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Physical Review A

Quantum transport in bipartite lattices via Landau-Zener tunneling

Stefano Longhi, Giuseppe Della Valle

Published Oct 31, 2012• 16 citations
Publisher

Abstract

A scheme for directed transport of quantum particles in a static bipartite lattice driven by an ac force, based on a sequence of Landau-Zener transitions, is proposed theoretically. As compared to directed transport in bipartite lattices exploiting the phenomenon of coherent destruction of tunneling recently suggested by Creffield [Phys. Rev. Lett. 99, 110501 (2007)], the present scheme realizes a robust quantum state transport owing to the adiabaticity of the particle transfer. The transport is realized by an external force with a sawtooth profile and does not require modulation of lattice parameters (intersite couplings and energy levels). The effects of lattice disorder and particle interaction on the directed quantum transport are discussed.

DOI
10.1103/physreva.86.043633

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A scheme for directed transport of quantum particles in a static bipartite lattice driven by an ac force, based on a sequence of Landau-Zener transitions, is proposed theoretically. As compared to directed transport in bipartite lattices exploiting the phenomenon of coherent destruction of tunneling recently suggested by Creffield [Phys. Rev. Lett. 99, 110501 (2007)], the present scheme realizes a robust quantum state transport owing to the adiabaticity of the particle transfer. The transport is realized by an external force with a sawtooth profile and does not require modulation of lattice parameters (intersite couplings and energy levels). The effects of lattice disorder and particle interaction on the directed quantum transport are discussed.
We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a much easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al. [ Phys. Rev. Lett. 99 (2007) 110501 ], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.
Coherent transport of quantum particles in binary superlattices driven by an ac force can realize a kind of quantum walk (QW) that can be referred to as Bloch–Zener QW. In this regime, the particle wavepacket undergoes a sequence of Zener tunnelling events that mimic a discrete QW on a lattice, provided that the impulse of the ac force over one semi-cycle of oscillation is properly adjusted. In the Bloch–Zener QW, the coin states are related to the particle occupation of the two minibands, and thus it does not require any internal degrees of freedom of the particle.
We investigate coherent control of a single atom interacting with an optical bipartite lattice via a combined high-frequency modulation. Our analytical results show that the quantum tunneling and dynamical localization can depend on phase difference between the modulation components, which leads to a different route for the coherent destruction of tunneling and a convenient phase-control method for stabilizing the system to implement the directed transport of atom. The similar directed transport and the phase-controlled quantum transition are revealed for the corresponding many-particle system. The results can be referable for experimentally manipulating quantum transport and transition of cold atoms in the tilted and shaken optical bipartite lattice or of analogical optical two-mode quantum beam splitter, and also can be extended to other optical and solid-state systems.
The dynamics of two correlated bosons hopping on a one-dimensional lattice and driven by a sinusoidal force is analytically investigated by means of a multiple-time-scale asymptotic analysis of the driven Bose-Hubbard Hamiltonian. By assuming the ratio $\ensuremath{\epsilon}=J/\ensuremath{\omega}$ between the tunneling rate JJJ and modulation frequency $\ensuremath{\omega}$ of the driving field as a small parameter, the perturbative analysis shows that, under appropriate driving conditions, coherent destruction of tunneling can be simultaneously realized for both paired and unpaired states up to the long time scale $\ensuremath{\sim}$$1/(\ensuremath{\omega}{\ensuremath{\epsilon}}^{2})$ in the regime corresponding to an energy quantum $\ensuremath{\hbar}\ensuremath{\omega}$ of the driving field of the same order of magnitude as the particle interaction energy $\ensuremath{\hbar}{U}_{0}$. The predictions of the perturbative analysis are confirmed by direct numerical simulations of the two-particle Bose-Hubbard Hamiltonian and by direct quasienergy-band computation.
We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains by using a many-body generalization recently reported Chen et al. [Nature Phys. 7, 61 (2011)], within the decoupling approximation and the one-level band scheme. The energy spectrum shows evidence of the structure of the avoided level crossings as a function of the onsite interparticle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle Landau-Zener predictions. In the strong-coupling regime, we find that there is a critical value of the onsite interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.