Phase Space Crystals: A New Way to Create a Quasienergy Band Structure

TL;DR

This paper introduces phase space crystals, a novel method to engineer quasienergy band structures in driven systems using discrete symmetries in phase space, enabling in situ tunability of energy bands.

Contribution

It proposes the concept of phase space crystals based on discrete phase space symmetry and models their band structure using a tight-binding approximation.

Findings

Demonstrates how driving fields induce n-fold discrete periodicity in phase space.

Shows the feasibility of creating tunable quasienergy band structures.

Provides an explicit model for realizing phase space crystals.

Abstract

A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field coupling highly nonlinearly to one of its degrees of freedom (e.g., ~ q^n). The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose an explicit model to realize such a phase space crystal and analyze its band structure in the frame of a tight-binding approximation. The phase space crystal opens new ways to engineer energy band structures, with the added advantage that its properties can be changed in situ by tuning the driving field's parameters.