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arXiv:1205.0979 · Physical Review A

Jaynes-Cummings model with a collective atomic mode

Shi‐Biao Zheng

Published Apr 7, 2008• 24 citations
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Abstract

We study the dynamics of a single control atom and an atomic sample interacting with a nonresonant cavity mode. The control atom is driven by an auxiliary classical field. Under certain conditions, the coherent energy exchange between the control atom and the atomic sample induced by the cavity mode is described by the Jaynes-Cummings model. The idea provides a possibility for quantum-state engineering and reconstruction for collective atomic modes.

DOI
10.1103/physreva.77.045802

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We study the dynamics of a single control atom and an atomic sample interacting with a nonresonant cavity mode. The control atom is driven by an auxiliary classical field. Under certain conditions, the coherent energy exchange between the control atom and the atomic sample induced by the cavity mode is described by the Jaynes-Cummings model. The idea provides a possibility for quantum-state engineering and reconstruction for collective atomic modes.
We study the dynamics of a coupled cavity system composed of three cavities, and propose a scheme for the coherent manipulation of two collective atomic modes by a control atom. In the scheme, the control atom and two atomic ensembles interact with the local cavity mode, while the control atom is externally driven by a laser field. We show that under certain conditions, the dynamics of the whole system are reduced to an effective coherent coupling between the control atom and two collective atomic modes, while the cavity fields are only virtually excited. We also study the dynamics of the entanglement generation of the two distant collective atomic modes. The scheme provides a potential application for quantum-state engineering and quantum control.
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.
The realization of a Jaynes-Cummings model in the optical domain is proposed for an atomic ensemble. The scheme exploits the collective coupling of the atoms to a quantized cavity mode and the nonlinearity introduced by coupling to high-lying Rydberg states. A two-photon transition resonantly couples the single-atom ground state $|g\ensuremath{\rangle}$ to a Rydberg state $|e\ensuremath{\rangle}$ via a nonresonant intermediate state $|i\ensuremath{\rangle}$, but due to the interaction between Rydberg atoms only a single atom can be resonantly excited in the ensemble. This restricts the state space of the ensemble to the collective ground state $|G\ensuremath{\rangle}$ and the collectively excited state $|E\ensuremath{\rangle}$ with a single Rydberg excitation distributed evenly on all atoms. The collectively enhanced coupling of all atoms to the cavity field with coherent coupling strengths which are much larger than the decay rates in the system leads to the strong coupling regime of the resulting effective Jaynes-Cummings model. We use numerical simulations to show that the cavity transmission can be used to reveal detailed properties of the Jaynes-Cummings ladder of excited states and that the atomic nonlinearity gives rise to highly nontrivial photon emission from the cavity. Finally, we suggest that the absence of interactions between remote Rydberg atoms may, due to a combinatorial effect, induce a cavity-assisted excitation blockade whose range is larger than the typical Rydberg dipole-dipole interaction length.
In this paper, we present a scheme to prepare the W state and the GHZ state of many atomic ensembles based on the dynamics of the atomic system of a single control atom and an atomic ensemble dispersively coupling with a cavity, where the control atom is illuminated by a highly detuned auxiliary classical field at the same time. The dynamics of the atomic system can be described by an effective Jaynes–Cummings model (JCM) with the atomic ensemble as the bosonic mode. The preparation of the entangled states is deterministic. Because the cavity is always in the vacuum state during the whole evolution process, our scheme is less sensitive to the cavity decay.