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

Physical Review A

Measurement-induced quantum fluctuations and bistability of a relativistic electron in a Penning trap

M. Rigo, G. Alber, Francisca Mota-Furtado, Patrick F. O’Mahony

Published Jul 1, 1998• 5 citations
Publisher

Abstract

A detailed quantum-mechanical description of an electron in a Penning trap is developed in which nonlinear relativistic effects as well as stochastic effects arising from radiative damping and the continuous measurement of the electronic motion are taken into account. A master equation is derived that describes the influence of these environmental effects on the bistable dynamics of the electron. Manifestations of measurement-induced fluctuations on the bistable dynamics of individual continuous measurement processes are investigated with the help of the quantum state diffusion model.

DOI
10.1103/physreva.58.478

Related papers

Externally induced metastability of an electron in a Penning trap: Analytical results

S. Brouard, Jesús Plata

The effect of a driving field on the cyclotron mode of a relativistic electron in a Penning trap is studied analytically. The Hamiltonian dynamics of this driven nonlinear oscillator is analyzed by using linearization techniques and displaced squeezed-state formalism. With the approximate analytical expressions obtained for the eigenstates in this approach, a simplified treatment of the dissipative dynamics is carried out and some of the nontrivial features found in a recent numerical study [D. Enzer and G. Gabrielse, Phys. Rev. Lett. 78, 1211 (1997)] are unraveled. The emergence of different time scales and the generation of a metastable statistical mixture are understood in terms of the changes induced in the structure of the master equation by the nonuniform characteristics of the eigenstates; the partial revivals of specific coherent states are accounted for by the evolution of particular coherences. The control of these effects by a proper choice of the driving parameters is discussed.

Physical Review A•Nov 14, 2001•2 citations

Continuous Stern-Gerlach effect and the quantum-state diffusion model of state reduction

T. Steimle, G. Alber

A quantum-mechanical description of the continuous Stern-Gerlach effect is developed in which environmental effects, as well as effects arising from the continuous measurement of the electronic z motion, are taken into account. Master equations are presented that describe the behavior of a quantum statistical ensemble of continuous measurement processes. On the basis of these master equations and with the help of the quantum-state diffusion model a theoretical description of individual continuous measurement processes is developed. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Apr 1, 1996•8 citations

Bayesian analysis of nonlinear fluctuating-measurement systems

Masahiro Agu

Bayesian analysis of the physical-measurement process is formulated with respect to the physical quantity being subject to the master equation. Here nonlinear dynamics of the measurement system and its own fluctuations are taken into account with the use of a nonlinear Langevin equation. The coupled nonlinear equations of the most probable path and of the variance of the fluctuations around the path are derived with the results of the measurement taken into account. The theory is applied to the measurement in which the field is detected with the use of a cavity resonator or laser amplifier. The minimum uncertainty in the estimate of the most probable path of the field is determined as a function of the variance of the fluctuations of the measurement system itself.

Physical Review A•Oct 1, 1981•0 citations

Continuous position measurements and the quantum Zeno effect

M. J. Gagen, Howard M. Wiseman, Gerard J Milburn

We present a model of continuous (in time) position measurements on a quantum system using a single pseudoclassical meter. The nonselective evolution of the system is described by a master equation which is identical to that obtained from previous models. The selective evolution is described by a stochastic nonlinear Schr\"odinger equation. The significance of this equation is that the stochastic term has a physical interpretaion. By carefully choosing the parameters which define the meter and the system-meter coupling, we obtain a meter pointer with well-defined position which undergoes fluctuations. This ``jitter'' in the pointer position gives rise to the stochastic dynamical collapse of the system wave function. By the inclusion of feedback on the meter, the pointer is made to relax towards an appropriate readout. We apply this model to the selective measurement of the position of a particle in a double-well potential. In contrast to a recent claim [H. Fearn and W. E. Lamb, Jr., Phys. Rev. A 46, 1199 (1992)] we show that truly continuous position measurements lead to a quantum Zeno effect in certain parameter regimes. This is manifest by the changing of the particle dynamics from coherent tunneling between the well minima to incoherent flipping, as in a random telegraph. As the measurement strength increases, the average length of time the particle remains stuck in one well increases proportionally.

Physical Review A•Jul 1, 1993•86 citations

Relativistic Path-Integral Origin of the Dirac Equation, Quantum Collapse, Decoherence and Non-Hermitian Phenomena

Wen, Wei

Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamical explanation of quantum measurement remain unresolved. Historically, these two problems have been treated as separate, but here we show they are intimately linked. We construct a self-consistent relativistic path integral that yields the Dirac and other standard wave equations under differetialable potentials. More importantly, we find that this propagator contains a latent, nonlocal correlation that is activated by realistic electromagnetic noise. This correlation unifies unitary evolution and wave-function collapse into a single dynamical mechanism: while differentiable potentials preserve unitary driving, nondifferentiable noise activates a bounded-martingale stochastic process that induces collapse. We show that the characteristics of quantum measurement are naturally derived from this stochastic dynamical process, thereby turning the axioms of quantum measurement from postulates into dynamical consequences. Furthermore, averaging this stochastic evolution over the noise record recovers the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, providing a first-principles derivation of decoherence free from the method of Born-Markov approximation. Extending this approach to composite systems establishes a stochastic foundation for effective non-Hermitian descriptions while preserving relativistic causality. Finally, because the noise spectrum governs the collapse process, engineering ``colored'' noise can actively accelerate or steer state reduction, suggesting new routes toward fast qubit reset and enhanced quantum control.

