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理论物理通讯：英文版

Continuous Quantum Nondemolition Measurements of a Particle in Electromagnetic and Gravitational Fields

Zhu, Chunhua, Zha, Chao-Zheng

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.

Related papers

Continuous Quantum Nondemolition Measurements of a Particle in Electromagnetic and Gravitational Fields

Chunhua Zhu, Chao-Zheng Zha

The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.

Communications in Theoretical Physics•Sep 1, 2005•0 citations

QUANTUM NONDEMOLITION MEASUREMENTS OF A PARTICLE IN ELECTRIC AND GRAVITATIONAL FIELDS

Abel Camacho, A. Camacho-Galván

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.

arXiv:gr-qc/0104082•International Journal of Modern Physics D•Dec 1, 2001•1 citation

Quantum nondemolition measurements in a Paul trap

A. Camacho

In this work a family of quantum nondemolition variables for the case of a particle caught in a Paul trap is obtained. Afterwards, in the context of the so called restricted path integral formalism, a continuous measuring process for this family of parameters is considered, and then the corresponding propagators are calculated. In other words, the time evolution of a particle in a Paul trap, when the corresponding quantum nondemolition parameter is being continuously monitored, is deduced. The probabilities associated with the possible measurement outputs are also obtained, and in this way new theoretical results emerge, which could allow us to confront the predictions of this restricted path integral formalism with the readouts of some future experiments. 1

•Jan 1, 2000•4 citations

Quantum Nondemolition Measurements and Non-Newtonian Gravity

Abel Camacho

In the present work the detection, by means of a nondemolition measurement, of a Yukawa term, coexisting simultaneously with gravity, has been considered. In other words, a nondemolition variable for the case of a particle immersed in a gravitational field containing a Yukawa term is obtained. Afterwards the continuous monitoring of this nondemolition parameter is analyzed, the corresponding propagator is evaluated, and the probabilities associated with the possible measurement outputs are found. The relevance of these kind proposals in connection with some unified theories of elementary particles has also been underlined.

arXiv:gr-qc/0101104•Kluwer Academic Publishers eBooks•Dec 19, 2005•0 citations

QUANTUM MEASUREMENTS AND PAUL TRAPS IN GRAVITATIONAL BACKGROUNDS

A. CAMACHO

In the present work we solve the motion equations of a particle in a Paul trap embedded in the gravitational field of a spherically symmetric mass. One of the ideas behind this work concerns the analysis of the effects that the gravity-induced quantum noise, stemming from the bodies in the neighborhood of the Paul trap, could have upon the enhancement of the quantum behavior of this system. This will be done considering a series expansion for the gravitational field of the source, and including in the Hamiltonian of the Paul trap only the first two terms. Higher-order contributions will be introduced as part of the environment of the system, and in consequence will not appear in the Hamiltonian. In other words, we put forward an argument that allows us to differentiate those gravitational degrees of freedom that will appear as an uncontrollable influence on the Paul trap. Along the ideas of the so-called restricted path integral formalism, we take into account the continuous monitoring of the position of our particle, and in consequence the corresponding propagators and probabilities, associated with the different measurements outputs, are obtained. Afterwards, the differential equation related to a quantum nondemolition variable is posed and solved, i.e., a family of quantum nondemolition parameters is obtained. Finally, a qualitative analysis of the effects on the system, of the gravity-induced environment, will be done.

arXiv:quant-ph/0110071•International Journal of Modern Physics D•Jan 1, 2002•0 citations

Continuous Quantum Nondemolition Measurements

Michael B. Mensky

This chapter discusses the type of measurement in the framework of the path-integral method. It begins from the simplest case of measurement of the linear momentum of a free particle, which allows one to see all the typical features characteristic of quantum nondemolition (QND) measurements. The idea of QND measurement is to measure a variable such that the unavoidable disturbance of the complementary one does not disturb the evolution of the chosen variable. The weight factor describes monitoring of the momentum, which for a free particle turns out to be a QND variable. This can be seen from the formula for the probability distribution of the measurement results. Usual relation between linear momentum and velocity is violated in the modified dynamics. From the physical point of view this is a consequence of measurement, of the influence of a measuring device.

CRC Press eBooks•Oct 19, 2017•0 citations
The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.
In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.
In this work a family of quantum nondemolition variables for the case of a particle caught in a Paul trap is obtained. Afterwards, in the context of the so called restricted path integral formalism, a continuous measuring process for this family of parameters is considered, and then the corresponding propagators are calculated. In other words, the time evolution of a particle in a Paul trap, when the corresponding quantum nondemolition parameter is being continuously monitored, is deduced. The probabilities associated with the possible measurement outputs are also obtained, and in this way new theoretical results emerge, which could allow us to confront the predictions of this restricted path integral formalism with the readouts of some future experiments. 1
In the present work the detection, by means of a nondemolition measurement, of a Yukawa term, coexisting simultaneously with gravity, has been considered. In other words, a nondemolition variable for the case of a particle immersed in a gravitational field containing a Yukawa term is obtained. Afterwards the continuous monitoring of this nondemolition parameter is analyzed, the corresponding propagator is evaluated, and the probabilities associated with the possible measurement outputs are found. The relevance of these kind proposals in connection with some unified theories of elementary particles has also been underlined.
In the present work we solve the motion equations of a particle in a Paul trap embedded in the gravitational field of a spherically symmetric mass. One of the ideas behind this work concerns the analysis of the effects that the gravity-induced quantum noise, stemming from the bodies in the neighborhood of the Paul trap, could have upon the enhancement of the quantum behavior of this system. This will be done considering a series expansion for the gravitational field of the source, and including in the Hamiltonian of the Paul trap only the first two terms. Higher-order contributions will be introduced as part of the environment of the system, and in consequence will not appear in the Hamiltonian. In other words, we put forward an argument that allows us to differentiate those gravitational degrees of freedom that will appear as an uncontrollable influence on the Paul trap. Along the ideas of the so-called restricted path integral formalism, we take into account the continuous monitoring of the position of our particle, and in consequence the corresponding propagators and probabilities, associated with the different measurements outputs, are obtained. Afterwards, the differential equation related to a quantum nondemolition variable is posed and solved, i.e., a family of quantum nondemolition parameters is obtained. Finally, a qualitative analysis of the effects on the system, of the gravity-induced environment, will be done.
This chapter discusses the type of measurement in the framework of the path-integral method. It begins from the simplest case of measurement of the linear momentum of a free particle, which allows one to see all the typical features characteristic of quantum nondemolition (QND) measurements. The idea of QND measurement is to measure a variable such that the unavoidable disturbance of the complementary one does not disturb the evolution of the chosen variable. The weight factor describes monitoring of the momentum, which for a free particle turns out to be a QND variable. This can be seen from the formula for the probability distribution of the measurement results. Usual relation between linear momentum and velocity is violated in the modified dynamics. From the physical point of view this is a consequence of measurement, of the influence of a measuring device.