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arXiv:1104.0647 · Physical Review A

Dissipative dynamics of the Josephson effect in binary Bose-Einstein-condensed mixtures

S. N. Burmistrov

Published Jun 21, 2011• 2 citations
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Abstract

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.

DOI
10.1103/physreva.83.063627

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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 dissipative dynamics of a Josephson junction in Bose gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action that describes the dynamics of the phase difference across the junction is derived using the functional integration method. The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low-frequency limit involving the radiation terms. The asymmetric case of the Bose gases with the different order parameters is calculated as well.
We study the dynamics of Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double well potential. Two interesting mixture genuine effects are identified. First, we find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. Secondly, in the balanced population case, the Josephson oscillations behave as if the interatomic interactions have been partially cancelled. This effect could be used as a new procedure to measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are physically interpreted in terms of an analytical description of the binary mixture using a two-mode model.
We study the quantum behaviour of a binary mixture of Bose–Einstein condensates in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. We focus on the small tunnelling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then, the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short- and the long-time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunnelling. In the second case, the short-timescale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schrödinger cat states is considered and shown to affect the momentum distribution.
We analyze theoretically Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double-well potential. We find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. In the balanced population case, the Josephson oscillations unveil a dependence with the different spin collision channels. This effect could be used to experimentally measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are in close agreement with an analytical description of the binary mixture using a two-mode model.
It is important to know the decoherence mechanism of a qubit based on Josephson junctions. At low temperatures, as quasiparticle concentration becomes exponentially small, one needs to consider energy transfer from tunneling electrons to other degrees of freedom to find dissipation in Josephson junctions and decoherence in qubits. Here we discuss the energy transfer to two-level systems, i.e., the transitions between two different configurations of ions inside an insulating layer separated by a potential barrier. We derive a general equation of motion for the phase difference between two superconducting electrodes and we find a retarded dissipation term due to electromagnetic mechanism and also contribution due to electron tunneling mechanism. Using the equation of motion we calculate the decay of Rabi oscillations and frequency shift in qubits due to the presence of the two-level systems. In the long-time limit our results coincide with those obtained by Martinis et al. [Martinis et al., Phys. Rev. Lett. 95, 210503 (2005)] within the Fermi's Golden Rule approach up to a numerical factor.