Adaptive rotating-wave approximation for driven open quantum systems

Baker, Brian; Li, Andy C. Y.; Irons, Nicholas; Earnest, Nathan; Koch, Jens

doi:10.1103/PhysRevA.98.052111

Title: Adaptive rotating-wave approximation for driven open quantum systems

Journal Article · Thu Nov 08 00:00:00 EST 2018 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.98.052111· OSTI ID:1498555

Baker, Brian ^[1];

^[2]; Irons, Nicholas ^[1]; Earnest, Nathan ^[3]; Koch, Jens ^[1]

Northwestern Univ., Evanston, IL (United States)
Northwestern Univ., Evanston, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Univ. of Chicago, Chicago, IL (United States)

In this study we present a numerical method to approximate the long-time asymptotic solution $$\rho_\infty(t)$$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation theory to rank individual drive terms according to their dynamical relevance, and adaptively determines an effective Hamiltonian. In the constructed rotating frame, $$\rho_\infty$$ is approximated by a time-independent, nonequilibrium steady-state. This steady-state can be computed with much better numerical efficiency than asymptotic long-time evolution of the system in the lab frame. We illustrate the use of this method by simulating recent transmission measurements of the heavy-fluxonium device, for which ordinary time-dependent simulations are severely challenging due to the presence of metastable states with lifetimes of the order of milliseconds.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 1498555

Report Number(s):: arXiv:1808.01247; FERMILAB-PUB-18-754-CD; PLRAAN; 1722213

Journal Information:: Physical Review A, Vol. 98, Issue 5; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

References (46)

