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Pointer basis induced by collisional decoherence

Busse, M., Hornberger, K.

Published Jan 1, 2010• 17 citations
OpenAlex

Abstract

We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wavefunctions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.

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Pointer basis induced by collisional decoherence

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We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wavefunctions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.
We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wavefunctions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.
We show that the pointer basis distinguished by collisional decoherence consists of exponentially localized, solitonic wave packets. Based on the orthogonal unraveling of the quantum master equation, we characterize their formation and dynamics, and we demonstrate that the statistical weights arising from an initial superposition state are given by the required projection. Since the spatial width of the pointer states can be obtained by accounting for the gas environment in a microscopically realistic fashion, one may thus calculate the coherence length of a strongly interacting gas.
We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their equations of motion in phase space turn into those of classical diffusion, yielding a clear picture of the quantum-classical transition induced by environmental decoherence.
In the present work, I identify the pointer states of quantum Brownian motion as rotated Gaussian states in phase space. By means of a particular piecewise deterministic unraveling, the pointer state unraveling, I determine the trajectories of the position and momentum expectation of the pointer states. They turn out to be described by a diffusion process in phase space and, in the semiclassical limit, they turn into the Langevin equation of classical Brownian motion. For collisional decoherence, the non-dissipative limit of the quantum linear Boltzmann equation, which describes the dynamics of a marker particle in an ideal gaseous environment, I examine the width of the pointer states and thereby extend previous results to more than one dimension. Crucially, it follows that pointer states do not exist for all parameter values in that case. By expanding the Lindblad operators of the quantum linear Boltzmann equation, I derive a new Lindblad master equation, dissipative collisional decoherence, which shows a decoherence behavior similar to that of collisional decoherence and also incorporates frictional as well as diffusion effects. Moreover this equation exhibits soliton-like solutions as candidates for the pointer states.
Classical properties of an open quantum system emerge through its interaction with other degrees of freedom (decoherence). We treat the case where this interaction produces a Markovian master equation for the system. We derive the corresponding distinguished local basis (pointer basis) by three methods. The first demands that the pointer states mimic as closely as possible the local nonunitary evolution. The second demands that the local entropy production be minimal. The third imposes robustness on the inherent quantum and emerging classical uncertainties. All three methods lead to localized Gaussian pointer states, their formation and diffusion being governed by well-defined quantum Langevin equations.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.