Discrete time symmetry breaking in quantum circuits: exact solutions and tunneling

Abstract

We discuss general properties of discrete time quantum symmetry breaking in degenerate parametric oscillators. Recent experiments in superconducting quantum circuit with Josephson junction nonlinearities give rise to new properties of strong parametric coupling and nonlinearities. Exact analytic solutions are obtained for the steady-state of this single-mode case of subharmonic generation. We also obtain analytic solutions for the tunneling time over which the time symmetry-breaking is lost above threshold. We find that additional anharmonic terms found in the superconducting case increase the tunneling rate, and can also lead to new regimes of tristability as well as bistability. Our analytic results are confirmed by number state calculations.

arXiv comment34 pages, 5 figures

References in corpus (13)

• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Modeling spontaneous breaking of time-translation symmetry
• Probing a dissipative phase transition via dynamical optical hysteresis
• Observation of time quasicrystal and its transition to superfluid time crystal
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Power-laws in the dynamic hysteresis of quantum nonlinear photonic resonators
• Functional Wigner representation of BEC quantum dynamics
• Non-critically squeezed light via spontaneous rotational symmetry breaking
• Applications of the Fokker-Planck equation in circuit quantum electrodynamics

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• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• Phase-space simulations of feedback coherent Ising machines
• Condensed matter physics in big discrete time crystals
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout