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Physical Review A

Controlling transport and entanglement of two particles in a bipartite lattice

Kuo Hai, Wenhua Hai, Qiong Chen

Published Nov 15, 2010• 23 citations
Publisher

Abstract

We consider two Bose particles held in a bipartite lattice with two different separations fitting the nearest-neighbor tight-binding approximation. Applying a strong driving field of high frequency and a large interaction intensity, we analytically construct entangled Floquet states and slowly varying Rabi-oscillation states of the system. Under the interaction-independent and interaction-dependent conditions of the selective coherent destruction of tunneling, we propose a scheme for manipulating separated and co-site transports of the two particles in the same or opposite directions. The results could be useful for transporting quantum information carried by a few particles in a bipartite superlattice.

DOI
10.1103/physreva.82.053412

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We consider two Bose particles held in a bipartite lattice with two different separations fitting the nearest-neighbor tight-binding approximation. Applying a strong driving field of high frequency and a large interaction intensity, we analytically construct entangled Floquet states and slowly varying Rabi-oscillation states of the system. Under the interaction-independent and interaction-dependent conditions of the selective coherent destruction of tunneling, we propose a scheme for manipulating separated and co-site transports of the two particles in the same or opposite directions. The results could be useful for transporting quantum information carried by a few particles in a bipartite superlattice.
We study coherent control of spin-dependent dynamical localization (DL) and directed transport (DT) of a spin-orbit-coupled single atom held in a driven optical bipartite lattice. Under the high-frequency limit and nearest-neighbor tight-binding approximation, we find a new decoupling mechanism between states with the same (different) spins, which leads to two sets of analytical solutions describing DL and DT with (without) spin flipping. The analytical results are numerically confirmed, and perfect agreements are found. Extending the research to a system of spin-orbit-coupled single atoms, the spin current and quantum information transport with controllable propagation speed and distance are investigated. The results can be experimentally tested in the current setups and may be useful in quantum information processing.
Coherent control of quantum tunnelling is investigated analytically for two bosons held in a driven triple-well potential. In the high-frequency region within resonance, the non-Floquet states with slowly varying populations are constructed by the linear superposition of Floquet solutions. For the non-resonance case with appropriate reduced parameters, we obtain another set of analytical solutions and their numerical correspondences, which exhibits the selective tunnelling effect of atoms. Applying the presented analytical results, a scheme to transport two bosons from the first well to the third is suggested by adjusting the driving parameters.
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 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.