Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics
Abstract
Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. Here, we introduce counterdiabatic Born–Oppenheimer dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born–Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each sub-system. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.
- Authors:
-
- Heriot-Watt Univ., Edinburgh (United Kingdom). SUPA, Inst. of Photonics and Quantum Sciences; Univ. of Massachusetts, Boston, MA (United States). Dept. of Physics
- Univ. of Massachusetts, Boston, MA (United States). Dept. of Physics; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; SUPA
- OSTI Identifier:
- 1483508
- Report Number(s):
- LA-UR-18-22569
Journal ID: ISSN 1367-2630
- Grant/Contract Number:
- 89233218CNA000001; EP/L015110/1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 8; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Atomic and Nuclear Physics; quantum dynamics; quantum control; Born–Oppenheimer approximation; transitionless quantum driving
Citation Formats
Duncan, Callum W., and Campo, Adolfo del. Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics. United States: N. p., 2018.
Web. doi:10.1088/1367-2630/aad437.
Duncan, Callum W., & Campo, Adolfo del. Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics. United States. https://doi.org/10.1088/1367-2630/aad437
Duncan, Callum W., and Campo, Adolfo del. Tue .
"Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics". United States. https://doi.org/10.1088/1367-2630/aad437. https://www.osti.gov/servlets/purl/1483508.
@article{osti_1483508,
title = {Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics},
author = {Duncan, Callum W. and Campo, Adolfo del},
abstractNote = {Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. Here, we introduce counterdiabatic Born–Oppenheimer dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born–Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each sub-system. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.},
doi = {10.1088/1367-2630/aad437},
journal = {New Journal of Physics},
number = 8,
volume = 20,
place = {United States},
year = {Tue Aug 07 00:00:00 EDT 2018},
month = {Tue Aug 07 00:00:00 EDT 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 8 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity
journal, February 2010
- Chen, Xi; Ruschhaupt, A.; Schmidt, S.
- Physical Review Letters, Vol. 104, Issue 6
Adiabatic Population Transfer with Control Fields
journal, November 2003
- Demirplak, Mustafa; Rice, Stuart A.
- The Journal of Physical Chemistry A, Vol. 107, Issue 46
Assisted Adiabatic Passage Revisited †
journal, April 2005
- Demirplak, Mustafa; Rice, Stuart A.
- The Journal of Physical Chemistry B, Vol. 109, Issue 14
Optimally robust shortcuts to population inversion in two-level quantum systems
journal, September 2012
- Ruschhaupt, A.; Chen, Xi; Alonso, D.
- New Journal of Physics, Vol. 14, Issue 9
Fast-Forward Assisted STIRAP
journal, March 2015
- Masuda, Shumpei; Rice, Stuart A.
- The Journal of Physical Chemistry A, Vol. 119, Issue 14
High-fidelity quantum driving
journal, December 2011
- Bason, Mark G.; Viteau, Matthieu; Malossi, Nicola
- Nature Physics, Vol. 8, Issue 2
Experimental Implementation of Assisted Quantum Adiabatic Passage in a Single Spin
journal, June 2013
- Zhang, Jingfu; Shim, Jeong Hyun; Niemeyer, Ingo
- Physical Review Letters, Vol. 110, Issue 24
Scrutinizing the double superconducting gaps and strong coupling pairing in (Li1−xFex)OHFeSe
journal, January 2016
- Du, Zengyi; Yang, Xiong; Lin, Hai
