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arXiv:quant-ph/0207016 · Physical Review A

Quantum-trajectory approach to stochastically induced quantum-interference effects in coherently driven two-level atoms

A. Karpati, Петер Адам, Wojciech Gawlik, Bogdan Lobodzinski, József Janszky

Published Aug 28, 2002• 7 citations
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Abstract

Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum-trajectory method. A method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.

DOI
10.1103/physreva.66.023821

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Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum-trajectory method. A method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.
Abstract Stochastic perturbation of two‐level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. Narrow resonances as hole burning and dispersive Fano‐like profile occur in the spectra in the regime where the noise dominates the Rabi oscillations. It is shown that in this case the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.
A system of coherently driven two-level atoms is analysed in the presence of two independent stochastic perturbations: one due to collisions and a second due to phase fluctuations of the driving field. The behaviour of the quantum interference induced by the collisional noise is considered in detail. The quantum-trajectory method is utilized to reveal the phase correlations between the dressed states involved in the interfering transition channels. It is shown that the quantum interference induced by the collisional noise is remarkably robust against phase noise. This effect is due to the fact that the phase noise, similarly to collisions, stabilizes the phase difference between the dressed states.
The absorption spectrum is considered for a two-level atom coherently driven by a laser field and incoherently perturbed by stochastic noise. In the noise-dominated regime where incoherent perturbation far exceeds coherent excitation, the amplifying and dispersionlike components in the standard absorption spectrum [B. R. Mollow, Phys. Rev. A 5, 2217 (1972); F. Y. Wu et al., Phys. Rev. Lett 38, 1077 (1977)] develop into an absorption peak and a narrow dip, respectively. The modified absorption spectrum is attributed to the quantum interference induced by stochastic noise.
The quantum trajectories method is illustrated for the resonance fluorescence of a two-level atom driven by a multichromatic field. We discuss the method for the time evolution of the fluorescence intensity in the presence of bichromatic and trichromatic driving fields. We consider the special case wherein one multichromatic field component is strong and resonant with the atomic transition whereas the other components are much weaker and arbitrarily detuned from the atomic resonance. We find that the phase-dependent modulations of the Rabi oscillations, recently observed experimentally [Q. Wu, D. J. Gauthier, and T. W. Mossberg, Phys. Rev. A 49, R1519 (1994)] for the special case when the weaker component of a bichromatic driving field is detuned from the atomic resonance by the strong-field Rabi frequency, appear also for detunings close to the subharmonics of the Rabi frequency. Furthermore, we show that for the atom initially prepared in one of the dressed states of the strong field component the modulations are not sensitive to the phase. We extend the calculations to the case of a trichromatic driving field and find that apart from the modulations of the amplitude there is a modulation of the frequency of the Rabi oscillations. Moreover, the time evolution of the fluorescence intensity depends on the phase regardless of the initial conditions and a phase-dependent suppression of the Rabi oscillations can be observed when the sideband fields are tuned to the subharmonics of the strong-field Rabi frequency.
In the experiment with barium vapor (close approximation of a two-level system) we found spectra of resonance fluorescence having the form of a pressure-broadened line with a narrow, not collisionally broadened, dip. They are interpreted as the result of collisionally-induced quantum interference among possible spontaneous emission channels of a dressed atom subjected to stochastic perturbation. Also, the analogy between these effects and the coherent population trapping in three-level systems is pointed out.
We investigate nonlinear wave mixing in two-level atoms wherein, using a dressed state formalism, it is shown that the signal arises as a consequence of quantum interference between relevant probability amplitudes for photon emission. We then report a theoretical study of the modifications that are induced in the four-wave mixing signals when the transition frequency of the atoms is stochastically modulated. Such modulations, which arise from perturbations in the immediate environment of the atoms, are shown to cause significant alterations in the nonlinear response of the atoms. We also describe how one can, via an investigation of the four-wave mixing signal, differentiate between Markov and non-Markov fluctuations in the transition frequency of the two-level system. The calculations rely on a recently developed Monte Carlo procedure that can be used to obtain exact solutions to a wide variety of spectroscopic problems, with minimal restrictions on atom, field, and noise parameters.