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arXiv:quant-ph/0101036 · Optics Letters

Cavity-damping-induced transitions in a driven atom–cavity system

Hyunchul Nha, Kyungwon An

Published Jun 15, 2001• 9 citations
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Abstract

We investigate the fluorescence spectrum of a two-level atom in a cavity when the atom is driven by a classical field. We show that forbidden dipole transitions in the Jaynes-Cummings ladder structure are induced in the presence of cavity damping, which deteriorates the degree of otherwise perfect destructive interference among the transition channels. With the larger cavity decay, these transitions are more enhanced.

DOI
10.1364/ol.26.000923

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Cavity-damping-induced transitions in a driven atom-cavity system

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Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•5 citations
We investigate the fluorescence spectrum of a two-level atom in a cavity when the atom is driven by a classical field. We show that forbidden dipole transitions in the Jaynes-Cummings ladder structure are induced in the presence of cavity damping, which deteriorates the degree of otherwise perfect destructive interference among the transition channels. With the larger cavity decay, these transitions are more enhanced.
Spectra of the atomic resonance fluorescence and of the cavity-transmitted light in a driven Jaynes-Cummings system are studied theoretically, where the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, anomalous resonance peaks occur at $\ifmmode\pm\else\textpm\fi{}\sqrt{n}{g}^{\ensuremath{'}} (n=2,3,\dots{}),$ with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}},$ both in the atomic fluorescence and the cavity transmission. These peaks as well as the observed shift of the vacuum Rabi splitting are explained in terms of the quasienergy levels induced dynamically by the strong driving field. For a stronger driving field, it is shown that the spectrum of the cavity transmission deviates from that of the atomic fluorescence. In the presence of significant damping, the spectrum of the cavity transmission approaches a singlet structure in the strong driving-field limit, and it is found additionally that a bimodal photon-number distribution, which results in a unique quintuplet spectrum of the atomic fluorescence, does not show up in the cavity transmission.
Resonance fluorescence of a driven Jaynes-Cummings system is studied theoretically when the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, there occur anomalous resonance peaks at $\ifmmode\pm\else\textpm\fi{}\sqrt{2}{g}^{\ensuremath{'}},\ifmmode\pm\else\textpm\fi{}\sqrt{3}{g}^{\ensuremath{'}},$ etc., with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}}.$ These new peaks and the observed shift of the vacuum Rabi splitting are to be explained in the language of the quasienergy levels induced dynamically by the strong driving field. In the presence of significant damping the spectrum reflects the photon-number distribution inside the cavity, and particularly, a bimodality of the distribution results in a unique quintuplet resonance fluorescence spectrum.
We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.
The phase dependence of the cavity quantum dynamics in a driven equidistant three-level ladder-type system found in a quantum well structure with perpendicular transition dipoles is investigated in the good cavity limit. The pumping laser phases are directly transferred to the superposed amplitudes of the cavity-quantum-well interaction. Their phase difference may be tuned in order to obtain destructive quantum interferences. Therefore, the cavity field vanishes although the emitter continues to be pumped.
The damped and coherently-driven JaynesndashndashndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.