- Nature Communications, Vol. 7, Issue 1
Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system
journal, November 2016
- Zhou, Brian B.; Baksic, Alexandre; Ribeiro, Hugo
- Nature Physics, Vol. 13, Issue 4
Fast-forward of adiabatic dynamics in quantum mechanics
journal, November 2009
- Masuda, Shumpei; Nakamura, Katsuhiro
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, Issue 2116
Fast atomic transport without vibrational heating
journal, January 2011
- Torrontegui, E.; Ibáñez, S.; Chen, Xi
- Physical Review A, Vol. 83, Issue 1
Optimized sympathetic cooling of atomic mixtures via fast adiabatic strategies
journal, November 2011
- Choi, Stephen; Onofrio, Roberto; Sundaram, Bala
- Physical Review A, Vol. 84, Issue 5
Squeezing and robustness of frictionless cooling strategies
journal, October 2012
- Choi, Stephen; Onofrio, Roberto; Sundaram, Bala
- Physical Review A, Vol. 86, Issue 4
Ehrenfest dynamics and frictionless cooling methods
journal, November 2013
- Choi, Stephen; Onofrio, Roberto; Sundaram, Bala
- Physical Review A, Vol. 88, Issue 5
Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving
journal, April 2014
- Deffner, Sebastian; Jarzynski, Christopher; del Campo, Adolfo
- Physical Review X, Vol. 4, Issue 2
Shortcuts to adiabaticity using flow fields
journal, December 2017
- Patra, Ayoti; Jarzynski, Christopher
- New Journal of Physics, Vol. 19, Issue 12
Fast forward to the classical adiabatic invariant
journal, March 2017
- Jarzynski, Christopher; Deffner, Sebastian; Patra, Ayoti
- Physical Review E, Vol. 95, Issue 3
Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
journal, September 2016
- An, Shuoming; Lv, Dingshun; del Campo, Adolfo
- Nature Communications, Vol. 7, Issue 1
Frictionless quantum quenches in ultracold gases: A quantum-dynamical microscope
journal, September 2011
- del Campo, A.
- Physical Review A, Vol. 84, Issue 3
Shortcuts to adiabaticity in a time-dependent box
journal, September 2012
- Campo, A. del; Boshier, M. G.
- Scientific Reports, Vol. 2, Issue 1
Shortcuts to Adiabaticity by Counterdiabatic Driving
journal, September 2013
- del Campo, Adolfo
- Physical Review Letters, Vol. 111, Issue 10
Fast optimal transition between two equilibrium states
journal, September 2010
- Schaff, Jean-François; Song, Xiao-Li; Vignolo, Patrizia
- Physical Review A, Vol. 82, Issue 3
Shortcut to adiabaticity for an interacting Bose-Einstein condensate
journal, January 2011
- Schaff, J. -F.; Song, X. -L.; Capuzzi, P.
- EPL (Europhysics Letters), Vol. 93, Issue 2
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas
journal, April 2015
- Rohringer, W.; Fischer, D.; Steiner, F.
- Scientific Reports, Vol. 5, Issue 1
Shortcuts to adiabaticity in the strongly coupled regime: Nonadiabatic control of a unitary Fermi gas
journal, January 2018
- Deng, Shujin; Diao, Pengpeng; Yu, Qianli
- Physical Review A, Vol. 97, Issue 1
Superadiabatic quantum friction suppression in finite-time thermodynamics
journal, April 2018
- Deng, Shujin; Chenu, Aurélia; Diao, Pengpeng
- Science Advances, Vol. 4, Issue 4
Assisted Finite-Rate Adiabatic Passage Across a Quantum Critical Point: Exact Solution for the Quantum Ising Model
journal, September 2012
- del Campo, Adolfo; Rams, Marek M.; Zurek, Wojciech H.
- Physical Review Letters, Vol. 109, Issue 11
Universality of phase transition dynamics: Topological defects from symmetry breaking
journal, March 2014
- del Campo, Adolfo; Zurek, Wojciech H.
- International Journal of Modern Physics A, Vol. 29, Issue 08
Controlling quantum critical dynamics of isolated systems
journal, February 2015
- del Campo, A.; Sengupta, K.
