Analytic Approximation of the Tavis-Cummings Ground State via Projected States

Abstract

We show that an excellent approximation to the exact quantum solution of the ground state of the Tavis-Cummings model is obtained by means of a semi-classical projected state. This state has an analytical form in terms of the model parameters and, in contrast to the exact quantum state, it allows for an analytical calculation of the expectation values of field and matter observables, entanglement entropy between field and matter, squeezing parameter, and population probability distributions. The fidelity between this projected state and the exact quantum ground state is very close to 1, except for the region of classical phase transitions. We compare the analytical results with those of the exact solution obtained through the direct Hamiltonian diagonalization as a function of the atomic separation energy and the matter-field coupling.

22 pages, 13 figures, accepted for publication in Physics Scripta

References in corpus (4)

• Observation of Strong Coupling between One Atom and a Monolithic Microresonator
• Cavity QED with a Bose-Einstein condensate
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Coherent State Description of the Ground State in the Tavis-Cummings Model and its Quantum Phase Transitions

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• Characterization of the quantum phase transition in a two-mode Dicke model for different cooperation numbers
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• Quantum phase transition of two-level atoms interacting with a finite radiation field