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Journal of Physics B Atomic Molecular and Optical Physics

Spin observables in an atomic CQE system

Osvaldo Civitarese, M. Reboiro, Diego Tielas

Published Mar 7, 2013• 6 citations
Publisher

Abstract

A cavity quantum electrodynamical Hamiltonian is solved to study spin observables, such as the orientation and fluctuations of the total spin and entropy, in a system of N two-level atoms placed in a resonant cavity. The eigenstates of the Hamiltonian are calculated, both exactly and approximately. We calculate the time evolution of spin observables such as spin and entropy squeezing. Conclusions are drawn about the validity of the approximations in the limit of a large number of atoms.

DOI
10.1088/0953-4075/46/6/065502

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A cavity quantum electrodynamical Hamiltonian is solved to study spin observables, such as the orientation and fluctuations of the total spin and entropy, in a system of N two-level atoms placed in a resonant cavity. The eigenstates of the Hamiltonian are calculated, both exactly and approximately. We calculate the time evolution of spin observables such as spin and entropy squeezing. Conclusions are drawn about the validity of the approximations in the limit of a large number of atoms.
We investigate the dynamics of an arbitrary atomic system (n-level atom or many n-level atoms) interacting with a resonant quantized mode of an electromagnetic field in a lossless cavity. Initially, the field is taken in a coherent state with a large average photon number. If the initial atomic state is chosen as an eigenstate of the atomic Hamiltonian in the classical field limit (semiclassical eigenstates), then the evolution of the system wave function is approximately factorized into the field and atomic parts. Explicit analytical expressions are given for the factorized wave functions. The time evolution of an arbitrary initial atomic state can be fully described in terms of factorized states. As examples, we discuss trapping states, and collapses and revivals of the atomic energy.
We study the time evolution of the quantum field inside a cavity coupled to a beam of two-level atoms of temperature T, given that each atom, after having crossed the cavity, interacts with a classical field and finally with a detector measuring its state. It is shown numerically that, if the atom-quantum field coupling is weak and % is large, for any given realization of the measurements, any initial state of the cavity field localizes after some time into a squeezed state. The center a of the squeezed state moves randomly on a line in the complex plane, but the squeezing parameters r and Φ show very little fluctuation. Their mean values r and Φ are independent of the realization, the initial state, and the atom-field coupling constant. The time evolution of r and Φ is computed in the limit of weak atom-field coupling and large. It is found that r increases with T; i.e., the squeezing is enhanced by increasing the temperature of the atomic beam. The limitation on the degree of squeezing that can be reached is discussed.
We study the von Neumann entropy of the partial trace of a system of 2 two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single-mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanishes.
We examine the single-atom entropy squeezing and the atom–field entanglement in a system of two moving two-level atoms interacting with a single-mode coherent field in a lossless resonant cavity. Our numerical calculations indicate that the squeezing period, the squeezing time and the maximal squeezing can be controlled by appropriately choosing the atomic motion and the field-mode structure. The atomic motion leads to a periodical time evolution of entanglement between the two-atom and the field. Moreover, there exists corresponding relation between the time evolution properties of the atomic entropy squeezing and that of the entanglement between the two atoms and the field.