Superconducting quantum bits Clarke, John; Wilhelm, Frank K. Nature, Vol. 453, Issue 7198 https://doi.org/10.1038/nature07128	journal	June 2008
Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics Wallraff, A.; Schuster, D. I.; Blais, A. Nature, Vol. 431, Issue 7005 https://doi.org/10.1038/nature02851	journal	September 2004
Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy Mananga, Eugène S.; Charpentier, Thibault The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3610943	journal	July 2011
Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback Vijay, R.; Macklin, C.; Slichter, D. H. Nature, Vol. 490, Issue 7418 https://doi.org/10.1038/nature11505	journal	October 2012
Asymptotic Floquet states of open quantum systems: the role of interaction Hartmann, M.; Poletti, D.; Ivanchenko, M. New Journal of Physics, Vol. 19, Issue 8 https://doi.org/10.1088/1367-2630/aa7ceb	journal	August 2017
Decoherence in Josephson Qubits from Dielectric Loss Martinis, John M.; Cooper, K. B.; McDermott, R. Physical Review Letters, Vol. 95, Issue 21 https://doi.org/10.1103/PhysRevLett.95.210503	journal	November 2005
Nonadiabatic effects in periodically driven dissipative open quantum systems Reimer, Viktor; Pedersen, Kim G. L.; Tanger, Niklas Physical Review A, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevA.97.043851	journal	April 2018
Scaling the Ion Trap Quantum Processor Monroe, C.; Kim, J. Science, Vol. 339, Issue 6124 https://doi.org/10.1126/science.1231298	journal	March 2013
Optimized driving of superconducting artificial atoms for improved single-qubit gates Chow, J. M.; DiCarlo, L.; Gambetta, J. M. Physical Review A, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevA.82.040305	journal	October 2010
Excitation of polyatomic molecules by radiation Larsen, David M.; Bloembergen, N. Optics Communications, Vol. 17, Issue 3 https://doi.org/10.1016/0030-4018(76)90253-4	journal	June 1976
On the generators of quantum dynamical semigroups Lindblad, G. Communications in Mathematical Physics, Vol. 48, Issue 2 https://doi.org/10.1007/BF01608499	journal	June 1976
Floquet-Liouville supermatrix approach: Time development of density-matrix operator and multiphoton resonance fluorescence spectra in intense laser fields Ho, Tak-San; Wang, Kwanghsi; Chu, Shih-I Physical Review A, Vol. 33, Issue 3 https://doi.org/10.1103/PhysRevA.33.1798	journal	March 1986
Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering Bukov, Marin; D'Alessio, Luca; Polkovnikov, Anatoli Advances in Physics, Vol. 64, Issue 2 https://doi.org/10.1080/00018732.2015.1055918	journal	March 2015
Superconducting quantum circuits at the surface code threshold for fault tolerance Barends, R.; Kelly, J.; Megrant, A. Nature, Vol. 508, Issue 7497 https://doi.org/10.1038/nature13171	journal	April 2014
Driven quantum tunneling Grifoni, Milena; Hänggi, Peter Physics Reports, Vol. 304, Issue 5-6 https://doi.org/10.1016/S0370-1573(98)00022-2	journal	October 1998
Protected gates for superconducting qubits Brooks, Peter; Kitaev, Alexei; Preskill, John Physical Review A, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevA.87.052306	journal	May 2013
Nonlinear response of the vacuum Rabi resonance Bishop, Lev S.; Chow, J. M.; Koch, Jens Nature Physics, Vol. 5, Issue 2 https://doi.org/10.1038/nphys1154	journal	December 2008
Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation Blais, Alexandre; Huang, Ren-Shou; Wallraff, Andreas Physical Review A, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevA.69.062320	journal	June 2004
Effective operator formalism for open quantum systems Reiter, Florentin; Sørensen, Anders S. Physical Review A, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevA.85.032111	journal	March 2012
Circuit QED and engineering charge-based superconducting qubits Girvin, S. M.; Devoret, M. H.; Schoelkopf, R. J. Physica Scripta, Vol. T137 https://doi.org/10.1088/0031-8949/2009/T137/014012	journal	December 2009
Generation of Fock states in a superconducting quantum circuit Hofheinz, Max; Weig, E. M.; Ansmann, M. Nature, Vol. 454, Issue 7202 https://doi.org/10.1038/nature07136	journal	July 2008
Quantum computing with trapped ions Haffner, H.; Roos, C.; Blatt, R. Physics Reports, Vol. 469, Issue 4 https://doi.org/10.1016/j.physrep.2008.09.003	journal	December 2008
Completely positive dynamical semigroups of N-level systems Gorini, Vittorio Journal of Mathematical Physics, Vol. 17, Issue 5 https://doi.org/10.1063/1.522979	journal	January 1976
Driven Open Quantum Systems and Floquet Stroboscopic Dynamics Restrepo, S.; Cerrillo, J.; Bastidas, V. M. Physical Review Letters, Vol. 117, Issue 25 https://doi.org/10.1103/PhysRevLett.117.250401	journal	December 2016
Analytical solutions for laser excitation of multilevel systems in the rotating-wave approximation Einwohner, T. H.; Wong, J.; Garrison, J. C. Physical Review A, Vol. 14, Issue 4 https://doi.org/10.1103/PhysRevA.14.1452	journal	October 1976
Perturbative approach to Markovian open quantum systems Li, Andy C. Y.; Petruccione, F.; Koch, Jens Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep04887	journal	May 2014
Completely Positive Approximate Solutions of Driven Open Quantum Systems Haddadfarshi, Farhang; Cui, Jian; Mintert, Florian Physical Review Letters, Vol. 114, Issue 13 https://doi.org/10.1103/PhysRevLett.114.130402	journal	April 2015
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
Collective Quantum Jumps of Rydberg Atoms Lee, Tony E.; Häffner, H.; Cross, M. C. Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.023602	journal	January 2012
Charge-insensitive qubit design derived from the Cooper pair box Koch, Jens; Yu, Terri M.; Gambetta, Jay Physical Review A, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevA.76.042319	journal	October 2007
A model for isotope separation via molecular multiphoton photodissociation Mukamel, Shaul; Jortner, Joshua Chemical Physics Letters, Vol. 40, Issue 1 https://doi.org/10.1016/0009-2614(76)80140-6	journal	May 1976
Quantum Computations with Cold Trapped Ions Cirac, J. I.; Zoller, P. Physical Review Letters, Vol. 74, Issue 20 https://doi.org/10.1103/PhysRevLett.74.4091	journal	May 1995
Markovian master equations Davies, E. B. Communications in Mathematical Physics, Vol. 39, Issue 2 https://doi.org/10.1007/BF01608389	journal	June 1974
Demonstrating a Driven Reset Protocol for a Superconducting Qubit Geerlings, K.; Leghtas, Z.; Pop, I. M. Physical Review Letters, Vol. 110, Issue 12 https://doi.org/10.1103/PhysRevLett.110.120501	journal	March 2013
The Theory of Open Quantum Systems Breuer, Heinz-Peter; Petruccione, Francesco Oxford University Press https://doi.org/10.1093/acprof:oso/9780199213900.001.0001	book	January 2007
Superconducting Circuits for Quantum Information: An Outlook Devoret, M. H.; Schoelkopf, R. J. Science, Vol. 339, Issue 6124 https://doi.org/10.1126/science.1231930	journal	March 2013
Dynamic steady state of periodically driven quantum systems Yudin, V. I.; Taichenachev, A. V.; Basalaev, M. Yu. Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevA.93.013820	journal	January 2016
Circuit QED with fluxonium qubits: Theory of the dispersive regime Zhu, Guanyu; Ferguson, David G.; Manucharyan, Vladimir E. Physical Review B, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevB.87.024510	journal	January 2013
Realization of a $Λ$ System with Metastable States of a Capacitively Shunted Fluxonium Earnest, N.; Chakram, S.; Lu, Y. Physical Review Letters, Vol. 120, Issue 15 https://doi.org/10.1103/PhysRevLett.120.150504	journal	April 2018
Quantum coherence and entanglement with ultracold atoms in optical lattices Bloch, Immanuel Nature, Vol. 453, Issue 7198 https://doi.org/10.1038/nature07126	journal	June 2008
QuTiP: An open-source Python framework for the dynamics of open quantum systems Johansson, J. R.; Nation, P. D.; Nori, Franco Computer Physics Communications, Vol. 183, Issue 8 https://doi.org/10.1016/j.cpc.2012.02.021	journal	August 2012
Floquet theorem with open systems and its applications Dai, C. M.; Shi, Z. C.; Yi, X. X. Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevA.93.032121	journal	March 2016
Microwave photonics with superconducting quantum circuits Gu, Xiu; Kockum, Anton Frisk; Miranowicz, Adam Physics Reports, Vol. 718-719 https://doi.org/10.1016/j.physrep.2017.10.002	journal	November 2017
Quantum Logic Gates in Optical Lattices Brennen, Gavin K.; Caves, Carlton M.; Jessen, Poul S. Physical Review Letters, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevLett.82.1060	journal	February 1999
Floquet-Markovian description of the parametrically driven, dissipative harmonic quantum oscillator Kohler, Sigmund; Dittrich, Thomas; Hänggi, Peter Physical Review E, Vol. 55, Issue 1 https://doi.org/10.1103/PhysRevE.55.300	journal	January 1997
Rotating-frame transformations: A new approximation for multiphoton absorption and dissociation in laser fields Whaley, K. B.; Light, J. C. Physical Review A, Vol. 29, Issue 3 https://doi.org/10.1103/PhysRevA.29.1188	journal	March 1984

