Floquet analysis of the modulated two-mode Bose-Hubbard model

TL;DR

This paper uses Floquet theory to analyze how periodic modulation affects tunneling and state formation in a two-mode Bose-Hubbard system, revealing resonance behaviors, tunneling control, and methods to generate NOON states.

Contribution

It provides a detailed Floquet analysis of tunneling enhancement, resonance conditions, and NOON state creation in a modulated two-mode Bose-Hubbard model, extending understanding of dynamic control in quantum systems.

Findings

Tunneling is enhanced over a wide frequency range with amplitude modulation.

Resonance conditions can be predicted from the non-modulated Hamiltonian spectrum.

Methods to create NOON states via detuning and adiabatic frequency variation are demonstrated.

Abstract

We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using the spectrum of the non-modulated Hamiltonian. Furthermore, we use Floquet analysis to explain the coherent destruction of tunneling (CDT) occurring in a large-amplitude modulated system. Finally, we present two ways to create a NOON state (a superposition of $N$ particles in mode 1 with zero particles in mode 2 and vice versa). One is based on a coherent oscillation caused by detuning from a partial CDT. The other makes use of an adiabatic variation of the modulation frequency. This results in a Landau-Zener type of transition between the ground state and a NOON-like state.