Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity
Abstract
We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational Gaudin-type integrability, and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop “dressing tails” of higher-body terms, reminiscent of the dressed local integrals of motion found in many-body localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation.
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1570503
- Alternate Identifier(s):
- OSTI ID: 1574856; OSTI ID: 1580949
- Grant/Contract Number:
- AC02-76SF00515; SC0019380; AC02-05CH11231
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 9 Journal Issue: 4; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS; Dynamic phase transitions; Quantum statistical mechanics; Spin dynamics; Atomic ensemble; Quantum dots; Chaos & nonlinear dynamics; Integrable systems; Atomic and Molecular Physics; Statistical Physics
Citation Formats
Bentsen, Gregory, Potirniche, Ionut-Dragos, Bulchandani, Vir B., Scaffidi, Thomas, Cao, Xiangyu, Qi, Xiao-Liang, Schleier-Smith, Monika, and Altman, Ehud. Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity. United States: N. p., 2019.
Web. doi:10.1103/PhysRevX.9.041011.
Bentsen, Gregory, Potirniche, Ionut-Dragos, Bulchandani, Vir B., Scaffidi, Thomas, Cao, Xiangyu, Qi, Xiao-Liang, Schleier-Smith, Monika, & Altman, Ehud. Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity. United States. doi:10.1103/PhysRevX.9.041011.
Bentsen, Gregory, Potirniche, Ionut-Dragos, Bulchandani, Vir B., Scaffidi, Thomas, Cao, Xiangyu, Qi, Xiao-Liang, Schleier-Smith, Monika, and Altman, Ehud. Tue .
"Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity". United States. doi:10.1103/PhysRevX.9.041011.
@article{osti_1570503,
title = {Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity},
author = {Bentsen, Gregory and Potirniche, Ionut-Dragos and Bulchandani, Vir B. and Scaffidi, Thomas and Cao, Xiangyu and Qi, Xiao-Liang and Schleier-Smith, Monika and Altman, Ehud},
abstractNote = {We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational Gaudin-type integrability, and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop “dressing tails” of higher-body terms, reminiscent of the dressed local integrals of motion found in many-body localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation.},
doi = {10.1103/PhysRevX.9.041011},
journal = {Physical Review. X},
number = 4,
volume = 9,
place = {United States},
year = {2019},
month = {10}
}
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DOI: 10.1103/PhysRevX.9.041011
DOI: 10.1103/PhysRevX.9.041011
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Works referenced in this record:
Separation of variables in the Gaudin model
journal, October 1989
- Sklyanin, E. K.
- Journal of Soviet Mathematics, Vol. 47, Issue 2
Local Conservation Laws and the Structure of the Many-Body Localized States
journal, September 2013
- Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.
- Physical Review Letters, Vol. 111, Issue 12
Photon-Mediated Interactions Between Distant Artificial Atoms
journal, November 2013
- van Loo, A. F.; Fedorov, A.; Lalumiere, K.
- Science, Vol. 342, Issue 6165
Quantum spin dynamics with pairwise-tunable, long-range interactions
journal, August 2016
- Hung, C. -L.; González-Tudela, Alejandro; Cirac, J. Ignacio
- Proceedings of the National Academy of Sciences, Vol. 113, Issue 34
Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008
- Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
- Nature, Vol. 452, Issue 7189
Measuring the scrambling of quantum information
journal, October 2016
- Swingle, Brian; Bentsen, Gregory; Schleier-Smith, Monika
- Physical Review A, Vol. 94, Issue 4
Level Clustering in the Regular Spectrum
journal, September 1977
- Berry, M. V.; Tabor, M.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 356, Issue 1686
Quantum phase magnification
journal, June 2016
- Hosten, O.; Krishnakumar, R.; Engelsen, N. J.
- Science, Vol. 352, Issue 6293
Cavity QED Engineering of Spin Dynamics and Squeezing in a Spinor Gas
journal, November 2017
- Masson, Stuart J.; Barrett, M. D.; Parkins, Scott
- Physical Review Letters, Vol. 119, Issue 21
Chaos in quantum channels
journal, February 2016
- Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.
