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Journal of Physics Conference Series

Geometric phase in vacuum condensates, application to Unruh effect and to quantum thermometer

Antonio Capolupo

Published Jul 3, 2015• 0 citations
Publisher

Abstract

We report on the recent results revealing the presence of the geometric phase in all the systems characterized by particle creation from vacuum and vacuum condensates. This fact makes the geometric phase a useful tool in the study and the understanding of disparate phenomena. Its possible application ranges from the dynamical Casimir effect to the Hawking effect, from quantum field theory in curved space to the study of CP and CPT symmetries, from the graphen physics to superconductivity and to the Bose Einstein condensate. Here, we consider the possibility of the detection of the Unruh effect and of the fabrication of a very precise quantum thermometer. We analyze the Mukunda-Simon phase for a two level atom system and consider two case: 1) atoms accelerated in electromagnetic field, and 2) atoms interacting with thermal states. The Mukunda-Simon phase generalizes the Berry phase to the case of non-cyclic and non-adiabatic evolutions; therefore it represents a more useful instrument in experimental implementations with respect to the Berry phase.

DOI
10.1088/1742-6596/626/1/012060

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We report on the recent results revealing the presence of the geometric phase in all the systems characterized by particle creation from vacuum and vacuum condensates. This fact makes the geometric phase a useful tool in the study and the understanding of disparate phenomena. Its possible application ranges from the dynamical Casimir effect to the Hawking effect, from quantum field theory in curved space to the study of CP and CPT symmetries, from the graphen physics to superconductivity and to the Bose Einstein condensate. Here, we consider the possibility of the detection of the Unruh effect and of the fabrication of a very precise quantum thermometer. We analyze the Mukunda-Simon phase for a two level atom system and consider two case: 1) atoms accelerated in electromagnetic field, and 2) atoms interacting with thermal states. The Mukunda-Simon phase generalizes the Berry phase to the case of non-cyclic and non-adiabatic evolutions; therefore it represents a more useful instrument in experimental implementations with respect to the Berry phase.
In our previous work the possibility to use the Aharonov-Anandan invariant as a tool in the analysis of disparate systems has been shown, including Hawking and Unruh effects, as well as graphene physics and thermal states. We show that the vacuum condensation, characterizing such systems, is also related with geometric phases and we analyze the properties of the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution. In particular, we consider two-level atoms accelerated by an external potential and interacting with a thermal state. We propose the realization of Mach-Zehnder interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature.
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like Bs0−Bˉs0B_{s}^{0}-\bar{B}_{s}^{0}Bs0​−Bˉs0​ and the K0−Kˉ0K^{0}-\bar{K}^{0}K0−Kˉ0 are linked to the parameter zzz describing the CPTCPTCPT violation. A non zero phase difference between particle and antiparticle arises only in the presence of CPTCPTCPT symmetry breaking. Then the geometric phase can represent a completely new test for the CPTCPTCPT invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature. We are glad to dedicate this paper to Professor Gaetano Vilasi in the occasion of his 70th birthday.
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including atomic and molecular physics, condensed matter physics, optics, and classical dynamics. In this article, the basic theory of the geometric phase is presented along with a number of representative applications. The article begins with an account of the geometric phase for cyclic adiabatic evolutions. An elementary derivation is given along with a worked example for two-state systems. The implications of time-reversal are explained, as is the fundamental connection between the geometric phase and energy level degeneracies. We also discuss methods of experimental observation. A brief account is given of geometric magnetism; this is a Lorenz-like force of geometric origin which appears in the dynamics of slow systems coupled to fast ones. A number of theoretical developments of the geometric phase are presented. These include an informal discussion of fibre bundles, and generalizations of the geometric phase to degenerate eigenstates (the nonabelian case) and to nonadiabatic evolution. There follows an account of applications. Manifestations in classical physics include the Hannay angle and kinematic geometric phases. Applications in optics concern polarization dynamics, including the theory and observation of Pancharatnam's phase. Applications in molecular physics include the molecular Aharonov-Bohm effect and nuclear magnetic resonance studies. In condensed matter physics, we discuss the role of the geometric phase in the theory of the quantum Hall effect.
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.