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Physical Review A

Pulse matching and correlation of phase fluctuations in Λ systems

Michael Fleischhauer, Thomas Richter

Published Mar 1, 1995• 77 citations
Publisher

Abstract

The interaction of a bichromatic quantized field with three-level \ensuremath{\Lambda}-type atoms is analyzed on the basis of c-number Langevin equations. In the presence of ground-state coherence one particular combination of field modes is selectively absorbed leading to a correlation of the output fields. This correlation manifests itself in a matching of Fourier components of the field modes and in a strong reduction of the diffusion of the difference phase. This correlation phenomenon is studied for the case of externally generated coherence as well as for coherence produced by population trapping in conjunction with a nonadiabatic atomic response.

DOI
10.1103/physreva.51.2430

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The interaction of a bichromatic quantized field with three-level \ensuremath{\Lambda}-type atoms is analyzed on the basis of c-number Langevin equations. In the presence of ground-state coherence one particular combination of field modes is selectively absorbed leading to a correlation of the output fields. This correlation manifests itself in a matching of Fourier components of the field modes and in a strong reduction of the diffusion of the difference phase. This correlation phenomenon is studied for the case of externally generated coherence as well as for coherence produced by population trapping in conjunction with a nonadiabatic atomic response.
A quantum analysis of the interaction of two propagating, quasimonochromatic fields with three-level \ensuremath{\Lambda}-type atoms is presented. It is shown that the recently predicted effect of pulse matching [S. Harris, Phys. Rev. Lett. 70, 552 (1993)]--the generation of fields with matched Fourier components--is due to the nonadiabatic response of the medium. This effect leads to a correlation of the high-frequency phase fluctuations of the fields, and may therefore be used to reduce the noise in short-time measurements of phase differences.
We consider the effect of the noise difference phase of a bichromatic field upon coherent population trapping resonances in the simplest three-level system in Λ configuration. The quasi-stationary solution of Bloch optical equations, which was found with some assumptions, shows that the presence of exciting short-correlated fluctuations of the phase of radiation reduces the contrast of the resonance line without affecting its spectral width. For the Gaussian phase noise the contrast suppression factor is χ = exp[−ϕ rms 2 ], where ϕ rms 2 is phase dispersion. The experimental results obtained earlier by our group are analyzed.
The interaction of a model three-level Λ system with electromagnetic radiation is considered under the conditions where a coherence (an off-diagonal matrix element) between lower sublevels arises upon spontaneous decay of an excited state. The cases of bichromatic and incoherent broadband fields are analyzed. It is shown that the occurrence of coherence may significantly change the character of evolution of the system under study with time. These changes are most pronounced for broadband fields. Some features of this phenomenon are considered for multilevel atomic systems.
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.
Equations are derived which describe the dynamics of three-level atoms with a Λ level scheme, interacting with two coherent resonance fields under conditions such that cooperative relaxation predominates over incoherent spontaneous emission. A numerical calculation of the temporal dynamics of the values of the atomic populations is performed. It is shown that coherent population trapping in the presence of cooperative decay is possible. The quantities characterizing this phenomenon are calculated—the width of the black line and the transition time to coherent trapping in this scheme.
We investigate the behavior of a three-level atomic system with \ensuremath{\Lambda} structure of levels in the field of a sequence of short frequency-chirped bichromatic laser pulses (BLP's) in the adiabatic passage regime of interaction. We show that the efficiency of the population transfer in this atomic system is sensitive to the relative phase of the pulses forming the BLP when the atom is prepared in a coherent superposition of its two ground states initially. We propose to use this sensitivity for coherent fast and robust writing and reading of optical phase information. The initial preparation of the atom in the ``dark'' superposition state is suggested through the action of a sequence of a few frequency-chirped BLP's with duration longer than the atomic relaxation time.