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Journal of Optics B Quantum and Semiclassical Optics

Balancing the dynamic Stark shift in a driven Jaynes–Cummings system

Dmitri S. Mogilevtsev, S. Ya. Kilin

Published Feb 13, 2004• 2 citations
Publisher

Abstract

In this work we discuss the possibility of balancing a dynamic Shark shift in a Jaynes–Cummings system by simultaneously driving the cavity and the atom with classical fields, of the same frequency. For a lossless Jaynes–Cummings system this can lead to unusual atomic population dynamics. For a lossy Jaynes–Cummings system such balancing can lead to complete suppression of resonance fluorescence even for leaky cavities.

DOI
10.1088/1464-4266/6/4/002

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In this work we discuss the possibility of balancing a dynamic Shark shift in a Jaynes–Cummings system by simultaneously driving the cavity and the atom with classical fields, of the same frequency. For a lossless Jaynes–Cummings system this can lead to unusual atomic population dynamics. For a lossy Jaynes–Cummings system such balancing can lead to complete suppression of resonance fluorescence even for leaky cavities.
We calculate the quasienergies and steady states of a coupled two-level atom and quantized electromagnetic cavity mode with the cavity mode driven by a periodic classical field. The atom, the cavity mode, and the classical field are all on resonance. The quasienergies give shifted Jaynes-Cummings level splittings. These splittings are reduced by the interaction with the driving field and vanish at a threshold value of the driving field strength. Above the threshold, discrete quasienergies and normalizable steady states do not exist. Below the threshold, for weak driving fields, the steady states are squeezed and displaced Jaynes-Cummings eigenstates. We discuss the relevance of these results to work in cavity quantum electrodynamics.
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 analyze the time-dependent physical spectrum of a driven Jaynes-Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes-Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly-Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes-Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom-cavity coupling.
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.