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arXiv:cond-mat/9810338

Josephson effect between Bose condensates

Fernando Sols

Published Oct 26, 1998• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/9810338

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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.
The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.
These lectures address Bose and Fermi ultracold dilute alkali gases. For Bose gases I discuss general BEC concepts, superfluidity, the Josephson effect, and issues related to the establishment of a "phase standard". For Fermi gases I discuss prospects for Cooper pairing and its detection. The four lectures on alkali Bose gases which I actually gave at the School were based on a review paper in preparation for Reviews of Modern Physics. In order to avoid extensive duplication of the contents of that review, what I present here, condensed into three lectures, is a melange of informal commentary on the results presented there and some material which for space and other reasons had to be omitted. This material is ideally read in conjunction with the review. The fourth lecture, on the Fermi alkali gases, is presented here in (nearly) the form in which it was actually given.
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.
The realization of Bose-Einstein Condensation (BEC) in dilute gases of ultracold atoms has revolutionized quantum physics by offering an unprecedented platform to study quantum phenomena on macroscopic scales. Ultracold atomic systems, cooled to temperatures near absolute zero, exhibit collective behaviors governed by quantum statistics, coherence, and interactions. This article discusses the theoretical and experimental frameworks underpinning the formation of BECs, focusing on the trapping, cooling, and coherence properties of ultracold bosonic gases. Further, we delve into the role of quantum phase transitions, atom-atom interactions, and external field manipulation in controlling condensate dynamics. The implications of BECs extend into precision measurements, quantum simulation, and quantum computing, positioning them as a cornerstone in modern atomic and condensed matter physics.
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.
In this paper, we have used a technique , when a weak link is created between two systems which have undergone some type of gauge symmetry breaking. In fact the Josephson effect has been observed in superfluid .Bose condensate atomic gases is generally expected. A system whose gauge symmetry has been spontaneously broken can be described by order parameter that behaves in much respect like a macroscopic function)(rΨ. For Bose Einstein Condensates of dilute alkali gases )(rΨis the wave function of the macroscopically occupied one atomic state