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arXiv:1109.2735 · Laser Physics Letters

Fractional photon-assisted tunneling of ultra-cold atoms in periodically shaken double-well lattices

Martin Esmann, Jonathan D. Pritchard, Christoph Weiß

Published Nov 10, 2011• 9 citations
arXivHTMLPDF

Abstract

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].

DOI
10.1002/lapl.201110109

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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.
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.
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.
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.
We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly correlated glasses or flux-lattice models decorated with arbitrary patterns of localized defects.