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Journal of Physics A Mathematical and Theoretical

Environmental effects on the phase space dynamics and decoherence time scale of a charged particle in a Penning trap

Michael Genkin, Eva Lindroth

Published Sep 1, 2009• 8 citations
Publisher

Abstract

We study the time evolution of a charged particle in a Penning trap in the framework of open quantum systems. The interaction with the environment is taken into account by imposing Lindblad operators which are linear in the canonical variables. For the special case of a proton in an asymmetric Penning trap, we compare the dynamics with earlier results obtained from the unitary time-dependent Schrödinger equation. A possibility of estimating the spatial decoherence time of the system is discussed, and approximate decoherence time scales are given for different ions.

DOI
10.1088/1751-8113/42/38/385302

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We study the time evolution of a charged particle in a Penning trap in the framework of open quantum systems. The interaction with the environment is taken into account by imposing Lindblad operators which are linear in the canonical variables. For the special case of a proton in an asymmetric Penning trap, we compare the dynamics with earlier results obtained from the unitary time-dependent Schrödinger equation. A possibility of estimating the spatial decoherence time of the system is discussed, and approximate decoherence time scales are given for different ions.
The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.
The time-dependent Schrödinger equation of an ion moving in an asymmetric Penning trap is solved. Properties of the evolution of squeezed and Schrödinger cat states in the trap are studied. Analytic expressions for the energy expectation values, dispersions and correlations of the position and momentum operators of different macroscopic states, solutions of the time-dependent Schrödinger equation of the trap, are obtained. The probability densities in coordinate and momentum representations are also given. As an example, the behaviour of Schrödinger cat states of a proton moving in the trap is described numerically.
The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.
Abstract Chapter 22 investigates the dynamics of open quantum systems that interact with their environment. We discuss the time-evolution of the joint system in terms of a time-ordered exponential of an integral over the Hamiltonian and determine a similar formulation for a Liouvillian super-operator. Based on these ideas we develop the notion of dynamical maps and apply the Born-Markov approximation to arrive at a dynamical semi-group and general Markovian master equations. We then turn to a specific example of such an equation of motion for the density operator: the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation which captures both dissipative dynamics and decoherence using Lindblad operators. We employ the GKLS equation to model the absorption, and spontaneous as well as stimulated emission of radiation by a two-level atom. We then discuss the Jaynes-Cummings model that describes the interaction of such an atom with a single mode of the electromagnetic field in a cavity
Neutrinos lose coherence as they propagate, which leads to the fading away of oscillations. In this work, we model neutrino decoherence induced in open quantum systems from their interaction with the environment. We first present two different models in the quantum mechanical framework, in which the environment is modeled as forced harmonic oscillators with white noise interactions, or two-level systems with stochastic phase kicks. We then look at the decoherence process in the quantum field theoretic framework induced by elastic scatterings with environmental particles. The exponential decay is obtained as a common feature for all models, which shows the universality of the decoherence processes. We discuss connections to the GKSL master equation approach and give a clear physical meaning of the Lindblad operators. We demonstrate that the universality of exponential decay of coherence is based on the Born-Markov approximation. The models in this work are suitable to be extended to describe real physical processes that could be non-Markovian.
We theoretically investigate the non-Markovian dynamical decoherence of a quantum system coupled to nonequilibrium environments with nonstationary statistical properties. We show the time evolution of the decoherence factor in real-imaginary space to study the environment-induced energy renormalization and backaction of coherence which are associated with the unitary and nonunitary parts of the quantum master equation, respectively. It is also shown that the nonequilibrium decoherence dynamics displays a transition between Markovian and non-Markovian and the transition boundary depends on the environmental parameters. The results are helpful for further understanding non-Markovian dynamics and coherence backaction on an open quantum system from environments.