- Journal of High Energy Physics, Vol. 2016, Issue 2
Squeezing the collective spin of a dilute atomic ensemble by cavity feedback
journal, February 2010
- Schleier-Smith, Monika H.; Leroux, Ian D.; Vuletić, Vladan
- Physical Review A, Vol. 81, Issue 2
Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen–Cooper–Schrieffer–type integrable systems
journal, March 2009
- Skrypnyk, T.
- Journal of Mathematical Physics, Vol. 50, Issue 3
Spinor Self-Ordering of a Quantum Gas in a Cavity
journal, October 2018
- Kroeze, Ronen M.; Guo, Yudan; Vaidya, Varun D.
- Physical Review Letters, Vol. 121, Issue 16
Gaudin model, Bethe Ansatz and critical level
journal, December 1994
- Feigin, Boris; Frenkel, Edward; Reshetikhin, Nikolai
- Communications in Mathematical Physics, Vol. 166, Issue 1
Constructing local integrals of motion in the many-body localized phase
journal, February 2015
- Chandran, Anushya; Kim, Isaac H.; Vidal, Guifre
- Physical Review B, Vol. 91, Issue 8
Probing Scrambling Using Statistical Correlations between Randomized Measurements
journal, June 2019
- Vermersch, B.; Elben, A.; Sieberer, L. M.
- Physical Review X, Vol. 9, Issue 2
Supersolid formation in a quantum gas breaking a continuous translational symmetry
journal, March 2017
- Léonard, Julian; Morales, Andrea; Zupancic, Philip
- Nature, Vol. 543, Issue 7643
Black holes and the butterfly effect
journal, March 2014
- Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2014, Issue 3
Extreme Decoherence and Quantum Chaos
journal, January 2019
- Xu, Zhenyu; García-Pintos, Luis Pedro; Chenu, Aurélia
- Physical Review Letters, Vol. 122, Issue 1
Gapless spin-fluid ground state in a random quantum Heisenberg magnet
journal, May 1993
- Sachdev, Subir; Ye, Jinwu
- Physical Review Letters, Vol. 70, Issue 21
Tuning quantum measurements to control chaos
journal, March 2017
- Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
- Scientific Reports, Vol. 7, Issue 1
Dicke Quantum Spin Glass of Atoms and Photons
journal, December 2011
- Strack, Philipp; Sachdev, Subir
- Physical Review Letters, Vol. 107, Issue 27
Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
journal, September 2015
- Barontini, G.; Hohmann, L.; Haas, F.
- Science, Vol. 349, Issue 6254
Implementation of Cavity Squeezing of a Collective Atomic Spin
journal, February 2010
- Leroux, Ian D.; Schleier-Smith, Monika H.; Vuletić, Vladan
- Physical Review Letters, Vol. 104, Issue 7
Frustration and Glassiness in Spin Models with Cavity-Mediated Interactions
journal, December 2011
- Gopalakrishnan, Sarang; Lev, Benjamin L.; Goldbart, Paul M.
- Physical Review Letters, Vol. 107, Issue 27
Sign-Changing Photon-Mediated Atom Interactions in Multimode Cavity Quantum Electrodynamics
journal, May 2019
- Guo, Yudan; Kroeze, Ronen M.; Vaidya, Varun D.
- Physical Review Letters, Vol. 122, Issue 19
Transport and conservation laws
journal, May 1997
- Zotos, X.; Naef, F.; Prelovsek, P.
- Physical Review B, Vol. 55, Issue 17
Remarks on the notion of quantum integrability
journal, February 2011
- Caux, Jean-Sébastien; Mossel, Jorn
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, Issue 02
Spins coupled to a spin bath: From integrability to chaos
journal, February 2010
- Schliemann, John
- Physical Review B, Vol. 81, Issue 8
Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity
journal, August 2017
- Mivehvar, Farokh; Piazza, Francesco; Ritsch, Helmut
- Physical Review Letters, Vol. 119, Issue 6
Integrals of motion in the many-body localized phase
journal, February 2015
- Ros, V.; Müller, M.; Scardicchio, A.
- Nuclear Physics B, Vol. 891
Quantum phases of spinful Fermi gases in optical cavities
journal, April 2018
- Colella, E.; Citro, R.; Barsanti, M.
- Physical Review B, Vol. 97, Issue 13
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet
journal, May 2017
- Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
- Nature Physics, Vol. 13, Issue 8
New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras
journal, January 2005
- Skrypnyk, T.
- Physics Letters A, Vol. 334, Issue 5-6
Near-Unitary Spin Squeezing in
journal, June 2019
- Braverman, Boris; Kawasaki, Akio; Pedrozo-Peñafiel, Edwin
- Physical Review Letters, Vol. 122, Issue 22
An integrable case of the p + i p pairing Hamiltonian interacting with its environment
journal, January 2016
- Lukyanenko, Inna; Isaac, Phillip S.; Links, Jon
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 8
Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser
journal, July 2018
- Norcia, Matthew A.; Lewis-Swan, Robert J.; Cline, Julia R. K.
- Science, Vol. 361, Issue 6399
The link between integrability, level crossings and exact solution in quantum models
journal, December 2008
- Owusu, H. K.; Wagh, K.; Yuzbashyan, E. A.
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 3
Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
journal, January 1984
- Bohigas, O.; Giannoni, M. J.; Schmit, C.
- Physical Review Letters, Vol. 52, Issue 1
Formation of a Spin Texture in a Quantum Gas Coupled to a Cavity
journal, May 2018
- Landini, M.; Dogra, N.; Kroeger, K.
- Physical Review Letters, Vol. 120, Issue 22
Equilibration of quasi-integrable systems
journal, February 2019
- Goldfriend, Tomer; Kurchan, Jorge
- Physical Review E, Vol. 99, Issue 2
Resilience of scrambling measurements
journal, June 2018
- Swingle, Brian; Yunger Halpern, Nicole
- Physical Review A, Vol. 97, Issue 6
Entangling atoms in bad cavities
journal, August 2002
- Sørensen, Anders Søndberg; Mølmer, Klaus
- Physical Review A, Vol. 66, Issue 2
Coherent Atom Interactions Mediated by Dark-State Polaritons
journal, May 2002
- André, A.; Duan, L. -M.; Lukin, M. D.
- Physical Review Letters, Vol. 88, Issue 24
A bound on chaos
journal, August 2016
- Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 8
Cavity-Quantum-Electrodynamical Toolbox for Quantum Magnetism
journal, March 2019
- Mivehvar, Farokh; Ritsch, Helmut; Piazza, Francesco
- Physical Review Letters, Vol. 122, Issue 11
Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering
journal, November 2003
- Black, Adam T.; Chan, Hilton W.; Vuletić, Vladan
- Physical Review Letters, Vol. 91, Issue 20
Remarks on the Sachdev-Ye-Kitaev model
journal, November 2016
- Maldacena, Juan; Stanford, Douglas
- Physical Review D, Vol. 94, Issue 10
Chaos in Holography
journal, September 2016
- Jensen, Kristan
- Physical Review Letters, Vol. 117, Issue 11
Coupling superconducting qubits via a cavity bus
journal, September 2007
- Majer, J.; Chow, J. M.; Gambetta, J. M.
- Nature, Vol. 449, Issue 7161
Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms
journal, January 2019
- Davis, Emily J.; Bentsen, Gregory; Homeier, Lukas
- Physical Review Letters, Vol. 122, Issue 1
Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model
journal, April 2019
- Lewis-Swan, R. J.; Safavi-Naini, A.; Bollinger, J. J.
- Nature Communications, Vol. 10, Issue 1
On integrable Hamiltonians for higher spin XXZ chain
journal, January 2003
- Bytsko, Andrei G.
