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arXiv:1707.06952 · Europhysics Letters (EPL)

Geometric phase corrections on a moving particle in front of a dielectric mirror

Fernando C. Lombardo, Paula I. Villar

Published Jun 1, 2017• 6 citations
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Abstract

We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the moving qubit under the presence of the quantum vacuum field and the dielectric mirror. We find a velocity dependence in the correction to the unitary geometric phase due to quantum frictional effects. We also show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures as Ramsey-like interferometry.

DOI
10.1209/0295-5075/118/50003

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We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the moving qubit under the presence of the quantum vacuum field and the dielectric mirror. We find a velocity dependence in the correction to the unitary geometric phase due to quantum frictional effects. We also show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures as Ramsey-like interferometry.
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the moving qubit under the presence of the quantum vacuum field and the dielectric mirror. We find a velocity dependence in the correction to the unitary geometric phase due to quantum frictional effects. We also show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures as Ramsey-like interferometry.
We compute the non-unitary geometric phase for the moving atom under the presence of the vacuum field and a dielectric mirror, analytically and numerically. We consider the atom (represented by a two-level system) moving in front of a dielectric plate, and study how decoherence of the particle's internal degrees of freedom can be found in the corrections to the geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and by integrating over the vacuum field and the microscopic degrees of freedom of the plate we may calculate friction effects. We find a velocity dependance in the correction to the unitary geometric phase due to quantum frictional effects. We also show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard interferometry procedures.
In this work, we consider a particle moving in front of a dielectric plate and study two of the most relevant effects of the vacuum field fluctuations: the dissipation and the decoherence of the particle's internal degrees of freedom. We consider the particle to follow a classical, macroscopically fixed trajectory. To study the dissipative effects, we calculate the in-out effective action by functionally integrating over the vacuum field and the microscopic degrees of freedom of both the plate and the particle. This in-out effective action develops an imaginary part and, hence, a nonvanishing probability for the decay (because of friction) of the initial vacuum state. We analyze how the dissipation is affected by the relative velocity between the particle and the plate and the properties of the microscopic degrees of freedom. In order to study the effects of decoherence over the internal degrees of freedom of the particle, we calculate the closed time path or Schwinger-Keldysh influence action, by functionally integrating over the vacuum field and the microscopic degrees of freedom of the plate. We estimate the decoherence time as the time needed by two different quantum configurations (of the internal degree of freedom of the particle) to be possible to differentiate from one another. We analyze the way in which the presence of the mirror affects the decoherence and the possible ways to maximize or reduce its effects.
In this paper we study the dissipative effects and decoherence induced on a particle moving at constant speed in front of a dielectric plate in quantum vacuum, developing a closed-time-path (CTP) integral formulation in order to account for the corrections to these phenomena generated by finite temperatures. We compute the frictional force of the moving particle and find that it contains two different contributions: a pure quantum term due to quantum fluctuations (even present at vanishing temperatures) and a temperature-dependent component generated by thermal fluctuations (the bigger the contribution, the higher the temperature). We further estimate the decoherence timescale for the internal degree of freedom of the quantum particle. As expected, decoherence time is reduced by temperature; however, this feature is stronger for large velocities and for resonant situations. When the particle approaches relativistic speed, decoherence time becomes independent of temperature. The finite temperature corrections to the force or even in the decoherence timescale could be used to track traces of quantum friction through the study of the velocity dependence since the sole evidence of this dependence provides an indirect testimony of the existence of a quantum frictional force.
The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take advantage of the geometric phase to sense the corrections induced while a neutral particle travels at constant velocity in front of an imperfect sheet in quantum vacuum. As it is already known, two bodies in relative motion at constant velocity experience a quantum contactless dissipative force, known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. However, we give details of an innovative experiment designed to track traces of the quantum friction by measuring the velocity dependence of corrections to the geometric phase. We notice that the environmentally induced corrections can be decomposed in different contributions: corrections induced by the presence of the dielectric sheet and the motion of the particle in quantum vacuum. As the geometric phase accumulates over time, its correction becomes relevant at a relative short timescale, while the system still preserves purity. The experimentally viable scheme presented would be the first one in tracking traces of quantum friction through the study of decoherence effects on a NV center in diamond.
Abstract The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take advantage of the geometric phase to sense the corrections induced while a neutral particle travels at constant velocity in front of an imperfect sheet in quantum vacuum. As it is already known, two bodies in relative motion at constant velocity experience a quantum contactless dissipative force, known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. However, we give details of an innovative experiment designed to track traces of the quantum friction by measuring the velocity dependence of corrections to the geometric phase. We notice that the environmentally induced corrections can be decomposed in different contributions: corrections induced by the presence of the dielectric sheet and the motion of the particle in quantum vacuum. As the geometric phase accumulates over time, its correction becomes relevant at a relative short timescale, while the system still preserves purity. The experimentally viable scheme presented would be the first one in tracking traces of quantum friction through the study of decoherence effects on a NV center in diamond.