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THE SCIENTIFIC TEMPER

Study of Josephson Effect Between Bose Condensate

Raju Prasad Singh, R.K. Verma

Published Jul 25, 2019• 0 citations
Publisher

Abstract

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

DOI
10.58414/scientifictemper.2020.11.1.18

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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
For two-component Fermi gases at zero temperature, through a general derivation based on the BCS wave function, our research shows that the nonuniform molecular Bose-Einstein condensate has off-diagonal long-range order and can be described well by an order parameter when the size of molecules is much smaller than the size of the whole system. We also give the equation of state and nonlinear evolution equation for the order parameter of nonuniform molecular condensates, which is similar to the Gross-Pitaevskii equation of atomic Bose condensate. The nonlinear evolution equation is applied to consider the Josephson effect for two weakly linked molecular condensates in the presence of nonuniform magnetic field. We find clear particle-number oscillation where spatially dependent binding energy of molecules plays an important role.
The fundamental problem is analyzed, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement that, though gauge symmetry breaking helps for describing Bose-Einstein condensation, but the latter, in principle, does not require any symmetry breaking. This, however, is not correct. The analysis is based on the known mathematical theorems. But in order not to overcomplicate the presentation and to make it accessible to all readers, technical details are often omitted here. The emphasis is made on the following basic general facts: Spontaneous breaking of gauge symmetry is the necessary and sufficient condition for Bose-Einstein condensation. Condensate fluctuations, in thermodynamic limit, are negligible. Their catastrophic behavior can arise only as a result of incorrect calculations, when a Bose-condensed system is described without gauge symmetry breaking. It is crucially important to employ the representative statistical ensembles equipped with all conditions that are necessary for a unique and mathematically correct description of the given statistical system. Only then one is able to develop a self-consistent theory, free of paradoxes.
Why does spontaneous symmetry breaking occur? Why is a state breaking symmetry realized? We explore an idea that measurement selects such a state even if a system is given in a state respecting the symmetry of the system. We point out that the spectrum of the relevant observable is important, and simply apply the projection postulate for quantum measurement. We first show that this approach correctly describes the well-known interference of Bose-Einstein condensates. We then examine a fermionic system and prove that superconducting states with a definite relative phase are selected by the measurement of the current flowing between two superconductors, eliminating the need to assume the presence of an a priori phase to explain the Josephson effect.
Josephson weak links between samples of macroscopic quantum systems such as superconductors, superfluids, and Bose-Einstein condensates provide a unique tool with which to explore quantum mechanics and an opportunity to create applications based on macroscopic quantum physics. In this review we describe the development of the field of weak links in superfluid 3He.{}^{3}\mathrm{He}.3He. We review the basic techniques used to study this system and then describe the experimental and theoretical milestones that have led to our present understanding.
Summary form only given. The recent experimental observation of Bose-Einstein condensation (BEC) of trapped, dilute gas of alkali atoms, and their manipulation have opened a new chapter in the physics of systems involving the interplay of macroscopics and quantum coherence. Here, we study the 'secondary' quantum effects, i.e., the quantum corrections to the semi-classical Gross-Pitaevskii equation, for two weakly-linked Bose-Einstein condensates. We hence generalize the Josephson current-phase relations by including the effects of quantum fluctuations of the pertinent observables. Such equations will also describe the quantum fluctuations in the Josephson dynamics between two weakly linked mesoscopic superconducting grains.