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Communications in Theoretical Physics

Effective Two-State Model and NOON States for Double-Well Bose-Einstein Condensates in Strong-Interaction Regime

Xiaoxue Yang, Ying Wu

Published Aug 1, 2009• 4 citations
Publisher

Abstract

The model of double-well Bose–Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states |N, 0〉 and |0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Fock states.

DOI
10.1088/0253-6102/52/2/10

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The model of double-well Bose–Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states |N, 0〉 and |0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Fock states.
We study undistinguishable two-species Bose-Einstein condensates (BECs) trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling strength in the adiabatic Rosen-Zener type effectively. Starting from two typical initial states, we study the evolution of the system and find that the interspecies interaction can produce totally distinct results, which is expected to provide a route to manipulate the BEC distribution.
Abstract Ultracold gases provide an excellent platform for the realization of quantum interferometers. In the case of implementations based on Bose-Einstein condensates in double well potentials, an effective two-mode model allows to study how the interactions among particles affect the sensitivity of the interferometer. In this work we review the properties of such a model and its application to interferometric protocols, focusing on the achievable sensitivity in the presence of interactions turned on. In particular we study the full interferometric sequence when the initial state is a Twin Fock state, which is perfectly number squeezed. We found that in the presence of interactions and for certain values of the holding time in which a phase difference between the two modes is accumulated, the same sensitivity as in the non interacting case is recovered when using the population imbalance between the two wells as observable. Finally, we characterize the behaviour of the sensitivity by looking at the δ-derivative and the variance of the operator used for the measurement and studying the squeezing parameters.
We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.