Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
arXiv:2504.15347 · doi:10.1103/6vj6-v7yh
Abstract
Quantum Kerr parametric oscillators (KPOs) are systems out of equilibrium with a wide range of applications in quantum computing, quantum sensing, and fundamental research. They have been realized in superconducting circuits and photonic platforms. In this work, we explore the onset of ground-state and excited-state quantum phase transitions in KPOs, focusing on the role of the phase-space rotational symmetry when the driving frequency is times the oscillator's natural frequency, specifically for . These cases are experimentally accessible in superconducting circuits, where the Floquet quasienergy spectrum can also be studied as a function of tunable control parameters. Using the classical Hamiltonian of the system, we identify the critical points associated with quantum phase transitions and analyze the emergence of both real and avoided level crossings, examining their influence on the energy spectrum and tunneling dynamics. Our findings provide insights into the engineering of robust quantum states, quantum dynamics control, and onset of quantum phase transitions with implications for critical quantum sensing.
15 pages, 9 figures
References in corpus (55)
- Exciton-polariton condensates
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Observation of quantum state collapse and revival due to the single-photon Kerr effect
- Squeezed states of light and their applications in laser interferometers
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
- Excited state quantum phase transitions in many-body systems
- Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing
- Quantum phase transitions in the interacting boson model
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
- Switching via quantum activation: A parametrically modulated oscillator
- Excited-state quantum phase transitions
- Nanomechanical squeezing with detection via a microwave cavity
- Critical parametric quantum sensing
- Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
- Phase Space Crystals: A New Way to Create a Quasienergy Band Structure
- Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
- Quantum dynamics of a few-photon parametric oscillator
- Impact of Quantum Phase Transitions on Excited Level Dynamics
- Structure of eigenstates and quench dynamics at an excited state quantum phase transition
- A quantum parametric oscillator with trapped ions
- High-performance microresonator optical parametric oscillator on a silicon chip
- Quantum interference in the classically forbidden region: a parametric oscillator
- Quantum quench dynamics in Dicke superradiance models
- On the static effective Hamiltonian of a rapidly driven nonlinear system
- Spectral Phase Transitions in Optical Parametric Oscillators
- Entropy, chaos and excited-state quantum phase transitions in the Dicke model
- The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
- Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom
- Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator
- Multiple-period Floquet states and time-translation symmetry breaking in quantum oscillators
- Preparing quasienergy states on demand: A parametric oscillator
- High-accuracy Ising machine using Kerr-nonlinear parametric oscillators with local four-body interactions
- Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
- Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
- Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
- Simulating Chemistry on Bosonic Quantum Devices
- Effects of excited state quantum phase transitions on system dynamics
- Multiphoton antiresonance
- Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator
- Dissipative phase transitions in -photon driven quantum nonlinear resonators
- Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies
- Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
- Correlated oscillations in Kerr parametric oscillators with tunable effective coupling
- Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
- Effective versus Floquet theory for the Kerr parametric oscillator
- Quantum localization measures in phase space
- Symmetries of the squeeze-driven Kerr oscillator
- Driving superconducting qubits into chaos
- Quantum metrology with a squeezed Kerr oscillator
- Structurally stable subharmonic regime of a driven quantum Josephson circuit
- A Roadmap for Simulating Chemical Dynamics on a Parametrically Driven Bosonic Quantum Device
- Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator