Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1203.5869 · Physical Review A

Geometric phase for an accelerated two-level atom and the Unruh effect

Jiawei Hu, Hongwei Yu

Published Mar 5, 2012• 56 citations
arXivHTMLPDF

Abstract

We study, in the framework of open quantum systems, the geometric phase acquired by a uniformly accelerated two-level atom undergoing nonunitary evolution due to its coupling to a bath of fluctuating vacuum electromagnetic fields in the multipolar scheme. We find that the phase variation due to the acceleration can be in principle observed via atomic interferometry between the accelerated atom and the inertial one, thus providing an evidence of the Unruh effect.

DOI
10.1103/physreva.85.032105

Related papers

Dynamical behavior and geometric phase for a circularly accelerated two-level atom

Yao Jin, Jiawei Hu, Hongwei Yu

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 $\ensuremath{\theta}\ensuremath{\in}(0,\frac{\ensuremath{\pi}}{2})\ensuremath{\cup}(\frac{\ensuremath{\pi}}{2},\ensuremath{\pi})$.

arXiv:1406.5576•Physical Review A•Jun 25, 2014•20 citations

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

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 $z$.

arXiv:2202.10888•Physical review. D/Physical review. D.•Aug 15, 2022•3 citations

The geometric phase of a two-level atom under the Hawking effect in a Kerr black hole

Jiliang Jing, Zhipeng Cao, Xiaobao Liu +1 more

Abstract We study the Hawking effect in terms of the geometric phase for a two-level atom coupled to vacuum fluctuations in the background of Kerr black hole in a gedanken experiment. Since the atom interacts with a bath of fluctuating massless scalar field, its geometric phase for the nonunitary evolution turns out to be affected by the spacetime curvature that backscatters the vacuum field modes. We examine the geometric phase for two kinds of vacua, i.e. the Unruh vacuum and the Candelas–Chrzanowski–Howard vacuum. We find that for both of these two cases, the geometric phase of the static atom locating outside the infinite redshift surface (or the stationary atom locating inside the ergosphere) exposes that the atom behaves as if it were immersed in a thermal radiation at the Hawking temperature from the Kerr black hole. Therefore, our results show that one in principle can reveal the Hawking effect in the Kerr black hole by analyzing the correction of the geometric phase as opposed to that in a flat spacetime.

Classical and Quantum Gravity•Jan 14, 2020•5 citations

Entanglement dynamics for uniformly accelerated two-level atoms

Jiawei Hu, Hongwei Yu

We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.

arXiv:1501.03321•Physical Review A•Jan 21, 2015•91 citations

Entanglement dynamics for uniformly accelerated two-level atoms coupled with electromagnetic vacuum fluctuations

Yiquan Yang, Jiawei Hu, Hongwei Yu

We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born--Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependent on the polarization directions of the atoms. For the two-atom system with certain acceleration and separation, the polarization directions of the atoms may determine whether entanglement generation, revival or enhancement happens, while for entanglement degradation, they affect the decay rate of entanglement. A comparison between the entanglement evolution of accelerated atoms and that of static ones immersed in a thermal bath at the Unruh temperature shows that they are the same only when the acceleration is extremely small.

arXiv:1609.06820•Physical Review A•Sep 30, 2016•36 citations

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

Hongwei Yu, Jiawei Hu

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.

arXiv:1212.2695•Physical Review A•Dec 12, 2012•10 citations
We study, in the framework of open quantum systems, the geometric phase acquired by a uniformly accelerated two-level atom undergoing nonunitary evolution due to its coupling to a bath of fluctuating vacuum electromagnetic fields in the multipolar scheme. We find that the phase variation due to the acceleration can be in principle observed via atomic interferometry between the accelerated atom and the inertial one, thus providing an evidence of the Unruh effect.
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 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.
Abstract We study the Hawking effect in terms of the geometric phase for a two-level atom coupled to vacuum fluctuations in the background of Kerr black hole in a gedanken experiment. Since the atom interacts with a bath of fluctuating massless scalar field, its geometric phase for the nonunitary evolution turns out to be affected by the spacetime curvature that backscatters the vacuum field modes. We examine the geometric phase for two kinds of vacua, i.e. the Unruh vacuum and the Candelas–Chrzanowski–Howard vacuum. We find that for both of these two cases, the geometric phase of the static atom locating outside the infinite redshift surface (or the stationary atom locating inside the ergosphere) exposes that the atom behaves as if it were immersed in a thermal radiation at the Hawking temperature from the Kerr black hole. Therefore, our results show that one in principle can reveal the Hawking effect in the Kerr black hole by analyzing the correction of the geometric phase as opposed to that in a flat spacetime.
We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born--Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependent on the polarization directions of the atoms. For the two-atom system with certain acceleration and separation, the polarization directions of the atoms may determine whether entanglement generation, revival or enhancement happens, while for entanglement degradation, they affect the decay rate of entanglement. A comparison between the entanglement evolution of accelerated atoms and that of static ones immersed in a thermal bath at the Unruh temperature shows that they are the same only when the acceleration is extremely small.
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.