The overlap of localized wave functions in a two-mode approximation leads to interaction (cross-collision) between ultra-cold atoms trapped in distinct sites of a double-well potential. We show that this interaction can significantly change the atom tunneling rate for special trap configurations resulting in an effective linear Rabi regime of population oscillation between the trap wells. In this sense, we demonstrate that cross-collisional effects can significantly extend the validity of the two-mode model approach allowing it to be alternatively employed to explain the recently observed increase of tunneling rates due to nonlinear interactions. Moreover, we investigate the extension for ultra-cold atoms trapped in an optical lattice. Control over the cross-collisional terms, obtained through manipulation of the optical trapping potential, can be used as an engineering tool to study many-body physics.
The overlap of localized wave functions in a two-mode approximation leads to interaction (cross-collision) between ultra-cold atoms trapped in distinct sites of a double-well potential. We show that this interaction can significantly change the atom tunneling rate for special trap configurations resulting in an effective linear Rabi regime of population oscillation between the trap wells. In this sense, we demonstrate that cross-collisional effects can significantly extend the validity of the two-mode model approach allowing it to be alternatively employed to explain the recently observed increase of tunneling rates due to nonlinear interactions. Moreover, we investigate the extension for ultra-cold atoms trapped in an optical lattice. Control over the cross-collisional terms, obtained through manipulation of the optical trapping potential, can be used as an engineering tool to study many-body physics.
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.
In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an ``improved two-mode model'' (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled ``interaction tunneling,'' that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem.
We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double-well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground-state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.
Abstract Controlling the tunneling of atoms of one species using a different atom species is a fundamental step in the development of a new class of atom quantum devices, where detection, motion control, and other functions over the atoms, can be achieved by exploiting the interaction between two different atomic species. Here, we theoretically study coherent oscillations of a non-self-interacting Bose–Einstein condensate (BEC) species in a triple-well potential controlled by a self-interacting species self-trapped in the central well of the potential. In this system, a blockade, due to the interspecies interaction, prevents atoms of the non-self-interacting species from populating the central well. Thus, for an initial population imbalance between the left- and right-hand wells of the non-self-interacting species, coherent BEC oscillations are induced between these two wells, resembling those of Rabi-like BEC oscillations in a double-well potential. The oscillation period is found to scale linearly with the number of self-trapped atoms as well as with the interspecies interaction strength. This behavior is corroborated by the quantum many-particle and the mean-field models of the system. We show that BEC oscillations can be described by using an effective bosonic Josephson junction with a tunneling amplitude that depends on the number of the self-trapped atoms in the central well. We also consider the effect of the self-trapped atom losses on the coherent oscillations. We show, by using quantum trajectories, that this type of losses leads to a dynamical change in the oscillation period of the non-self-interacting species, which in turn allows the number of self-trapped atoms lost from the system to be estimated.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.