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arXiv:cond-mat/0411567 · New Journal of Physics

Dephasing and breakdown of adiabaticity in the splitting of Bose–Einstein condensates

Luca Pezzè, Augusto Smerzi, G. P. Berman, A. R. Bishop, Lee A. Collins

Published Apr 2, 2005• 12 citations
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Abstract

We study the quantum dynamics of a Bose–Einstein condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic timescales of the splitting process and compare our results with numerical analyses available in the literature. In the first stage of the dynamics, the relative phase of the two condensates evolves adiabatically. At a critical time t ad , small-amplitude phase fluctuations around the average trajectory increase exponentially fast, signalling the breakdown of adiabaticity. After this stage, it is still not possible to neglect the tunnelling exchange between the two wells. We find highly non-trivial dependences of the dephasing time on t ad and on the ramping time of the interwell barrier.

DOI
10.1088/1367-2630/7/1/085

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We study the quantum dynamics of a Bose–Einstein condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic timescales of the splitting process and compare our results with numerical analyses available in the literature. In the first stage of the dynamics, the relative phase of the two condensates evolves adiabatically. At a critical time t ad , small-amplitude phase fluctuations around the average trajectory increase exponentially fast, signalling the breakdown of adiabaticity. After this stage, it is still not possible to neglect the tunnelling exchange between the two wells. We find highly non-trivial dependences of the dephasing time on t ad and on the ramping time of the interwell barrier.
We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows us to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover, we can get some insight into the collective modes that are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.
Bose Einstein condensates (BECs) in double well potentials have drawn a lot of attention for the possibilities they offer to study fundamental quantum mechanical effects at the macroscopic level as well as for potential applications like interferometry, high precision measurements or thermometry. In contrast to Josephson junctions realized in superconductors and superfluids, in BEC the interatomic interactions play a crucial role leading to anharmonic Josephson oscillations, if the initial population imbalance of the two wells is below a critical value, and to macroscopic quantum self-trapping i.e, inhibition of large amplitude Josephson oscillations above the threshold for the population imbalance. In this paper, a novel technique to adiabatically control of BEC in a double-well potential is proposed. The adiabatic dynamics of a BEC in a double well potential can be described in terms of a dark variable resulting from a combination of the population imbalance and the spatial atomic coherence.
We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double-well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the nonlinear matter-wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom or molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self-trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC nonlinearity. The emergence of nonlinear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.
Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is "cut" by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the "memory" of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.
By using a two-mode description, we show that there exist the multistability, phase transition and associated critical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose–Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stable state or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energy goes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for the phase difference between the two wells accompanying with large fluctuations of atom numbers.
By using a two-mode description, we show that there exist the multistability, phase transition and associatedcritical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose-Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stablestate or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energygoes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for thephase difference between the two wells accompanying with large fluctuations of atom numbers.