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arXiv:1008.3777 · Physical Review A

Vacuum-induced Berry phases in single-mode Jaynes-Cummings models

Yu Liu, L. F. Wei, W. Z. Jia, J.-Q. Liang

Published Oct 5, 2010• 10 citations
arXivHTMLPDF

Abstract

Motivated by work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquired photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even if the field is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with a cavity quantum electrodynamics system is designed to detect the vacuum-induced Berry phase.

DOI
10.1103/physreva.82.045801

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Motivated by work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquired photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even if the field is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with a cavity quantum electrodynamics system is designed to detect the vacuum-induced Berry phase.
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he Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different direction since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number nnn of a two-atom Jaynes-Cummings model with Kerr like medium are investigated. It is found that there are some correspondence between their images, especially the existence of a curve in the Δ−εΔ-\varepsilonΔ−ε plane along which the energy, Berry phase and entropy all reach their special values. So it is available for detecting entanglement by applying Berry phase.
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.
The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.
The effect of the motion of mass center of a two-level atom on its transition in a quantized radiation field is studied in this paper by generalizing the Jaynes–Cummings model to include the coupling depending on space degrees of freedom. As an additional geometrical phase—Berry's phase in the oscillation, the effect of the induced gauge field resulting from the Born–Oppenheimer (BO) approximation explicitly exists in the transition probability between the up and down states of atomic quasispin. It is shown that when the atom's kinetic energy is small enough that the BO adiabatic approximation holds for the case with small atom's momentum or large detuning, the adiabatically approximate solutions are applicable and it is possible to localize an atom in the cavity.