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Zeitschrift für Naturforschung A

Bose -Einstein Condensation and Condensate Tunneling

Siegfried Großmann, Martin Holthaus

Published May 1, 1995• 50 citations
Publisher

Abstract

Abstract We consider Bose-Einstein condensation in a small cube and describe effects induced by the con­ finement. We also sketch an analogue of the Josephson effect for neutral particles, which can be realized when two almost degenerate states in a double well potential are occupied by a macroscopic number of Bosons. PACS number: 05.30.Jp

DOI
10.1515/zna-1995-4-501

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Abstract We consider Bose-Einstein condensation in a small cube and describe effects induced by the con­ finement. We also sketch an analogue of the Josephson effect for neutral particles, which can be realized when two almost degenerate states in a double well potential are occupied by a macroscopic number of Bosons. PACS number: 05.30.Jp
One of the most striking manifestations of the quantum collective behavior of matter is the Josephson effect: it allows for a classically forbidden current to flow without dissipation [125]. Traditional Josephson junctions are built by means of superconductors separated by thin non-conducting oxide barriers and they have drawn an intense interest for their striking phenomenology. A bosonic analog is the so-called Bosonic Josephson junction (BJJ) where two macroscopic populations of bosons are trapped in a double well geometry. Bose-Einstein condensation of dilute atomic gases has allowed for the demonstration of BJJs by trapping two condensates in double wells [126],[127].
We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double-well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn=n1−n2 measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.
I present an overview of the physics of the Josephson effect between Bose condensed systems, with emphasis on the recently achieved BEC's in trapped alkali gases. I focus mostly on those physical phenomena that are likely to be observed only (or more easily) in these novel systems. Thus I omit the discussion of problems which may be viewed as straightforward applications of well known Josephson physics. In particular, I review the external and the internal Josephson effects, and discuss how in the latter case it may be possible to explore the crossover between collective Josephson behavior and independent boson Rabi dynamics. I also describe novel macroscopic quantum phenomena such as self-trapping and interference between separate Bose condensates.
Bose-Einstein condensation is a phenomenon whereby atoms collectively enter a single macroscopic quantum state. The first such condensate was created in 1995, and since then a large amount of effort has been devoted to studying this unusual state of matter. In his Perspective, Burnett reviews the recent work and discusses results reported in the same issue by page Anderson and Kasevich. The work carried out at Yale University shows that Bose condensates can exhibit behavior similar to that seen in superconductors, known as the Josephson effect.
We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double- well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn = n₁ - n₂ measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.
New coherent states may be induced by pertinently engineering the topology of a network. As an example, we consider the properties of non-interacting bosons on a star network, which may be realized with a dilute atomic gas in a star-shaped deep optical lattice. The ground state is localized around the star centre and it is macroscopically occupied below the Bose–Einstein condensation temperature T c . We show that T c depends only on the number of the star arms and on the Josephson energy of the bosonic Josephson junctions and that the non-condensate fraction is simply given by the reduced temperature T / T c .