Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations

Zhang, Xin H. H.; Baranger, Harold U.

doi:10.1103/physreva.103.033711

Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations

Journal Article · Wed Mar 24 00:00:00 EDT 2021 · Physical Review A

DOI:https://doi.org/10.1103/physreva.103.033711· OSTI ID:1782488

^[1]; ^[2]

Duke Univ., Durham, NC (United States); Duke University, Dept of Physics
Duke Univ., Durham, NC (United States)

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 diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. Furthermore, the physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, Z₂ symmetry breaking, PT symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.

View Accepted Manuscript (DOE)

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0005237

OSTI ID:: 1782488

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 103; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (51)

Few-mode geometric description of a driven-dissipative phase transition in an open quantum system Krimer, Dmitry O.; Pletyukhov, Mikhail arXiv https://doi.org/10.48550/arxiv.1808.00030	text	January 2018
Quantum Optics Walls, D. F.; Milburn, Gerard J. https://doi.org/10.1007/978-3-540-28574-8	book	January 2008
Statistical Methods in Quantum Optics 2 Carmichael, Howard J. Theoretical and Mathematical Physics https://doi.org/10.1007/978-3-540-71320-3	book	January 2008
Condensed Matter Field Theory Altland, Alexander; Simons, Ben D. https://doi.org/10.1017/CBO9780511789984	book	August 2010
Quantum Phase Transitions Sachdev, Subir https://doi.org/10.1017/CBO9780511973765	book	January 2011
Field Theory of Non-Equilibrium Systems Kamenev, Alex https://doi.org/10.1017/CBO9781139003667	book	January 2011
Nonequilibrium Many-Body Theory of Quantum Systems Stefanucci, Gianluca; van Leeuwen, Robert https://doi.org/10.1017/CBO9781139023979	book	March 2013
Quantum many-body systems out of equilibrium Eisert, J.; Friesdorf, M.; Gogolin, C. Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3215	journal	February 2015
Non-Hermitian physics and PT symmetry El-Ganainy, Ramy; Makris, Konstantinos G.; Khajavikhan, Mercedeh Nature Physics, Vol. 14, Issue 1 https://doi.org/10.1038/nphys4323	journal	January 2018
Signatures of a dissipative phase transition in photon correlation measurements Fink, Thomas; Schade, Anne; Höfling, Sven Nature Physics, Vol. 14, Issue 4 https://doi.org/10.1038/s41567-017-0020-9	journal	December 2017
Analytical and numerical results for the steady state in cooperative resonance fluorescence Carmichael, H. J. Journal of Physics B: Atomic and Molecular Physics, Vol. 13, Issue 18 https://doi.org/10.1088/0022-3700/13/18/009	journal	September 1980
Making sense of non-Hermitian Hamiltonians Bender, Carl M. Reports on Progress in Physics, Vol. 70, Issue 6 https://doi.org/10.1088/0034-4885/70/6/R03	journal	May 2007
Keldysh field theory for driven open quantum systems Sieberer, L. M.; Buchhold, M.; Diehl, S. Reports on Progress in Physics, Vol. 79, Issue 9 https://doi.org/10.1088/0034-4885/79/9/096001	journal	August 2016
Quantum theory of optical bistability. I. Nonlinear polarisability model Drummond, P. D.; Walls, D. F. Journal of Physics A: Mathematical and General, Vol. 13, Issue 2 https://doi.org/10.1088/0305-4470/13/2/034	journal	February 1980
Classical critical dynamics in quadratically driven Kerr resonators Verstraelen, Wouter; Wouters, Michiel Physical Review A, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevA.101.043826	journal	April 2020
Nonequilibrium magnetic phases in spin lattices with gain and loss Huber, Julian; Kirton, Peter; Rabl, Peter Physical Review A, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevA.102.012219	journal	July 2020
Dissipative phase transition in a central spin system Kessler, E. M.; Giedke, G.; Imamoglu, A. Physical Review A, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevA.86.012116	journal	July 2012
Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities Torre, Emanuele G. Dalla; Diehl, Sebastian; Lukin, Mikhail D. Physical Review A, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevA.87.023831	journal	February 2013
Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators Casteels, W.; Storme, F.; Le Boité, A. Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevA.93.033824	journal	March 2016
Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions Bartolo, Nicola; Minganti, Fabrizio; Casteels, Wim Physical Review A, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevA.94.033841	journal	September 2016
Critical dynamical properties of a first-order dissipative phase transition Casteels, W.; Fazio, R.; Ciuti, C. Physical Review A, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevA.95.012128	journal	January 2017
Emergent equilibrium in many-body optical bistability Foss-Feig, M.; Niroula, P.; Young, J. T. Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.043826	journal	April 2017
Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement Casteels, Wim; Wouters, Michiel Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.043833	journal	April 2017
Dissipative phase transition in the open quantum Rabi model Hwang, Myung-Joong; Rabl, Peter; Plenio, Martin B. Physical Review A, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevA.97.013825	journal	January 2018
Spectral theory of Liouvillians for dissipative phase transitions Minganti, Fabrizio; Biella, Alberto; Bartolo, Nicola Physical Review A, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevA.98.042118	journal	October 2018
Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator Pietikäinen, I.; Tuorila, J.; Golubev, D. S. Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevA.99.063828	journal	June 2019
Non-Hermitian dynamics without dissipation in quantum systems Wang, Yu-Xin; Clerk, A. A. Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevA.99.063834	journal	June 2019
Validity of mean-field theory in a dissipative critical system: Liouvillian gap, PT -symmetric antigap, and permutational symmetry in the X Y Z model Huybrechts, Dolf; Minganti, Fabrizio; Nori, Franco Physical Review B, Vol. 101, Issue 21 https://doi.org/10.1103/PhysRevB.101.214302	journal	June 2020
Quantum Phase Transition in a Far-from-Equilibrium Steady State of an X Y Spin Chain Prosen, Tomaž; Pižorn, Iztok Physical Review Letters, Vol. 101, Issue 10 https://doi.org/10.1103/PhysRevLett.101.105701	journal	September 2008
Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems Diehl, Sebastian; Tomadin, Andrea; Micheli, Andrea Physical Review Letters, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevLett.105.015702	journal	July 2010
P T -Symmetric Quantum Liouvillean Dynamics Prosen, Tomaž Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.090404	journal	August 2012
Steady-State Phases and Tunneling-Induced Instabilities in the Driven Dissipative Bose-Hubbard Model Le Boité, Alexandre; Orso, Giuliano; Ciuti, Cristiano Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.233601	journal	June 2013
Critical Exponents Can Be Different on the Two Sides of a Transition: A Generic Mechanism Léonard, F.; Delamotte, B. Physical Review Letters, Vol. 115, Issue 20 https://doi.org/10.1103/PhysRevLett.115.200601	journal	November 2015
Probing a Dissipative Phase Transition via Dynamical Optical Hysteresis Rodriguez, S. R. K.; Casteels, W.; Storme, F. Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.247402	journal	June 2017
Quantum Critical Regime in a Quadratically Driven Nonlinear Photonic Lattice Rota, Riccardo; Minganti, Fabrizio; Ciuti, Cristiano Physical Review Letters, Vol. 122, Issue 11 https://doi.org/10.1103/PhysRevLett.122.110405	journal	March 2019
Few-Mode Geometric Description of a Driven-Dissipative Phase Transition in an Open Quantum System Krimer, Dmitry O.; Pletyukhov, Mikhail Physical Review Letters, Vol. 123, Issue 11 https://doi.org/10.1103/PhysRevLett.123.110604	journal	September 2019
Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition Heugel, Toni L.; Biondi, Matteo; Zilberberg, Oded Physical Review Letters, Vol. 123, Issue 17 https://doi.org/10.1103/PhysRevLett.123.173601	journal	October 2019
Squeezed Light Induced Symmetry Breaking Superradiant Phase Transition Zhu, C. J.; Ping, L. L.; Yang, Y. P. Physical Review Letters, Vol. 124, Issue 7 https://doi.org/10.1103/PhysRevLett.124.073602	journal	February 2020
Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity Geng, Z.; Peters, K. J. H.; Trichet, A. A. P. Physical Review Letters, Vol. 124, Issue 15 https://doi.org/10.1103/PhysRevLett.124.153603	journal	April 2020
Symmetry Breaking and Error Correction in Open Quantum Systems Lieu, Simon; Belyansky, Ron; Young, Jeremy T. Physical Review Letters, Vol. 125, Issue 24 https://doi.org/10.1103/PhysRevLett.125.240405	journal	December 2020
Phase Diagram and Critical Exponents of a Dissipative Ising Spin Chain in a Transverse Magnetic Field Werner, Philipp; Völker, Klaus; Troyer, Matthias Physical Review Letters, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevLett.94.047201	journal	January 2005
Dissipation-Driven Phase Transition in Two-Dimensional Josephson Arrays Capriotti, Luca; Cuccoli, Alessandro; Fubini, Andrea Physical Review Letters, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevLett.94.157001	journal	April 2005
Nonequilibrium Quantum Criticality in Open Electronic Systems Mitra, Aditi; Takei, So; Kim, Yong Baek Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevLett.97.236808	journal	December 2006
Gaussian trajectory approach to dissipative phase transitions: The case of quadratically driven photonic lattices Verstraelen, Wouter; Rota, Riccardo; Savona, Vincenzo Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.022037	journal	May 2020
Driven-Dissipative Quantum Kerr Resonators: New Exact Solutions, Photon Blockade and Quantum Bistability Roberts, David; Clerk, Aashish A. Physical Review X, Vol. 10, Issue 2 https://doi.org/10.1103/PhysRevX.10.021022	journal	April 2020
Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions Carmichael, H. J. Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031028	journal	September 2015
Observation of the Photon-Blockade Breakdown Phase Transition Fink, J. M.; Dombi, A.; Vukics, A. Physical Review X, Vol. 7, Issue 1 https://doi.org/10.1103/PhysRevX.7.011012	journal	January 2017
Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice Fitzpatrick, Mattias; Sundaresan, Neereja M.; Li, Andy C. Y. Physical Review X, Vol. 7, Issue 1 https://doi.org/10.1103/PhysRevX.7.011016	journal	February 2017
Confining the state of light to a quantum manifold by engineered two-photon loss Leghtas, Z.; Touzard, S.; Pop, I. M. Science, Vol. 347, Issue 6224 https://doi.org/10.1126/science.aaa2085	journal	February 2015
Emergence of PT-symmetry breaking in open quantum systems Huber, Julian; Kirton, Peter; Rotter, Stefan SciPost Physics, Vol. 9, Issue 4 https://doi.org/10.21468/SciPostPhys.9.4.052	journal	January 2020
Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition Vukics, A.; Dombi, A.; Fink, J. M. Quantum, Vol. 3 https://doi.org/10.22331/q-2019-06-03-150	journal	June 2019

Similar Records

Noise and fluctuations in semiclassical gravity

Journal Article · Wed Jun 15 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States) · OSTI ID:7239163

Dissipation and quantum fluctuations in granular superconductivity

Journal Article · Sat Aug 01 00:00:00 EDT 1987 · Phys. Rev. B: Condens. Matter; (United States) · OSTI ID:6459649

Unitary evolution with fluctuations and dissipation

Journal Article · Tue Jul 23 20:00:00 EDT 2019 · Physical Review C · OSTI ID:1558045

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
77 NANOSCIENCE AND NANOTECHNOLOGY
Cavity quantum electrodynamics
Collective effects in quantum optics
Nonlinear optics
Quantum optics
Quantum phase transitions
Squeezing of quantum noise

Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations

Citation Formats

References (51)

Similar Records

Related Subjects