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arXiv:2202.10888 · Physical review. D/Physical review. D.

Geometric phases acquired for a two-level atom coupled to fluctuating vacuum scalar fields due to linear acceleration and circular motion

Zixu Zhao, Baoyuan Yang

Published Aug 15, 2022• 3 citations
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Abstract

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 $z$, 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 $z$.

DOI
10.1103/physrevd.106.036013

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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 \ensuremathθ\ensuremath∈(0,\ensuremathπ2)\ensuremath∪(\ensuremathπ2,\ensuremathπ)\ensuremath{\theta}\ensuremath{\in}(0,\frac{\ensuremath{\pi}}{2})\ensuremath{\cup}(\frac{\ensuremath{\pi}}{2},\ensuremath{\pi})\ensuremathθ\ensuremath∈(0,2\ensuremathπ​)\ensuremath∪(2\ensuremathπ​,\ensuremathπ), 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 \ensuremathθ\ensuremath∈(0,\ensuremathπ)\ensuremath{\theta}\ensuremath{\in}(0,\ensuremath{\pi})\ensuremathθ\ensuremath∈(0,\ensuremathπ), 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 \ensuremathθ\ensuremath∈(0,\ensuremathπ)\ensuremath{\theta}\ensuremath{\in}(0,\ensuremath{\pi})\ensuremathθ\ensuremath∈(0,\ensuremathπ) for a smaller zzz.
We study, in the framework of open quantum systems, the time evolution of a circularly accelerated two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields. We find that both the spontaneous transition rates and the geometric phase for a circularly accelerated atom do not exhibit a clear sign of thermal radiation characterized by the Planckian factor in contrast to the linear acceleration case. The spontaneous transition rates and effective temperature of the atom are examined in detail in the ultrarelativistic limit and are shown to be always larger than those in the linear acceleration case with the same proper acceleration. Unlike the effective temperature, the geometric phase is dependent on the initial atomic states. We show that when the polar angle in Bloch sphere, $\ensuremath{\theta}$, that characterizes the initial state of the atom equals $\ensuremath{\pi}/2$, the geometric phases acquired due to circular and linear acceleration are the same. However, for a generic state with an arbitrary $\ensuremath{\theta}$, the phase will be in general different, and then we demonstrate in the ultrarelativistic limit that the geometric phase acquired for the atom in circular motion is always larger than that in linear acceleration with same proper acceleration for $\ensuremath{\theta}\ensuremath{\in}(0,\frac{\ensuremath{\pi}}{2})\ensuremath{\cup}(\frac{\ensuremath{\pi}}{2},\ensuremath{\pi})$.
In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom state parameter θ≠πθ\neqπθ=π, the quantum Fisher information can exist a maximum value and a local minimum value before reaching a stable value. In addition, in a short time, the quantum Fisher information varies with the initial state parameter, and the quantum Fisher information can take a maximum value at θ=0θ=0θ=0. The quantum Fisher information may exist two peak values at a certain moment. These features are different from the massless scalar fields case. With the time evolution, FmaxF_{max}Fmax​ firstly increases, then decreases, and finally, reaches the same value. However, FmaxF_{max}Fmax​ will arrive at a stable maximum value for the case of the massless scalar fields. Although the atom response to the vacuum fluctuation electromagnetic fields is different from the case of massless scalar fields, the quantum Fisher information eventually reaches a stable value.
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.
We have investigated the geometric phase acquired by a uniformly accelerated Unruh-DeWitt detector coupled to vacuum fluctuations of a massless conformal scalar field in anti-de Sitter (AdS) spacetime. Using the open-quantum-system formalism, we calculate the phase under three boundary conditions (Dirichlet, transparent, and Neumann) imposed on the field at the AdS boundary. Our findings reveal a sharp distinction between subcritical and supercritical accelerations. For subcritical accelerations, the detector evolves effectively as an isolated system, and the geometric phase is independent of both the AdS radius and the acceleration. For supercritical accelerations, however, topology-acceleration-induced phase corrections emerge and display pronounced boundary-condition dependence. When the AdS radius is smaller than the detector's proper wavelength, the magnitude of the correction at large accelerations follows the ordering Neumann>>>transparent>>>Dirichlet. Moreover, over a finite interval of the detector's weight parameter, both Dirichlet and Neumann boundary conditions produce a richer peak structure in the phase correction than the transparent case, with the detailed pattern governed by the competition between the acceleration and the detector's energy gap. Finally, for transparent boundary conditions in the supercritical regime, the AdS phase correction closely resembles its de Sitter counterpart.
We study the quantum Fisher information (QFI) of acceleration, in the open quantum systems, for a two-level atom with the circular motion coupled to a massless scalar field in the Minkowski vacuum without and with a reflecting boundary in the ultra-relativistic limit. As we amplify a, the saturation time decreases for θ≠π, but first increases and then decreases for θ=π. Without a boundary, there exists a peak value of QFI with a certain time. The QFI varies with the initial state parameter θ, and firstly takes peak value in the ground state of the atom. The variation of QFI with respect to θ gradually fades away with the evolution of time. With a boundary, the detection range of acceleration has been expanded. The QFI firstly takes the maximum in the excited state of the atom. In addition, we study the QFI of temperature for a static atom immersed in a thermal bath without and with a boundary. The relation between the saturation time and T is similar to a. Without a boundary, the QFI of temperature is similar to that of acceleration. With a boundary, the QFI firstly takes peak value in the ground state of the atom, which is different from the behavior of acceleration. The results provide references for the detection of Unruh-like effect.