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arXiv:0806.3395 · Physical Review Letters

Creation and Detection of a Mesoscopic Gas in a Nonlocal Quantum Superposition

Christoph Weiß, Yvan Castin

Published Jan 7, 2009• 107 citations
arXivHTMLPDF

Abstract

We investigate the scattering of a quantum matter wave soliton on a barrier in a one-dimensional geometry, and we show that it can lead to mesoscopic quantum superposition states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition, and we discuss in detail the experimental feasibility.

DOI
10.1103/physrevlett.102.010403

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We investigate the scattering of a quantum matter wave soliton on a barrier in a one-dimensional geometry, and we show that it can lead to mesoscopic quantum superposition states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition, and we discuss in detail the experimental feasibility.
The scattering of bright quantum solitons at barrier potentials in one-dimensional geometries is investigated. Such protocols have been predicted to lead to the creation of nonlocal quantum superpositions. The centre-of-mass motion of these bright matter-wave solitons generated from attractive Bose-Einstein condensates can be analysed with the effective potential approach. An application to the case of two particles being scattered at a delta potential allows analytical calculations not possible for higher particle numbers as well as a comparison with numerical results. Both for the dimer and a soliton with particle numbers on the order of N = 100, we investigate the signatures of the coherent superposition states in an interferometric setup and argue that experimentally an interference pattern would be particularly well observable in the centre-of-mass density. Quantum superposition states of ultra-cold atoms are interesting as input states for matter-wave interferometry as they could improve signal-to-noise ratios.
In this thesis, we study the dynamics of ultracold quantum gases with respect to micro-gravity experiments, discuss interferometric applications and aspects on collective scattering. We describe the dynamics of an ultracold quantum gas in a long-distance free-fall experiment, which is of relevance for the present QUANTUS experiment. We develop the quantum field theoretical description of a trapped, interacting degenerate quantum gas in a drop experiment in an inertial frame, the corotating frame of the Earth and the comoving frame of the drop capsule. This formalism provides us with an efficient description of the experiment, especially for numerical studies. Moreover, we review the ideas of gravitational sensing with the help of an interferometric setup. We show that in case of a spatially quasi-homogeneous condensate the same results as in single-atom interferometry can be obtained even in the presence of a nonlinear time evolution. A decline of the contrast in an interferogram is found, though. In addition, we propose a rotational sensor based on a superposition of a non-rotating state and a quantized vortex in a Bose-Einstein condensate. As an application for an interferometric experiment in a micro-gravity environment, we establish a number filter for matter waves. Our number filter allows for a number stabilization, i.e. after passing the filter, the number uncertainty is less than before. This can be achieved by using a nonlinear matter wave interferometer for a two-component BEC. An asymmetric splitting is required in order to observe the effect. Finally, we examine the collective scattering of a superfluid droplet impinging on a two-component Bose-Einstein condensate. We demonstrate that this mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles. We obtain resonant scattering phase shifts from a linear response theory. We find an energy-dependent transmission coefficient that is controllable between 0 and 100%.
Scattering in one dimension of an attractive ultracold bosonic cloud from a barrier can lead to the formation of two nonoverlapping clouds. Once formed, the clouds travel with constant velocity, in general different in magnitude from that of the incoming cloud, and do not disperse. The phenomenon and its mechanism---transformation of kinetic energy to internal energy of the scattered cloud---are obtained by solving the time-dependent many-boson Schr\"odinger equation. The analysis of the wave function shows that the object formed corresponds to a quantum superposition state of two distinct wave packets traveling through real space.
In matter wave interferometry, detectors detect individual particles; the wave picture (interference pattern) emerges only as a statistical aggregation, after a large number of particles have been detected. Feynman, mystified by such facts, declared that 'nobody understands quantum mechanics'. A few decades later, Ketterle summed up the situation as 'one gets used to preparing waves and detecting particles'. But why are matter waves detected only as particles? Is there a law of nature forbidding their detection as waves? This question does not seem to have been addressed. The present communication suggests that it may be possible to detect matter waves as waves if there exists a nonlocal interaction - due to wave-particle duality - that causes a nonlocal transfer of energy and momentum from microscopic objects to mesoscopic or macroscopic ones. It describes the principle of a possible wave detector and the scheme of an experiment. The experiment may be feasible in the foreseeable future with a mesoscopic detector made of carbon nanostructures, or in an earth satellite in an elliptical orbit. The detection of a single atom or molecule as a wave will have enormous consequences, both practical and conceptual.
Scattering quantum bright solitons off barriers has been predicted to lead to nonlocal quantum superpositions, in particular the NOON state. The focus of this paper lies on signatures of both high- and low-fidelity quantum superposition states. We numerically demonstrate that a one-dimensional geometry with the barrier potential situated in the middle of an additional---experimentally typical---harmonic confinement gives rise to particularly well-observable signatures. In the elastic-scattering regime we investigate signatures of NOON states on the NNN-particle level within an effective potential approach. We show that removing the barrier potential and subsequently recombining both parts of the quantum superposition leads to a high-contrast interference pattern in the center-of-mass coordinate for narrow and broad potential barriers. We demonstrate that the presented signatures can be used to clearly distinguish quantum superposition states from statistical mixtures and are sufficiently robust against experimentally relevant excitations of the center-of-mass wave function to higher-lying oscillator states. For two-particle solitons we extend these considerations to low-fidelity superposition states: even for strong deviations from the two-particle NOON state we find interference patterns with high contrast.