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Journal de Physique II

Coherent population trapping and Fano profiles

Brahim Lounis, Claude N. Cohen-Tannoudji

Published Apr 1, 1992• 87 citations
Publisher

Abstract

This paper presents a new approach to coherent population trapping in a $\Lambda$-type three level atomic configuration. This approach, which is based on scattering theory, applies when one of the two driving laser fields is much weaker than the other one. We show that the scattering amplitude of the weak field is the sum of 2 resonant amplitudes. The positions and the widths of these resonances are identified and physically interpreted in the low saturation limit, in terms of Rayleigh scattering, stimulated and spontaneous Raman scattering. Finally, we show that the interference between the two scattering amplitudes gives rise to Fano profiles in the curves giving the frequency dependence of the total scattering cross-section.

DOI
10.1051/jp2:1992153

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Journal of Modern Optics•Mar 1, 1995•18 citations
This paper presents a new approach to coherent population trapping in a Λ\LambdaΛ-type three level atomic configuration. This approach, which is based on scattering theory, applies when one of the two driving laser fields is much weaker than the other one. We show that the scattering amplitude of the weak field is the sum of 2 resonant amplitudes. The positions and the widths of these resonances are identified and physically interpreted in the low saturation limit, in terms of Rayleigh scattering, stimulated and spontaneous Raman scattering. Finally, we show that the interference between the two scattering amplitudes gives rise to Fano profiles in the curves giving the frequency dependence of the total scattering cross-section.
The spectroscopic properties of a single tightly trapped atom are studied, when the electronic levels are coupled by three laser fields in an NNN-shaped configuration of levels, whereby a $\ensuremath{\Lambda}$-type level system is weakly coupled to a metastable state. We show that depending on the laser frequencies the response can be tuned from coherent population trapping at two-photon resonance to a behavior at three photon resonance, where the metastable state can get almost unit occupation in a wide range of parameters. For certain parameter regimes the system switches spontaneously between dissipative and coherent dynamics over long time scales.
We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.
Abstract We study phase-dependent fluctuations of the resonance fluorescence of a single Λ-type three-level atom in the regime near coherent population trapping, i.e. alongside the two-photon detuning condition. To this end, we employ the method of conditional homodyne detection (CHD) which considers squeezing in the weak driving regime, and extends to non-Gaussian fluctuations for saturating and strong fields. In this framework, and using estimated parameter settings of the resonance fluorescence of a single trapped 138 Ba + ion, the light scattered from the probe transitions is found to manifest a non-classical character and conspicuous asymmetric third-order fluctuations in the amplitude-intensity correlation of CHD.
We study the effect of quantum interference on the population distribution and absorptive properties of a V-type three-level atom driven by two lasers of unequal intensities and different angular frequencies. Three coupling configurations of the lasers to the atom are analysed: (a) both lasers coupled to the same atomic transition, (b) each laser coupled to different atomic transition and (c) each laser coupled to both atomic transitions. Dressed states for the three coupling configurations are identified, and the population distribution and absorptive properties of the weaker field are interpreted in terms of transition dipole moments and transition frequencies among these dressed states. In particular, we find that in the first two cases there is no population inversion between the bare atomic states, but the population can be trapped in a superposition of the dressed states induced by quantum interference and the stronger field. We show, that the trapping of the population, which results from the cancellation of transition dipole moments, does not prevent the weaker field to be coupled to the cancelled (dark) transitions. As a result, the weaker field can be strongly amplified on transparent transitions. In the case of each laser coupled to both atomic transitions the population can be trapped in a linear superposition of the excited bare atomic states leaving the ground state unpopulated in the steady state. Moreover, we find that the absorption rate of the weaker field depends on the detuning of the strong field from the atomic resonances and the splitting between the atomic excited states. When the strong field is resonant to one of the atomic transitions a quasi-trapping effect appears in one of the dressed states. In the quasi-trapping situation all the transition dipole moments are different from zero, which allows the weaker field to be amplified on the inverted transitions. When the strong field is tuned halfway between the atomic excited states, the population is completely trapped in one of the dressed states and no amplification is found for the weaker field.
A three-level system driven by two coherent fields on two-photon resonance leads to the trapping of population in a superposition of initial and final states which is immune to further photoexcitation, manifesting itself in a narrow coherence minimum in the absorption spectrum. The authors analyse the effects of laser field bandwidths and cross-correlations on these phenomena. They find that the inclusion of laser bandwidths dephases atomic coherences which leads to the destruction of population trapping and of the narrow coherence minimum in the absorption spectrum. When the driving fields are not cross-correlated, the atomic coherences are similarly dephased in both lambda and ladder systems. If, however, the driving fields are critically cross-correlated, two-photon coherences in the lambda system are unaffected by laser fluctuations; trapping and the coherence minimum persist. For the ladder system, on the other hand, the cross-correlation does not restore the atomic coherences involved.
Master equation methods are used to investigate the effects of a broad-band squeezed vacuum on a three-level atom of the lambda configuration. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed vacuum the atom is driven by two coherent laser fields each of which, depending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for the atomic density matrix elements have oscillatory coefficients, thereby necessitating the use of Floquet methods. For the case of equal laser frequencies, which are also equal to the carrier frequency of the squeezed vacuum, the coefficients of the Bloch equations become time independent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the usual coherent population trapping effect at two-photon resonance is obtained, with the upper state population being zero. An unsqueezed thermal field partially destroys the trapping effect as the upper state population is no longer zero at two-photon resonance. The squeezed vacuum has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which occurs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of this coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of unequal laser frequencies, the coherence transfer process in combination with the squeezed vacuum can restore to some extent the population trapping. We show that other features that do not occur for two-level atoms, such as stationary population inversions between pairs of the atomic levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fields the population in the upper state depends on the relative phase only when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequency of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the degree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.