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arXiv:2408.07473 · Annalen der Physik

Threshold in Quantum Correlated Interference for a Particle Interacting with Two Scatterers

Frank V. Kowalski

Published Jan 17, 2022• 2 citations
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Abstract

Abstract Correlated interference is calculated for a microscopic particle retro‐reflecting from two spatially separated scatterers that are free to move, all three of which are treated as quantum bodies: the positions of the particle traversing this 1D interferometer and those of the interferometer components are all uncertain. Interference in a measurement of only the particle is shown to disappear for microscopic yet appear for mesoscopic scatterers, contrary to that of a quantum‐classical transition. A measurement of this threshold can verify quantum correlations in many‐body systems by measuring only the retro‐reflected microscopic particle. The decoherence of a mesoscopic scatterer is determined by this threshold without it having to traverse slits or beamsplitters.

DOI
10.1002/andp.202100322

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Abstract Correlated interference is calculated for a microscopic particle retro‐reflecting from two spatially separated scatterers that are free to move, all three of which are treated as quantum bodies: the positions of the particle traversing this 1D interferometer and those of the interferometer components are all uncertain. Interference in a measurement of only the particle is shown to disappear for microscopic yet appear for mesoscopic scatterers, contrary to that of a quantum‐classical transition. A measurement of this threshold can verify quantum correlations in many‐body systems by measuring only the retro‐reflected microscopic particle. The decoherence of a mesoscopic scatterer is determined by this threshold without it having to traverse slits or beamsplitters.
Reflection of a microscopic particle from a mesoscopic/macroscopic `mirror' generates two-body correlated interference from the incident and reflected particle substates and their associated mirror substates. The microscopic momentum exchanged generates two mirror substates which interfere to produce fringes which do not vanish as the mirror mass increases. The small displacement between these mirror states can yield negligible environmental decoherence times. Mirror coherence lengths impose constraints on the extent of this interference, which are mitigated using interference of the two-body states associated with the particle reflecting from both of the two surfaces of a slab of matter in a manner analogous to the classical interference of a pulse of light reflecting from a `thin film'. This two-body correlated interference is modeled as a particle traversing a finite well with both the particle and well treated quantum mechanically. Such a treatment predicts the expected `thin-film' interference but only as a special case of a more general result. It is also shown that measurements on only the reflected particle (yielding a marginal probability density function) can act as a probe to reveal the quantum state of the macroscopic reflector. For equal masses, coherence of the particle substate is transferred to the mirror substate, a quantum manifestation of a familiar classical result.
A two-body quantum correlation is calculated for a particle and an infinite potential well in which it is trapped or either a barrier or finite well over which it traverses. Correlated interference results when the incident and reflected particle substates and their associated well or barrier substates overlap. Measurement of the particle in this region causes a splitting of the well or barrier substate at subsequent times. The joint probability density, which is a function both of the different positions and different times at which the particle and well or barrier are measured, is derived assuming that no interaction occurs between the time each is measured.
Abstract An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize superposition principles that differ when applied to systems composed of three or more bodies. Interferometric discrepancies between these models that involve frequency shifts and recoil are shown to be difficult to measure. More pronounced differences involve quantum correlated interference. The collective model provides a missing connection between quantum and semiclassical theories. Scattering from an entangled state, which cannot be divided into disjoint parts, is proposed to involve such collective recoil. Collective scattering offers a viable supplement to the standard model, thereby providing insight into constructing tests of the superposition principle in systems with three or more bodies.
Motivated by a recent experiment by Buks et al. ( Nature 391 (1998) 871) we consider electron transport through an Aharonov-Bohm interferometer with a quantum dot in one of its arms. The quantum dot is coupled to a quantum system with a finite number of states acting as a which-path detector. The Aharonov-Bohm interference is calculated using a two-particle scattering approach for the joint transitions in detector and quantum dot. Tracing over the detector yields dephasing and a reduction of the interference amplitude. We show that the interference can be restored by a suitable measurement on the detector and propose a mesoscopic quantum eraser based on this principle.
We consider the scattering of particles (kinetic energy ε) by an obstacle which tunnels coherently between two positions (tunnel splitting Δ), for arbitrary values of ε/Δ and scattering strength U . The obstacle mimics two classical scatterers at fixed positions when ε≲Δ. Interference disappears when ε >> Δ, but can be recovered if the elastic-scattering channel is detected only. At intermediate values of ε there is a systematic interplay of the coherent tunnel motion and the ballistic particle motion. We show that the transmission probability can remain finite even in the limit U → ∞ because the particle can evade the obstacle systematically. We discuss the realization of a quantum obstacle in mesoscopic systems.