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arXiv:1212.2695 · Physical Review A

Detecting modified vacuum fluctuations due to the presence of a boundary by means of the geometric phase

Hongwei Yu, Jiawei Hu

Published Dec 12, 2012• 10 citations
arXivHTMLPDF

Abstract

We study the geometric phase acquired by an inertial atom whose trajectories are parallel to a reflecting boundary due its coupling to vacuum fluctuations of electromagnetic fields, by treating the atom as an open quantum system in a bath of the fluctuating vacuum fields, and show that the phase is position dependent as a result of the presence of the boundary which modifies the field quantum fluctuations. Our result therefore suggests a possible way of detecting vacuum fluctuations in experiments involving geometric phase.

DOI
10.1103/physreva.86.064103

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We study the geometric phase acquired by an inertial atom whose trajectories are parallel to a reflecting boundary due its coupling to vacuum fluctuations of electromagnetic fields, by treating the atom as an open quantum system in a bath of the fluctuating vacuum fields, and show that the phase is position dependent as a result of the presence of the boundary which modifies the field quantum fluctuations. Our result therefore suggests a possible way of detecting vacuum fluctuations in experiments involving geometric phase.
In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space, as we amplify acceleration, the geometric phase acquired purely due to linear acceleration case firstly is smaller than the circular acceleration case in the ultrarelativistic limit for the initial atomic state $\ensuremath{\theta}\ensuremath{\in}(0,\frac{\ensuremath{\pi}}{2})\ensuremath{\cup}(\frac{\ensuremath{\pi}}{2},\ensuremath{\pi})$, then equals to the circular acceleration case in a certain acceleration, and finally, is larger than the circular acceleration case. The spontaneous transition rates show a similar feature. This result is different from the case of a bath of fluctuating vacuum electromagnetic fields that has been studied. Considering the initial atomic state $\ensuremath{\theta}\ensuremath{\in}(0,\ensuremath{\pi})$, we find that the geometric phase acquired purely due to linear acceleration always equals to the circular acceleration case for the certain acceleration. The feature implies that, in a certain condition, one can simulate the case of the uniformly accelerated two-level atom by studying the properties of the two-level atom in circular motion. Adding a reflecting boundary, we observe that a larger value of a geometric phase can be obtained compared to the absence of a boundary. Besides, the geometric phase fluctuates along zzz, and the maximum of geometric phase is closer to the boundary for a larger acceleration. We also find that geometric phases can be acquired purely due to the linear acceleration case and circular acceleration case with $\ensuremath{\theta}\ensuremath{\in}(0,\ensuremath{\pi})$ for a smaller zzz.
We investigate, in the paradigm of open quantum systems, the dynamics of quantum coherence of a circularly accelerated atom coupled to a bath of vacuum fluctuating massless scalar field in a spacetime with a reflecting boundary. The master equation that governs the system evolution is derived. Our results show that in the case without a boundary, the vacuum fluctuations and centripetal acceleration will always cause the quantum coherence to decrease. However, with the presence of a boundary, the quantum fluctuations of the scalar field are modified, which makes that quantum coherence could be enhanced as compared to that in the case without a boundary. Particularly, when the atom is very close to the boundary, although the atom still interacts with the environment, it behaves as if it were a closed system and quantum coherence can be shielded from the effect of the vacuum fluctuating scalar field.
The dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency is studied, in the framework of open quantum systems, for a static polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields without and with the presence of a reflecting boundary. Our results show that in the case without a boundary, the electromagnetic vacuum fluctuations always cause the quantum Fisher information of the initial parameters and thus the precision limit of parameter estimation to decrease. Remarkably, however, with the presence of a boundary, the quantum Fisher information becomes position and atomic polarization dependent and, as a result, it may be enhanced as compared to that in the case without a boundary and may even be shielded from the influence of the vacuum fluctuations in certain circumstances as if it were a closed system.
In this paper, we analyze the decohering power behaviors for an atom immersed in a thermal bath of fluctuating electromagnetic field in the presence of a perfectly reflecting plane boundary. Firstly, we analytically solve the master equation that governs the system evolution. Then, we discuss the behaviors of decohering power for an atom affected by thermal fluctuating electromagnetic field. It is found that the behaviors of decohering power are dependent on the field temperature, atomic position and polarization. Decohering power fluctuates to relatively stable values with the increasing atom’s distance from the boundary, which suggests a possible way of detecting the vacuum fluctuating and boundary effect. Additional conditions on the electromagnetic field give one more freedom to manipulate the variations of decohering power. Decohering power variations can efficiently reflect the behaviors of quantum coherence affected by electromagnetic vacuum fluctuation, and it is shown that quantum coherence can be effectively enhanced with the presence of a reflecting boundary.
We present a bipartite two-level system coupled to electromagnetic quantum vacuum fluctuations through a general dipolar coupling. We derive the master equation in the framework of an open quantum system, assuming an environment composed of (i) solely vacuum fluctuations and (ii) the vacuum fluctuations and a conducting plate located at a fixed distance from the bipartite system. For both cases considered, we study the dynamics of the bipartite system and the temporal evolution of the concurrence of an initial entangled bipartite state. We further analyze the generation of entanglement due to the vacuum structure. Finally, we study the different induced contributions to the correction of the unitary geometric phase of a bipartite quantum state so as to explore the possibility of future experimental setups by exploring the influence of boundaries conditions in vacuum.