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arXiv:cond-mat/0103491 · Europhysics Letters (EPL)

Multiple-path interferometer with a single quantum obstacle

Henning Schomerus, Yves Noat, Jean Dalibard, C. W. J. Beenakker

Published Mar 1, 2002• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/epl/i2002-00512-5

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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.
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.
Here we report on the predicted effects of quantum interference induced by combining an arbitrary number of quantum optical states in a random multiple scattering medium. We identify the role of quantum interference on the degree of photon correlations between two transmission paths through the medium and the degree of continuous variable entanglement. The investigation is performed using a scattering matrix formalism and based on random matrix theory. In this way the ensemble averaged 2-channel photon correlations Cοψ and the degree of entanglement εοψ between output modes a and β are related to the classical shortand long-range correlation functions, Cι and C2, and the average conductance g. The expressions are non-perturbative and valid in the entire mesoscopic regime.
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.
The effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero, whereas the energy of the incoming particle E in can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming E in through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy E in thus resulting in the seeming loss of particles, violation of the time-reversal symmetry and, as a consequence, suppression of the weak localization. Both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances that uniquely determines the decoherence rate.
Quantum particles move in strange ways, even when they propagate freely in space. As a result of the uncertainty principle, it is not possible to control the initial conditions of particle emission in such a way that the particle will definitely pass through two precisely defined positions along its path, even if it is possible to line up the two positions with the emitter. However, there is also an upside to the quantum mechanical laws of motion: constructive quantum interferences can actually raise probabilities to values higher than those permitted by classical causality. Here, it is shown that conventional interferometric methods can be used to prepare photons in a quantum state in which a non-vanishing fraction of particles will hit both of two possible targets, even though the direct line-of-sight connecting the two targets is blocked at the source. The demonstration of the effect is complicated by the uncertainty principle because the physical detection of a particle at one target disturbs the motion of the particle, making it impossible to determine whether the initial state of motion would have allowed the particle to hit the other target or not. It is nonetheless possible to determine the minimal fraction of "magic bullet" particles that must have hit both targets by showing that the number of particles hitting target A is larger than the number of particles missing target B. Quantum interference effects can thus be used to optimize the path of particles in free space beyond the classical limit of motion along a straight line.
We study the coherent transport of a single photon in a one-dimensional coupled-resonator array, nonlocally coupled to a two-level system. Since its inherent structure is a Mach-Zehnder interferometer, we explain the destructive interference phenomenon of the transmission spectra according to the effect of which-way detection. The quantum realization of the present model is a nanoelectromechanical resonator array with two nearest resonators coupled to a single spin via their attached magnetic tips. Its classical simulation is a waveguide of a coupled-defected cavity array with double couplings to a side-defected cavity.