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Annalen der Physik

Berry phase of two atoms in the same quantized light field

Mai-Lin Liang, Jin-Han Zhang, Bing Yuan

Published Mar 5, 2007• 1 citation
Publisher

Abstract

Abstract The Berry phase of two atoms exposed to the same quantized light field has been studied. The interaction between each atom and the light field obeys the Jaynes‐Cummings model. Due to the quantization of the light field, the interaction Hamiltonians for the two atoms interacting with the field do not commute with each other, which induces new parts in the Berry phase. Meanwhile, there appears a phase which doesn't exist in the classical regime and is purely induced by the field quantization.

DOI
10.1002/andp.200751905-603

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Abstract The Berry phase of two atoms exposed to the same quantized light field has been studied. The interaction between each atom and the light field obeys the Jaynes‐Cummings model. Due to the quantization of the light field, the interaction Hamiltonians for the two atoms interacting with the field do not commute with each other, which induces new parts in the Berry phase. Meanwhile, there appears a phase which doesn't exist in the classical regime and is purely induced by the field quantization.
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.
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.
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.
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.
We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berry's phase results.
We address Berry phases that have been predicted to appear when a two-level system interacts with a quantized field, including the vacuum state. The issue became controversial after it was argued that the appearance of such Berry phases is an artifact of the rotating-wave approximation (RWA). As is widely believed, whenever the RWA applies, one may replace the Rabi model of a two-level system interacting with a quantized field by the analytically solvable Jaynes-Cummings model. Conflicting predictions of these two models under conditions that validate the RWA would signal a serious inconsistency of this approximation. We show that this is not the case and that claims to the contrary are inconsistent with analytical results concerning the Rabi model. We provide also numerical evidence supporting our analytical approach. Furthermore, we argue that the appearance of Berry phases in the addressed cases does not depend on adiabatic conditions nor on any particular Hamiltonian, but on the underlying vector space. Thus, the appropriate framework is given by the kinematic approach to geometric phases, which contains Berry's phase as a special case.