A. Matzkin

Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment

From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the ‘quantum Cheshire Cat’: if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat’s nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.

Weak values obtained in matter-wave interferometry

Stephan Sponar1,∗ Tobias Denkmayr1,† Hermann Geppert, Hartmut Lemmel, Alexandre Matzkin, and Yuji Hasegawa1‡ Atominstitut, Vienna University of Technology Stadionallee 2, 1020 Vienna, Austria Institut Laue-Langevin, 6, Rue Jules Horowitz, 38042 Grenoble Cedex 9, France 3 Laboratoire de Physique Théorique et Modélisation, CNRS Unité 8089, Université de Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France (Dated: April 9, 2014)

Null weak values and the past of a quantum particle

Nondestructive weak measurements (WMs) made on a quantum particle are useful in order to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WMs. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a nonoptical example for which apparent discontinuous trajectories are obtained by WMs. Our approach is compared to previous results.

Dynamical entanglement and chaos: The case of Rydberg molecules

A Rydberg molecule is composed of an outer electron that collides on the residual ionic core. Typical states of Rydberg molecules display entanglement between the outer electron and the core. In this work, we quantify the average entanglement of molecular eigenstates and further investigate the time evolution of entanglement production from initially unentangled states. The results are contrasted with the underlying classical dynamics, obtained from the semiclassical limit of the core-electron collision. Our findings indicate that entanglement is not simply correlated with the degree of classical chaos, but rather depends on the specific phase-space features that give rise to inelastic scattering. Hence mixed phase-space or even regular classical dynamics can be associated with high entanglement generation.

Is Bell’s Theorem Relevant to Quantum Mechanics? On Locality and Non‐Commuting Observables

Bell’s theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum‐mechanics, and conclude that Bell’s theorem is not expected to be relevant to quantum phenomena described by non‐commuting observables, irrespective of the issue of locality. Then, we try to disentangle the locality issue from the existence of joint distributions by introducing two models accounting for the EPR correlations but denying the existence of joint distributions. We will see that these models do not need to resort explicitly to non‐locality: the first model relies on conservation laws for ensembles, and the second model on an equivalence class by which ...

Classical and Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch in reality?

The de Broglie–Bohm (BB) interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned with the BB account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have regular or disordered characteristics depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences for the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the BB motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems. r 2007 Elsevier Ltd. All rights reserved.The de Broglie-Bohm interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned by the de Broglie-Bohm account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display the manifestation of classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have a regular or disordered aspect depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences on the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the de Broglie-Bohm motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems.

Non-Hermitian quantum mechanics: the case of bound state scattering theory

Excited bound states are often understood within scattering-based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a numerical example involving scattering by a short-range potential in a Coulomb field for which it is seen that even for a small but non-negligible non-Hermiticity index the non-Hermitian character of the problem must be taken into account. The computation of physical quantities in the relevant Hilbert spaces is also discussed.

Scattering-induced dynamical entanglement and the quantum-classical correspondence

The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence, regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition, quantum effects also come into play: for example, partial revivals, which are expected to persist in the semiclassical limit, affect the long-time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.

Can Bohmian trajectories account for quantum recurrences having classical periodicities

Abstract Quantum systems in specific regimes display recurrences at times matching the period of the closed trajectories of the corresponding classical system. This is the case of the excited hydrogen atom in a magnetic field, that we investigate from the point of view of the de Broglie–Bohm (BB) interpretation of quantum mechanics. Individual BB trajectories do not possess the classical periodicities and cannot account for the quantum recurrences, that can only be explained by considering the statistical ensemble of trajectories.

Effects of a transient barrier on wavepacket traversal

An analytical treatment of a propagating wavepacket incident on a transient barrier reveals an effect in which, for a particular time interval, the time-varying transmission probability exceeds that for the free propagation of the wavepacket. We show that this effect can be interpreted semiclassically. This effect is quantified and it is shown that its magnitude is in one-to-one correspondence with the strength of the barrier, a feature that has the potential to be used in a scheme for key generation. It is found that the speed with which the information about the barrier perturbation propagates across the wavepacket can exceed the group velocity of the wavepacket. An application to the speed-up of entanglement generation is also considered.