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arXiv:1101.5272 · Physical Review A

Fractional-photon-assisted tunneling in an optical superlattice: Large contribution to particle transfer

Martin Esmann, Niklas Teichmann, Christoph Weiß

Published Jun 29, 2011• 12 citations
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Abstract

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.

DOI
10.1103/physreva.83.063634

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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.
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].
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.
Fermions in an optical lattice near a wide Feshbach resonance are expected to be described by an effective Hamiltonian of the general Hubbard model with particle-correlated tunneling rates resulting from the strong atomic interaction [Duan, Phys. Rev. Lett. 95, 243202 (2005)]. Here, we propose a scheme to test the predictions of this effective Hamiltonian through manipulation of ultracold atoms in an inhomogeneous optical superlattice. The structure of the low-energy Hilbert space as well as the particle-correlated tunneling rates can be inferred from measurements of the time-of-flight images.
In a recent experiment [Phys. Rev. Lett. 100, 040404 (2008)], an analog of photon-assisted tunneling was observed for a Bose-Einstein condensate in an optical lattice subject to a constant force plus a sinusoidal shaking. Contrary to previous theoretical predictions, the width of the condensate was measured to be proportional to the square of the effective tunneling matrix element, rather than a linear dependence. For a simple model of two interacting bosons in a one-dimensional optical lattice, both analytical and numerical calculations indicate that such a transition from a linear to a quadratic dependence can be interpreted through the ballistic transport and the corresponding exact dispersion relation of bound boson pairs.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.