for decreasing Raman detuning. This behavior produces a narrowing of the dark resonance with the interaction time. The asymptotic evolution of the atomic system is completely characterized by the effective width ${\ensuremath{\Gamma}}_{\mathrm{NC}}$ of the noncoupled state. The analytic expression for this width evidences a quadratic dependence on the Raman detuning. This dependence implies that the width of the dark resonance decreases asymptotically with the inverse of the square root of the interaction time. This narrowing law, independent of the interaction scheme, has a general validity for CPT in open systems. Our analysis points out the differences between CPT with losses and CPT in closed systems.
The coherent population trapping (CPT) under resonance interaction of elliptically polarized light, with atoms having degenerated energy levels, is analytically treated in an invariant way, without using a specific coordinate frame. Tensors describing dark states are found in an explicit and invariant form for all atomic transitions, where CPT takes place. The correspondence between elliptical polarization vectors and pairs of unit spinors is established. It is shown that all dark states in the problem under consideration, can be constructed from these spinors, by taking multiple tensor products. In the case of an integer angular momentum, this general construction is reduced to a multiple tensor product of vectors. A general significance and some applications of these results are indicted.
We study resonant four-wave mixing process (omega) 4 equals (omega) 1 minus (omega) 2 plus (omega) 3 under conditions of coherent population trapping (CPT) when radiations with frequencies (omega) 1,2 are strong, and (omega) 1 minus (omega) 2 equals (omega) 20 ((omega) 20 is a frequency of electrodipole-forbidden transition). It is shown that under the CPT sufficiently large nonlinear polarization (the same as linear polarization or higher) may be created. We show that in atomic Ba vapor for cw lasers quantum conversion efficiency can be as high as several tens percent.
Coherent population trapping (CPT), under the resonant interaction of elliptically polarized light with atoms having degenerated energy levels, is analytically treated without the use of a specific coordinate frame. Tensors describing dark states are presented in an explicit and invariant form for all atomic transitions, where CPT takes place. A correspondence between elliptical polarization vectors and pairs of unit spinors is established. It is shown that all dark states in the problem under consideration can be constructed from these spinors by taking multiple tensor products. In the case of an integer angular momentum, this general construction is reduced to a multiple tensor product of vectors.
We have developed and experimentally studied a coherent population trapping (CPT) state preparation scheme for atomic clock application with co-propagating left and right circularly polarized lasers. With realization of constructive interference and spin-polarized dark state free in CPT state preparation, we have obtained CPT resonance signal 3 times larger than that of the conventional scheme used in atomic clock. Polarization fluctuations and CPT signal sensitivity to laser power behaviors are both improved with the scheme. Our study reveals that it is a promising candidate for both normal-size and chip-scale CPT atomic clocks.
Raman pulse atom interferometry is an important modality for precision measurements of inertial forces and tests of fundamental physics. Typical Raman atom optics use two coherent laser fields applied at gigahertz-scale detunings from optical resonance, so that spontaneous emission produces a minor or negligible source of decoherence. An additional consequence of spontaneous emission is coherent population trapping (CPT). We show that CPT produces coherences and population differences which induce systematic effects in Raman pulse atom interferometers. We do not believe that CPT has been previously identified as an error mechanism in Raman pulse atom interferometry. We present an experimental characterization of CPT coherences and population differences induced in laser-cooled cesium atoms by application of Raman pulses at detunings near 1 GHz, commensurate with detunings used in several precision measurement experiments. We are not aware of previous demonstrations of CPT-induced population difference. We argue that CPT effects could induce phase shifts of several milliradians in magnitude for typical experimental parameters and stipulate that these errors can be suppressed by propagation direction reversal in Raman interferometer-based precision measurements.