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arXiv:0905.2838 · Physical Review A

Fractional photon-assisted tunneling for Bose-Einstein condensates in a double well

Niklas Teichmann, Martin Esmann, Christoph Weiß

Published Jun 17, 2009• 35 citations
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Abstract

Half-integer-photon resonances in a periodically shaken double well are investigated on the level of the $N$-particle quantum dynamics. Contrary to nonlinear mean-field equations, the linear $N$-particle Schr\"odinger equation does not contain any nonlinearity which could be the origin of such resonances. Nevertheless, analytic calculations on the $N$-particle level explain why such resonances can be observed even for particle numbers as low as $N=2$. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.

DOI
10.1103/physreva.79.063620

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Half-integer-photon resonances in a periodically shaken double well are investigated on the level of the NNN-particle quantum dynamics. Contrary to nonlinear mean-field equations, the linear NNN-particle Schr"odinger equation does not contain any nonlinearity which could be the origin of such resonances. Nevertheless, analytic calculations on the NNN-particle level explain why such resonances can be observed even for particle numbers as low as N=2N=2N=2. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.
Fractional photon-assisted tunneling is investigated both numerically and analytically in a double-well lattice. While integer photon-assisted tunneling is a single-particle effect, fractional photon-assisted tunneling is an interaction-induced many-body effect. Double-well lattices with few particles in each double well are ideal to study this effect far from the mean-field effects. It is predicted that the 1/4-resonance is observable in such systems. Fractional photon-assisted tunneling provides a physically relevant model, for which N -th order time-dependent perturbation theory can be large although all previous orders are small. All predicted effects will be observable with an existing experimental setup [1].
Fractional-photon-assisted tunneling is investigated both analytically and numerically for few interacting ultracold atoms in the double wells of an optical superlattice. This can be realized experimentally by adding periodic shaking to an existing experimental setup [Cheinet et al., Phys. Rev. Lett. 101, 090404 (2008)]. Photon-assisted tunneling is visible in the particle transfer between the wells of the individual double wells. In order to understand the physics of the photon-assisted tunneling, an effective model based on the rotating-wave approximation is introduced. The validity of this effective approach is tested for wide parameter ranges that are accessible to experiments in double-well lattices. The effective model goes well beyond previous perturbation theory approaches and is useful for investigating in particular the fractional-photon-assisted tunneling resonances. Analytic results on the level of the experimentally realizable two-particle quantum dynamics show very good agreement with the numerical solution of the time-dependent Schr\"odinger equation. Far from being a small effect, both the one-half-photon and the one-third-photon resonances are shown to have large effects on the particle transfer.
We investigate the photon-assisted tunneling of a Bose-Einstein condensate in a periodically driven double-well potential. It is shown that the energy levels become nonequidistant due to the presence of the interatomic interaction, thereby leading to the occurrences of the fractional photon resonances. Depending on whether the resonance frequency shifts with the interatomic interaction, two distinct types of resonances are identified: nonshifting resonances and shifting resonances. In particular, certain nonshifting fractional resonances show an odd-even sensitivity to the atom number.
We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schr\"odinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.
We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.