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arXiv:1109.0041

Localization and entanglement through scattering measurements

James S. Douglas, Keith R. Burnett

Published Aug 31, 2011• 1 citation
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Abstract

We study the emergence of localization and entanglement in many-body systems as a result of scattering measurements. We show that consecutive scattering measurements on a many-body system can produce superposition states in position space. The resulting states are signaled in the scattering distribution and these states are robust under continued scattering. We also show that the average scattering distribution for an ensemble of experiments gives the initial state scattering distribution even when the initial state is completely destroyed by the scattering process.

DOI
10.48550/arxiv.1109.0041

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We study the emergence of localization and entanglement in many-body systems as a result of scattering measurements. We show that consecutive scattering measurements on a many-body system can produce superposition states in position space. The resulting states are signaled in the scattering distribution and these states are robust under continued scattering. We also show that the average scattering distribution for an ensemble of experiments gives the initial state scattering distribution even when the initial state is completely destroyed by the scattering process.
We describe how quasiclassical relative positions of particles emerge in an initially delocalized quantum system as scattering of a probe beam is observed. We show that in the multiparticle case this localization in position space occurs via intermediate states that are quantum superpositions of spatial configurations. These superpositions are robust to consecutive scattering events, and scattering alone does not lead to their decoherence. Instead the free evolution of the system combines with scattering to destroy these superpositions, leading the particles to adopt classical-like positions relative to one another.
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Scattering probe particles from a quantum system can provide experimental access to information about the system's state. However, measurement backaction and momentum transfer during scattering changes the state of the system, potentially destroying the state of the system we wish to probe. Here we investigate how to probe the system's initial state even in the presence of backaction and momentum transfer. We show that summing the scattering distributions of an ensemble of measurements reveals the initial state scattering pattern even when each of the individual measurements completely destroys the initial state. This procedure is effective provided the scattering takes place on a timescale that is short compared with the free evolution of the system.
We consider a many-body system consisting of a harmonic oscillator linearly coupled to NNN others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the NNN others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the NNN others and these are found entangled.