# Generation of atypical hopping and interactions by kinetic driving

## TL;DR

This paper demonstrates how periodic modulation of hopping in a Bose-Hubbard model can engineer unconventional Hamiltonians, leading to exotic many-body states like a superfluid with opposite momentum condensates.

## Contribution

It introduces a method of Floquet engineering that suppresses single-particle hopping while enabling higher-order processes, creating novel Hamiltonians and phases.

## Key findings

- Suppression of nearest-neighbor hopping via periodic driving.
- Emergence of a superfluid with opposite nonzero momenta.
- Transition from Mott insulator to exotic superfluid phase.

## Abstract

We study the effect of time-periodically varying the hopping amplitude in a one-dimensional Bose-Hubbard model, such that its time-averaged value is zero. Employing Floquet theory, we derive a static effective Hamiltonian in which nearest-neighbor single-particle hopping processes are suppressed, but all even higher-order processes are allowed. Unusual many-body features arise from the combined effect of nonlocal interactions and correlated tunneling. At a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by two quasi-condensates with opposite nonzero momenta. This work shows how driving of the hopping energy provides a novel form of Floquet engineering, which enables atypical Hamiltonians and exotic states of matter to be produced and controlled.