- Journal of Mathematical Physics, Vol. 44, Issue 9
Singular point analysis of the Gaudin equations
journal, June 2008
- Schmidt, J. R.
- Canadian Journal of Physics, Vol. 86, Issue 6
Dephasing and the Steady State in Quantum Many-Particle Systems
journal, March 2008
- Barthel, T.; Schollwöck, U.
- Physical Review Letters, Vol. 100, Issue 10
Integrable matrix theory: Level statistics
journal, September 2016
- Scaramazza, Jasen A.; Shastry, B. Sriram; Yuzbashyan, Emil A.
- Physical Review E, Vol. 94, Issue 3
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application
journal, March 1980
- Benettin, Giancarlo; Galgani, Luigi; Giorgilli, Antonio
- Meccanica, Vol. 15, Issue 1
Out-of-time-order operators and the butterfly effect
journal, September 2018
- Cotler, Jordan S.; Ding, Dawei; Penington, Geoffrey R.
- Annals of Physics, Vol. 396
Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point
journal, February 2013
- Vosk, Ronen; Altman, Ehud
- Physical Review Letters, Vol. 110, Issue 6
Supermode-density-wave-polariton condensation with a Bose–Einstein condensate in a multimode cavity
journal, February 2017
- Kollár, Alicia J.; Papageorge, Alexander T.; Vaidya, Varun D.
- Nature Communications, Vol. 8, Issue 1
Integrable spin-${\frac{1}{2}}$ Richardson–Gaudin XYZ models in an arbitrary magnetic field
journal, January 2019
- Claeys, Pieter W.; Dimo, Claude; De Baerdemacker, Stijn
- Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 8
Diagonalisation d'une classe d'hamiltoniens de spin
journal, January 1976
- Gaudin, M.
- Journal de Physique, Vol. 37, Issue 10
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015
- Nandkishore, Rahul; Huse, David A.
- Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
Bekenstein-Hawking Entropy and Strange Metals
journal, November 2015
- Sachdev, Subir
- Physical Review X, Vol. 5, Issue 4
Cavity-QED simulator of slow and fast scrambling
journal, May 2019
- Marino, J.; Rey, A. M.
- Physical Review A, Vol. 99, Issue 5
Solutions of the Gaudin equation and Gaudin algebras
journal, June 2005
- Balantekin, A. B.; Dereli, T.; Pehlivan, Y.
- Journal of Physics A: Mathematical and General, Vol. 38, Issue 25
Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
journal, October 2018
- Iyoda, Eiki; Katsura, Hosho; Sagawa, Takahiro
- Physical Review D, Vol. 98, Issue 8
Spin chains in magnetic field, non-skew-symmetric classical r-matrices and BCS-type integrable systems
journal, January 2009
- Skrypnyk, T.
- Nuclear Physics B, Vol. 806, Issue 3
Negative-Mass Instability of the Spin and Motion of an Atomic Gas Driven by Optical Cavity Backaction
journal, January 2018
- Kohler, Jonathan; Gerber, Justin A.; Dowd, Emma
- Physical Review Letters, Vol. 120, Issue 1
Fermionic localization of the schwarzian theory
journal, October 2017
- Stanford, Douglas; Witten, Edward
- Journal of High Energy Physics, Vol. 2017, Issue 10
Decoherence, Chaos, and the Correspondence Principle
journal, May 1998
- Habib, Salman; Shizume, Kosuke; Zurek, Wojciech Hubert
- Physical Review Letters, Vol. 80, Issue 20
Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method
journal, August 1987
- Goldhirsch, Isaac; Sulem, Pierre-Louis; Orszag, Steven A.
- Physica D: Nonlinear Phenomena, Vol. 27, Issue 3
Non-skew-symmetric classical r -matrices and integrable cases of the reduced BCS model
journal, November 2009
- Skrypnyk, T.
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 47
Phenomenology of fully many-body-localized systems
journal, November 2014
- Huse, David A.; Nandkishore, Rahul; Oganesyan, Vadim
- Physical Review B, Vol. 90, Issue 17