Critical quantum geometric tensors of parametrically-driven nonlinear resonators

Abstract

Parametrically driven nonlinear resonators represent a building block for realizing fault-tolerant quantum computation and are useful for critical quantum sensing. From a fundamental viewpoint, the most intriguing feature of such a system is perhaps the critical phenomena, which can occur without interaction with any other quantum system. The non-analytic behaviors of its eigenspectrum have been substantially investigated, but those associated with the ground state wavefunction have largely remained unexplored. Using the quantum ground state geometric tensor as an indicator, we comprehensively establish a phase diagram involving the driving parameter $\epsilon$ and phase $\varphi$. The results reveal that with the increase in $\epsilon$, the system undergoes a quantum phase transition from the normal to the superradiant phase, with the critical point unaffected by $\varphi$. Furthermore, the critical exponent and scaling dimension are obtained by an exact numerical method, which is consistent with previous works. Our numerical results show that the phase transition falls within the universality class of the quantum Rabi model. This work reveals that the quantum metric and Berry curvature display diverging behaviors across the quantum phase transition.

arXiv commentAny comments or suggestions are welcome !

References in corpus (51)

• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Continuous Quantum Phase Transitions
• Dynamics of a Quantum Phase Transition
• Quantum criticality
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Computational Studies of Quantum Spin Systems
• Quantum critical scaling of the geometric tensors
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Encoding a qubit in a trapped-ion mechanical oscillator
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Quantum Critical Scaling of Fidelity Susceptibility
• Bias-preserving gates with stabilized cat qubits
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Superradiance transition in a system with a single qubit and a single oscillator
• Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Universal quantum computation with a nonlinear oscillator network
• Critical parametric quantum sensing
• A quantum transducer using a parametric driven-dissipative phase transition
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• A critical Schrödinger cat qubit
• Observation of a superradiant phase transition with emergent cat states
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• Unconventional Quantum Critical Points
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Fidelity Susceptibility in the Quantum Rabi Model
• Quantum Gate for Kerr Nonlinear Parametric Oscillator Using Effective Excited States
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Berry Phases and Quantum Phase Transitions
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Emergent space-time supersymmetry at disorder quantum critical point
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Quantum simulation of gravitational-like waves in minisuperspace with an artificial qubit
• Scheme for measuring topological transitions in a continuous variable system
• Quantum metric and metrology with parametrically-driven Tavis-Cummings models
• Signatures of a quantum phase transition on a single-mode bosonic model
• Critical sensing with a single bosonic mode without boson-boson interactions
• Quantum squeezing in a nonlinear mechanical oscillator

Cited by in corpus (5)

• Collective quantum enhancement in critical quantum sensing
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Identifying non-Hermitian critical points with quantum metric
• Critical quantum metrology in a stabilized two-photon Rabi model
• Quantum squeezing amplification with a weak Kerr nonlinear oscillator