Driven-Dissipative Quantum Kerr Resonators: New Exact Solutions, Photon Blockade and Quantum Bistability

@article{Roberts2020DrivenDissipativeQK,
  title={Driven-Dissipative Quantum Kerr Resonators: New Exact Solutions, Photon Blockade and Quantum Bistability},
  author={David C. Roberts and Aashish A Clerk},
  journal={Physical Review X},
  year={2020}
}
We present a new approach for deriving exact, closed-form solutions for the steady state of a wide class of driven-dissipative nonlinear resonators that is distinct from more common positive-$P$ function methods. Our method generalizes the coherent quantum absorber approach of Stannigel et al. to include nonlinear driving and dissipation, and relies crucially on exploiting the Segal-Bargmann representation of Fock space. Our solutions and method reveal a wealth of previously unexplored… 
Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations
We study a minimal model that has a driven-dissipative quantum phase transition, namely, a Kerr nonlinear oscillator subject to driving and dissipation. Using mean-field theory, exact
Driven-dissipative phase transition in a Kerr oscillator: From semi-classical $\mathcal{PT}$ symmetry to quantum fluctuations
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact
Method for driven-dissipative problems: Keldysh-Heisenberg equations
Driven-dissipative systems have recently attracted great attention due to the existence of novel physical phenomena with no analog in the equilibrium case. The Keldysh path-integral theory is a
Feedback-stabilized dynamical steady states in the Bose-Hubbard model
The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this paper, we investigate the
Exact description of quantum stochastic models as quantum resistors
We study the transport properties of generic out-of-equilibrium quantum systems connected to fermionic reservoirs. We develop a new perturbation scheme in the inverse system size, named 1/N
Entropy production dynamics in quench protocols of a driven-dissipative critical system
Driven-dissipative phase transitions are currently a topic of intense research due to the prospect of experimental realizations in quantum optical setups. The most paradigmatic model presenting such
Dissipative phase transition in systems with two-photon drive and nonlinear dissipation near the critical point
We study dissipative phase transition near the critical point for a system with two-photon driving and nonlinear dissipation. The proposed mean-field theory, which explicitly takes into account
Wigner negativity in the steady-state output of a Kerr parametric oscillator
The output field from a continuously driven linear parametric oscillator may exhibit considerably more squeezing than the intracavity field. Inspired by this fact, we explore the nonclassical
Quantum interactions with pulses of radiation
This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of
Multi-photon resonances in Josephson junction-cavity circuits
We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems
...
...

References

SHOWING 1-10 OF 83 REFERENCES
Exact results for Schrödinger cats in driven-dissipative systems and their feedback control
TLDR
It is demonstrated that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses, which are considered detrimental for the achievement of cat states.
Quantum theory of optical bistability. I. Nonlinear polarisability model
A quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium. This system displays bistability and hysteresis in
Wigner function for a driven anharmonic oscillator
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
Driven-dissipative preparation of entangled states in cascaded quantum-optical networks
We study the dissipative dynamics and the formation of entangled states in driven cascaded quantum networks, where multiple systems are coupled to a common unidirectional bath. Specifically, we
Applications of the Fokker-Planck equation in circuit quantum electrodynamics
We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the eld of circuit quantum electrodynamics. Using Fokker-Planck equations in
Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
TLDR
This work proposes an approach for fast, high-fidelity preparation and manipulation of cat states in a nonlinear cavity by the use of a parametric drive that is robust against single-photon loss and can be easily realized using superconducting circuits.
Spectral theory of Liouvillians for dissipative phase transitions
A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both
Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
A theory is developed to analytically represent a general class of driven-dissipative nonlinear resonators. The solvable model allows one to reveal the mesoscopic regime of interacting photons and
Transient macroscopic quantum superposition states in degenerate parametric oscillation: Calculations in the large-quantum-noise limit using the positive P representation.
  • Krippner, Munro, Reid
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1994
TLDR
Interference fringes which indicate the existence of the macroscopic superposition states are indeed predicted in regimes where the parametric nonlinearity is sufficiently large compared to the signal cavity losses.
Strongly Interacting Photons in a Nonlinear Cavity
We consider the dynamics of single photons in a nonlinear optical cavity. When the Kerr nonlinearities of atomic dark resonances are utilized, the cavity mode is well described by a spin- $1/2$
...
...