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Physical Review A

Dynamic control and probing of many-body decoherence in double-well Bose-Einstein condensates

Nir Bar‐Gill, Gershon Kurizki, Markus K. Oberthaler, Nir Davidson

Published Nov 16, 2009• 25 citations
Publisher

Abstract

We present an approach to dynamic decoherence control of finite-temperature Bose-Einstein condensates in a double-well potential. Due to the many-body interactions the standard ``echo'' control method becomes less effective. The approach described here takes advantage of the interaction-induced change of the spectrum, to obtain the optimal rate of $\ensuremath{\pi}$ flips of the relative phase between maximally distinguishable collective states. This method is particularly useful for probing and diagnosing the decoherence dynamics.

DOI
10.1103/physreva.80.053613

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We present an approach to dynamic decoherence control of finite-temperature Bose-Einstein condensates in a double-well potential. Due to the many-body interactions the standard ``echo'' control method becomes less effective. The approach described here takes advantage of the interaction-induced change of the spectrum, to obtain the optimal rate of \ensuremathπ\ensuremath{\pi}\ensuremathπ flips of the relative phase between maximally distinguishable collective states. This method is particularly useful for probing and diagnosing the decoherence dynamics.
We perform interferometry with one-dimensional Bose-Einstein condensates in a double well potential. Using dressed adiabatic potentials on an atomchip, we dynamically split BECs, imposing a macroscopic coherence on the system. Fluctuations of the order parameter are revealed as local shifts in the interference pattern and allow a quantization of the decoherence process with time. For the uncoupled system we ultimately recover individual phase fluctuating condensates, whereas finite tunnel coupling counteracts the decoherence and leads to an equilibrium characterized by a finite coherence length. Decoherence decay and equilibrium coherence lengths are used to determine temperature and coupling strength of the system.
The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates. In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.
For Bose–Einstein condensates in double wells, N -particle Rabi-like oscillations often seem to be damped. Far from being a decoherence effect, the apparent damping can indicate the emergence of quantum superpositions in the many-particle quantum dynamics. However, in an experiment it would be difficult to distinguish the apparent damping from decoherence effects. This paper suggests using controlled periodic shaking to quasi-instantaneously switch the sign of an effective Hamiltonian, thus implementing an 'echo' technique which distinguishes quantum superpositions from statistical mixtures. The scheme for the effective time reversal is tested by numerically solving the time-dependent N -particle Schrödinger equation.
Preparation of nontrivial quantum states without introducing unwanted excitations or decoherence remains a central challenge in utilizing ultracold atomic systems for quantum simulation. We employ optimal control methods to realize fast, coherent splitting of a one-dimensional Bose-Einstein condensate, achieving negligible classical excitations while preserving quantum correlations. Furthermore, we explore two-step protocols in which controlled classical motion is first induced and subsequently suppressed via tailored control sequences. Our experiments highlight the potential of optimal control for quantum state engineering and dynamical control in many-body quantum systems.
Summary form only given. Dynamical control of the atomic tunneling between two Bose-Einstein condensates (BEC's) confined in a double-well potential is predicted to occur when laser pulses induce transition between one of the condensate state and the excited state which brings about phase shifts for the condensate wave function, leading to transition between macroscopic quantum self-trapping, which is a self-maintained population imbalance between two BEC's due to interatomic interaction, and large amplitude oscillations. We investigate this phenomenon for the case of a three-level system with two condensate states and an excited state.
By employing a binary mixture of Bose-Einstein condensates in a symmetric double-well potential we study the collective dynamics of a two-coupled-Hamiltonian system. There we find three interesting collective dynamic regimes. Besides measure synchronization, phase synchronization and nonlocal measure synchronization have been found. We demonstrate that by varying the interspecies interaction strength, the transitions between different regimes can be found clearly. A diagram of dynamic regimes with experimentally adjustable parameters has also been presented.