Cited By (2)

Observation and stabilization of photonic Fock states in a hot radio-frequency resonator Gely, Mario F.; Kounalakis, Marios; Dickel, Christian Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aaw3101	journal	March 2019
Observation and stabilization of photonic Fock states in a hot radio-frequency resonator Gely, Mario F.; Kounalakis, Marios; Dickel, Christian arXiv https://doi.org/10.48550/arxiv.1901.07267	text	January 2019

Similar Records

Dynamical properties of a driven dissipative dimerized $S$ =1/2 chain

Journal Article · Fri Jan 22 00:00:00 EST 2021 · Physical Review. B · OSTI ID:1498555

Yarmohammadi, M.; Meyer, C.; Fauseweh, Benedikt; +2 more

Spatial correlations in driven-dissipative photonic lattices

Journal Article · Fri Dec 22 00:00:00 EST 2017 · New Journal of Physics · OSTI ID:1498555

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; +2 more

Adiabatic approximation for weakly open systems

Journal Article · Mon Aug 15 00:00:00 EDT 2005 · Physical Review. A · OSTI ID:1498555

Thunstroem, Patrik; Aaberg, Johan; Sjoeqvist, Erik

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
36 MATERIALS SCIENCE

Title: Adaptive rotating-wave approximation for driven open quantum systems

Citation Formats

References (46)

Cited By (2)

Similar Records

Related Subjects