Abstract
We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.
Highlights
Two weakly coupled Bose-Einstein condensates (BECs) in a double-well potential constitute a paradigmatic system for investigating the physics of bosonic Josephson junctions [1,2,3,4]
We find that in the regime of a small initial imbalance, where only one Bogoliubov mode is significantly occupied and the system performs plasma oscillations at the corresponding frequency [30], the evolution of the condensate is characterized by a periodic transfer of population between the ground state and the first excited state
We have analyzed the dynamics of a onedimensional Bose-Einstein condensate in a double-well potential [57], from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method [44]
Summary
Two weakly coupled Bose-Einstein condensates (BECs) in a double-well potential constitute a paradigmatic system for investigating the physics of bosonic Josephson junctions [1,2,3,4]. Due to the conceptual importance of these phenomena, BECs in double-well potentials and arrays of coupled boson Josephson junctions have been extensively investigated in the last two decades both theoretically [2,3,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and experimentally [4,6,31,32,33,34,35,36,37,38,39], as well as their counterparts with fermionic superfluid atomic samples [40,41,42,43] The physics of these systems is well captured by a twomode approximation of the Gross-Pitaevskii (GP) equation, each mode being localized in one of the two wells, which allows for an effective description in terms of only two parameters, namely, the population imbalance z(t ) and the phase difference φ(t ) between the left and right components. The dynamics of the system will be analyzed by means of an expansion over the Bogoliubov modes, by comparing with the exact evolution and the two-mode (TM) approach
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