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Physical Review A

Probe spectrum of multilevel atoms in a damped, weakly driven two-mode cavity

James Clemens

Published Jun 21, 2010• 3 citations
Publisher

Abstract

We calculate the probe spectrum for multilevel atoms in a damped, weakly driven cavity supporting two degenerate orthogonally polarized modes. One mode is weakly driven by a linearly polarized external field. The atoms, initially prepared in a ${m}_{F}=0$ hyperfine ground state, couple to the driven mode by making a $\ensuremath{\Delta}{m}_{F}=0$ transition and to the orthogonally polarized mode by making $\ensuremath{\Delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ transitions to other hyperfine sublevels. We compare probe spectra, the intensity of the driven mode, the undriven mode, and the atomic excitation probability as a function of the detuning of the driving laser from the cavity resonance for three- and four-level atomic models. In both cases the spectrum of the driven mode is a vacuum Rabi doublet familiar from the driven, damped Jaynes-Cummings model. The undriven mode spectrum is a triplet with the maximum on resonance for the three-level model while the four-level model has a four-peaked spectrum. We discuss the role of strong coupling to the undriven mode in accounting for the qualitative difference between the models.

DOI
10.1103/physreva.81.063818

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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.
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.
We calculate intensity autocorrelations and cross correlations for the light transmitted from a system consisting of a three-level Λ-type atom inside an optical cavity that supports two orthogonally polarized modes with one mode of the cavity weakly driven on resonance. We also include damping of the cavity modes and spontaneous emission from the atom using the framework of quantum trajectory theory. The correlation functions are compared with those of a two-level atom/cavity system as the coupling to the third level is increased, and we find a transition from photon bunching to photon antibunching. The three-level model allows the atom to couple to both field modes for which we calculate intensity cross correlations that exhibit nonclassical behaviors. Finally, we discuss the lack of entanglement between the field modes despite their common coupling to the same atom and the presence of atom-field entanglement.
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We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.