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New Journal of Physics

Controlling migration of a pair of correlated particles by doubly modulated fields

Yi Zheng, Shi-Jie Yang

Published Dec 21, 2015• 4 citations
Publisher

Abstract

The resonant tunneling of correlated bosons in optical lattices is investigated in the presence of doubly modulated AC-fields. The effective hopping coefficients are density-dependent. We can make use of this property to control the migration of a pair of strongly interacting particles in one- or two-dimensional uniform lattices via properly manipulating the phases, frequencies and amplitudes of the driven fields. We design a bifurcating quantum motion of the pair in contrast to the coherent quantum walk of the correlated pair in the absence of external fields.

DOI
10.1088/1367-2630/18/1/013005

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The resonant tunneling of correlated bosons in optical lattices is investigated in the presence of doubly modulated AC-fields. The effective hopping coefficients are density-dependent. We can make use of this property to control the migration of a pair of strongly interacting particles in one- or two-dimensional uniform lattices via properly manipulating the phases, frequencies and amplitudes of the driven fields. We design a bifurcating quantum motion of the pair in contrast to the coherent quantum walk of the correlated pair in the absence of external fields.
The correlated atoms in a tilted optical lattice driven by an ac field are studied within the Hubbard model. By making use of both photon-assisted tunneling and coherent destructive tunneling effects, we can move a pair of strongly correlated atoms in the lattice via manipulating the global amplitude of the driving field. We propose a scheme for creating entanglement between the particle pair and a single particle through interacting oscillations. Our model may provide a new building block for investigating quantum computing and quantum information processing with ultracold atoms in optical lattices.
A powerful method of manipulating the dynamics of quantum coherent particles is to control the phase of their tunneling. We consider a system of two electrons hopping on a quasi-one-dimensional lattice in the presence of a uniform magnetic field and study the effect of adding a time-periodic driving potential. We show that the dynamical phases produced by the driving can combine with the Aharonov-Bohm phases to give precise control of the localization and dynamics of the particles, even in the presence of strong particle interactions.
The dynamical control of tunneling processes of single particles plays a major role in science ranging from Shapiro steps in Josephson junctions to the control of chemical reactions via light in molecules. Here we show how such control can be extended to the regime of correlated tunneling of strongly interacting particles. Through a periodic modulation of a biased tunnel contact, we have been able to coherently control single-particle and correlated two-particle hopping processes. We have furthermore been able to extend this control to superexchange spin interactions in the presence of a magnetic-field gradient. Such photon-assisted superexchange processes constitute a novel approach to realize arbitrary XXZ spin models in ultracold quantum gases, where transverse and Ising-type spin couplings can be fully controlled in magnitude and sign.
Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and we predict the emergence of the nearest-neighbor interaction and density assisted tunneling. By specifically designing a bichromatic driving pattern for a one-dimensional lattice, we demonstrate that the doubly modulated fields can be tuned to realize desired quantum phases, e.g., the Mott insulator phase with selective defects and the density wave phase.
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.