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Acta Sinica Quantum Optica

A Field Equation Describing Damping Josephson Junction for the Bose-Einstein Condensates

Luo Yun-wen

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In this paper,we add a dissipative term-1/2γcψ to the GPE equation,and use it to analyze the damping effect of Josephson junction in the double-well trap model,and find that the total number of condensation and the amplitude of Josephson junction damp change along with time in an exponent declining way.

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S. Raghavan, Augusto Smerzi, Stefano Fantoni +1 more

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International Journal of Modern Physics B•Mar 10, 1999•0 citations
The dissipative dynamics of a pointlike Josephson junction in binary Bose-Einstein-condensed mixtures is analyzed within the framework of the model of a tunneling Hamiltonian. The transmission of unlike particles across a junction is described by the different transmission amplitudes. The effective action that describes the dynamics of the phase differences across the junction for each of two condensed components is derived by employing the functional integration method. In the low-frequency limit the dynamics of a Josephson junction can be described by two coupled equations in terms of the potential energy and dissipative Rayleigh function using a mechanical analogy. The interplay between mass currents of each mixture component appears in the second-order term in the tunneling amplitudes due to the interspecies hybridizing interaction. The asymmetric case of the binary mixtures with different concentrations and order parameters is considered as well.
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.
Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multimode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ is in resonance with the effective fluctuation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$, where both ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$ are strongly renormalized with respect to their noninteracting values. By evaluating and using the model parameters for the respective experiments, we describe quantitatively the presence or absence of damping.
The time-dependent non-equilibrium dynamics of a Bose–Einstein condensate (BEC) typically generates incoherent excitations out of the condensate due to the finite frequencies present in the time evolution. We present a detailed derivation of a general non-equilibrium Greenʼs function technique that describes the coupled time evolution of an interacting BEC and its single-particle excitations in a trap, based on an expansion in terms of the exact eigenstates of the trap potential. We analyze the dynamics of a Bose system in a small double-well potential with initially all particles in the condensate. When the trap frequency is larger than the Josephson frequency, , the dynamics changes at a characteristic time, , abruptly from the slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times , the Josephson oscillations are undamped, in agreement with the experiments. We analyze the physical origin of the finite scale as well as its dependence on the trap parameter Δ .
We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates at T =0 in a double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fractional population imbalance z(t) (related to the condensate phase difference) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-electron superconductor Josephson junctions (SJJ). The BJJ elliptic-function behavior has a singular dependence on a GPE parameter ratio Λ at a critical ratio Λ=Λc, beyond which a novel 'macroscopic quantum self-trapping' effect sets in with a non-zero time-averaged imbalance <z>≠0.