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

2013/05/31 by Lingzhen Guo, Michael Marthaler, Gerd Schön · 100 citations
Mathematics · Physics and Astronomy · #Atom (system on chip) #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Coupling (piping) #Crystal (programming language) #Electronic band structure #Field (mathematics) #Materials science #Mathematics #Phase (matter) #Phase space #Physics #Quantum mechanics #Random lasers and scattering media #Space (punctuation) #Strong Light-Matter Interactions #Symmetry (geometry) #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1103/physrevlett.111.205303

published in Physical Review Letters 111(20), 205303 (American Physical Society) · 8 pages, 4 figures

arxiv created 2013/11/04 · openalex publication_date 2013/11/13 · arxiv updated 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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., ~ qⁿ). 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.

Citations

• Colloquium: Artificial gauge potentials for neutral atoms
• Emission spectrum of the driven nonlinear oscillator
• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Floquet-Bloch Theory and Topology in Periodically Driven Lattices
• Strong localization of photons in certain disordered dielectric superlattices
• Bose-Einstein condensation in dark power-law laser traps
• Electric Field Effect in Atomically Thin Carbon Films
• Inhibited Spontaneous Emission in Solid-State Physics and Electronics
• Supernarrow Spectral Peaks near a Kinetic Phase Transition in a Driven Nonlinear Micromechanical Oscillator
• Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect

Cited by

• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry