Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator

Abstract

One-dimensional quantum systems that undergo spontaneous symmetry-breaking, having a symmetric (non-degenerate) and a broken-symmetry (doubly-degenerate) phase, have been intensely studied in different branches of physics. In most cases, the spontaneously-broken symmetry is parity. However, it is possible to obtain similar phases in systems without parity symmetry, through an antiunitary symmetry that implies a two-fold symmetry either on momentum or coordinate in the system's classical limit. To illustrate this phenomenon, we use a Kerr parametric oscillator (KPO) with one- and two-photon drives that, despite the breaking of parity symmetry, may have doubly-degenerate levels. Different realizations of squeezed KPOs convey a great deal of attention, as effective Hamiltonians for driven superconducting circuits and the occurrence of degeneracy in such systems could be of practical interest in their application to obtain protected qubits in parity-breaking setups. In addition to this, the reported spectral features strongly indicate the existence of additional symmetries in the system.

References in corpus (31)

• Circuit Quantum Electrodynamics
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Superconducting Quantum Computing: A Review
• The Future of Quantum Computing with Superconducting Qubits
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Quantum state of two trapped Bose-Einstein condensates with a Josephson coupling
• Excited-state quantum phase transitions
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• Kerr-free three-wave mixing in superconducting quantum circuits
• Phase Space Crystals: A New Way to Create a Quasienergy Band Structure
• Scalable quantum computer with superconducting circuits in the ultrastrong coupling regime
• On the static effective Hamiltonian of a rapidly driven nonlinear system
• The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
• Spectral Properties of Coupled Bose-Einstein Condensates
• Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator
• Multiple-period Floquet states and time-translation symmetry breaking in quantum oscillators
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator
• Simulating Chemistry on Bosonic Quantum Devices
• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
• Effective versus Floquet theory for the Kerr parametric oscillator
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Shaping photons: quantum computation with bosonic cQED
• Symmetries of the squeeze-driven Kerr oscillator
• Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Symmetries of Liouvillians of squeeze-driven parametric oscillators
• Classical Phase Space Crystals in an Open Environment
• Asymmetry Control in a Parametric Oscillator for the Quantum Simulation of Chemical Activation
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators