# Critical Response of a Quantum van der Pol Oscillator.

@article{Dutta2019CriticalRO, title={Critical Response of a Quantum van der Pol Oscillator.}, author={Shovan Dutta and N. Cooper}, journal={Physical review letters}, year={2019}, volume={123 25}, pages={ 250401 } }

Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent…

## 10 Citations

Dynamical Mean-Field Theory for Open Markovian Quantum Many Body Systems

- Physics
- 2020

Open quantum many body systems describe several quantum simulators, ranging from arrays of superconducting circuits hosting correlated states of light, to ultracold atoms in optical lattices in…

Observing Quantum Synchronization of a Single Trapped-Ion Qubit

- Education, Physics
- 2022

Synchronizing a few-level quantum system is of fundamental importance to understanding synchronization in deep quantum regime. Whether a two-level system, the smallest quantum system, can be…

Turing instability in quantum activator-inhibitor systems

- Physics
- 2021

Turing instability is a fundamental mechanism of nonequilibrium self-organization [1]. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated…

Complex dynamical properties of coupled Van der Pol-Duffing oscillators with balanced loss and gain

- Physics
- 2021

We consider a Hamiltonian system of coupled Van der Pol-Duffing(VdPD) oscillators with balanced loss and gain. The system is analyzed perturbatively by using Renormalization Group(RG) techniques as…

Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

- HistoryPhysical Review X
- 2021

Orazio Scarlatella, 2, 3 Aashish A. Clerk, Rosario Fazio, 6 and Marco Schiró ∗ JEIP, USR 3573 CNRS, Collége de France, PSL Research University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05,…

Highly nonclassical phonon emission statistics through two-phonon loss of van der Pol oscillator

- PhysicsJournal of Applied Physics
- 2020

The ability to produce nonclassical wave in a system is essential for advances in quantum communication and computation. Here, we propose a scheme to generate highly nonclassical phonon emission…

Algebraic theory of quantum synchronization and limit cycles under dissipation

- PhysicsSciPost Physics
- 2022

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical…

Dynamic Framework for Criticality-Enhanced Quantum Sensing.

- PhysicsPhysical review letters
- 2021

A dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs) based on critical quantum dynamics is proposed and its divergent feature when approaching the critical point is demonstrated.

Quantum limit cycles and the Rayleigh and van der Pol oscillators

- Physics
- 2020

Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum…

Relaxation oscillations and frequency entrainment in quantum mechanics.

- PhysicsPhysical review. E
- 2020

The previously known steady state of such quantum oscillators in the weakly nonlinear regime is shown to emerge as a special case and the hallmark of strong nonlinearity-relaxation oscillations-is shown in quantum mechanics.

## References

SHOWING 1-10 OF 68 REFERENCES

Quantum synchronization of quantum van der Pol oscillators with trapped ions.

- PhysicsPhysical review letters
- 2013

This work investigates how quantum fluctuations affect phase locking of one or many van der Pol oscillators and finds that phase locking is much more robust in the quantum model than in the equivalent classical model.

Quantum synchronization of two Van der Pol oscillators

- Physics
- 2014

Synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime is studied. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak…

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators.

- PhysicsPhysical review letters
- 2016

It is demonstrated that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system.

Oscillation collapse in coupled quantum van der Pol oscillators.

- PhysicsPhysical review. E
- 2017

It is shown within the mean-field theory that a number of globally coupled oscillators undergo a transition from the synchronized periodic motion to the collective oscillation collapse, and a quantum many-body simulation suggests that the increase in the number of oscillators leads to a lower steady-state mean phonon number.

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

- PhysicsNew Journal of Physics
- 2019

We study the spectral properties of Markovian driven-dissipative quantum systems, focusing on the nonlinear quantum van der Pol oscillator as a paradigmatic example. We discuss a generalized Lehmann…

Observing quantum synchronization blockade in circuit quantum electrodynamics

- Physics
- 2018

High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime.…

Wigner function for a driven anharmonic oscillator

- Physics
- 1999

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state…

Quantum response theory for nonequilibrium steady states

- PhysicsPhysical Review Research
- 2019

We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discuss…

Quantum synchronization of a driven self-sustained oscillator.

- PhysicsPhysical review letters
- 2014

This work investigates synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum- mechanical self-sustained oscillator coupled to an external harmonic drive, and shows that there is a steplike crossover to a synchronized state as a function of the driving strength.

Entanglement tongue and quantum synchronization of disordered oscillators.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

The synchronization of dissipatively coupled van der Pol oscillators in the quantum limit is studied, when each oscillator is near its quantum ground state and the critical coupling increases with detuning.