arXiv:2509.19377•Sep 20, 2025•0 citations

Measurements on relativistic quantum fields: II. Detector models

Charis Anastopoulos, Ntina Savvidou

This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.

arXiv:1509.01838•Sep 6, 2015•2 citations
A detailed quantum-mechanical description of an electron in a Penning trap is developed in which nonlinear relativistic effects as well as stochastic effects arising from radiative damping and the continuous measurement of the electronic motion are taken into account. A master equation is derived that describes the influence of these environmental effects on the bistable dynamics of the electron. Manifestations of measurement-induced fluctuations on the bistable dynamics of individual continuous measurement processes are investigated with the help of the quantum state diffusion model.
The effect of a driving field on the cyclotron mode of a relativistic electron in a Penning trap is studied analytically. The Hamiltonian dynamics of this driven nonlinear oscillator is analyzed by using linearization techniques and displaced squeezed-state formalism. With the approximate analytical expressions obtained for the eigenstates in this approach, a simplified treatment of the dissipative dynamics is carried out and some of the nontrivial features found in a recent numerical study [D. Enzer and G. Gabrielse, Phys. Rev. Lett. 78, 1211 (1997)] are unraveled. The emergence of different time scales and the generation of a metastable statistical mixture are understood in terms of the changes induced in the structure of the master equation by the nonuniform characteristics of the eigenstates; the partial revivals of specific coherent states are accounted for by the evolution of particular coherences. The control of these effects by a proper choice of the driving parameters is discussed.
A quantum-mechanical description of the continuous Stern-Gerlach effect is developed in which environmental effects, as well as effects arising from the continuous measurement of the electronic z motion, are taken into account. Master equations are presented that describe the behavior of a quantum statistical ensemble of continuous measurement processes. On the basis of these master equations and with the help of the quantum-state diffusion model a theoretical description of individual continuous measurement processes is developed. \textcopyright{} 1996 The American Physical Society.
Bayesian analysis of the physical-measurement process is formulated with respect to the physical quantity being subject to the master equation. Here nonlinear dynamics of the measurement system and its own fluctuations are taken into account with the use of a nonlinear Langevin equation. The coupled nonlinear equations of the most probable path and of the variance of the fluctuations around the path are derived with the results of the measurement taken into account. The theory is applied to the measurement in which the field is detected with the use of a cavity resonator or laser amplifier. The minimum uncertainty in the estimate of the most probable path of the field is determined as a function of the variance of the fluctuations of the measurement system itself.
We present a model of continuous (in time) position measurements on a quantum system using a single pseudoclassical meter. The nonselective evolution of the system is described by a master equation which is identical to that obtained from previous models. The selective evolution is described by a stochastic nonlinear Schr\"odinger equation. The significance of this equation is that the stochastic term has a physical interpretaion. By carefully choosing the parameters which define the meter and the system-meter coupling, we obtain a meter pointer with well-defined position which undergoes fluctuations. This ``jitter'' in the pointer position gives rise to the stochastic dynamical collapse of the system wave function. By the inclusion of feedback on the meter, the pointer is made to relax towards an appropriate readout. We apply this model to the selective measurement of the position of a particle in a double-well potential. In contrast to a recent claim [H. Fearn and W. E. Lamb, Jr., Phys. Rev. A 46, 1199 (1992)] we show that truly continuous position measurements lead to a quantum Zeno effect in certain parameter regimes. This is manifest by the changing of the particle dynamics from coherent tunneling between the well minima to incoherent flipping, as in a random telegraph. As the measurement strength increases, the average length of time the particle remains stuck in one well increases proportionally.
Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamical explanation of quantum measurement remain unresolved. Historically, these two problems have been treated as separate, but here we show they are intimately linked. We construct a self-consistent relativistic path integral that yields the Dirac and other standard wave equations under differetialable potentials. More importantly, we find that this propagator contains a latent, nonlocal correlation that is activated by realistic electromagnetic noise. This correlation unifies unitary evolution and wave-function collapse into a single dynamical mechanism: while differentiable potentials preserve unitary driving, nondifferentiable noise activates a bounded-martingale stochastic process that induces collapse. We show that the characteristics of quantum measurement are naturally derived from this stochastic dynamical process, thereby turning the axioms of quantum measurement from postulates into dynamical consequences. Furthermore, averaging this stochastic evolution over the noise record recovers the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, providing a first-principles derivation of decoherence free from the method of Born-Markov approximation. Extending this approach to composite systems establishes a stochastic foundation for effective non-Hermitian descriptions while preserving relativistic causality. Finally, because the noise spectrum governs the collapse process, engineering ``colored'' noise can actively accelerate or steer state reduction, suggesting new routes toward fast qubit reset and enhanced quantum control.
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.