- The European Physical Journal Special Topics, Vol. 224, Issue 1
Counterdiabatic driving of the quantum Ising model
journal, December 2014
- Damski, Bogdan
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 12
Transitionless quantum driving for spin systems
journal, June 2013
- Takahashi, Kazutaka
- Physical Review E, Vol. 87, Issue 6
Adiabatic tracking of quantum many-body dynamics
journal, December 2014
- Saberi, Hamed; Opatrný, Tomáš; Mølmer, Klaus
- Physical Review A, Vol. 90, Issue 6
Local shortcut to adiabaticity for quantum many-body systems
journal, June 2016
- Mukherjee, Victor; Montangero, Simone; Fazio, Rosario
- Physical Review A, Vol. 93, Issue 6
Shortcuts to adiabaticity for quantum annealing
journal, January 2017
- Takahashi, Kazutaka
- Physical Review A, Vol. 95, Issue 1
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
journal, August 2016
- Okuyama, Manaka; Takahashi, Kazutaka
- Physical Review Letters, Vol. 117, Issue 7
Minimizing irreversible losses in quantum systems by local counterdiabatic driving
journal, May 2017
- Sels, Dries; Polkovnikov, Anatoli
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 20
Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation
book, January 2007
- Köuppel, H.; Domcke, W.; Cederbaum, L. S.
- Advances in Chemical Physics
Zur Quantentheorie der Molekeln
journal, January 1924
- Born, M.; Heisenberg, W.
- Annalen der Physik, Vol. 379, Issue 9
Realizations of Magnetic-Monopole Gauge Fields: Diatoms and Spin Precession
journal, March 1986
- Moody, John; Shapere, A.; Wilczek, Frank
- Physical Review Letters, Vol. 56, Issue 9
The Born-Oppenheimer electric gauge force is repulsive near degeneracies
journal, July 1990
- Berry, M. V.; Lim, R.
- Journal of Physics A: Mathematical and General, Vol. 23, Issue 13
The Berry connection and Born–Oppenheimer method
journal, March 1992
- Bohm, A.; Kendrick, B.; Loewe, Mark E.
- Journal of Mathematical Physics, Vol. 33, Issue 3
Is the Molecular Berry Phase an Artifact of the Born-Oppenheimer Approximation?
journal, December 2014
- Min, Seung Kyu; Abedi, Ali; Kim, Kwang S.
- Physical Review Letters, Vol. 113, Issue 26
Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients
journal, October 1992
- Payne, M. C.; Teter, M. P.; Allan, D. C.
- Reviews of Modern Physics, Vol. 64, Issue 4
Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ( O
journal, July 1993
- Barnett, Robert N.; Landman, Uzi
- Physical Review B, Vol. 48, Issue 4
Chemical Reaction Dynamics Beyond the Born-Oppenheimer Approximation
journal, October 1998
- Butler, Laurie J.
- Annual Review of Physical Chemistry, Vol. 49, Issue 1
Time-Dependent Properties of Liquid Water: A Comparison of Car−Parrinello and Born−Oppenheimer Molecular Dynamics Simulations
journal, July 2006
- Kuo, I-Feng W.; Mundy, Christopher J.; McGrath, Matthew J.
- Journal of Chemical Theory and Computation, Vol. 2, Issue 5
Time-Reversible Born-Oppenheimer Molecular Dynamics
journal, September 2006
- Niklasson, Anders M. N.; Tymczak, C. J.; Challacombe, Matt
- Physical Review Letters, Vol. 97, Issue 12
Breakdown of the adiabatic Born–Oppenheimer approximation in graphene
journal, February 2007
- Pisana, Simone; Lazzeri, Michele; Casiraghi, Cinzia
- Nature Materials, Vol. 6, Issue 3
Extended Born-Oppenheimer Molecular Dynamics
journal, March 2008
- Niklasson, Anders M. N.
- Physical Review Letters, Vol. 100, Issue 12
Geometric integration in Born-Oppenheimer molecular dynamics
journal, December 2011
- Odell, Anders; Delin, Anna; Johansson, Börje
- The Journal of Chemical Physics, Vol. 135, Issue 22
Energy conserving, linear scaling Born-Oppenheimer molecular dynamics
journal, October 2012
- Cawkwell, M. J.; Niklasson, Anders M. N.
- The Journal of Chemical Physics, Vol. 137, Issue 13
Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics
journal, December 2013
- Lin, Lin; Lu, Jianfeng; Shao, Sihong
- Entropy, Vol. 16, Issue 1
Boson sampling for molecular vibronic spectra
journal, August 2015
- Huh, Joonsuk; Guerreschi, Gian Giacomo; Peropadre, Borja
- Nature Photonics, Vol. 9, Issue 9
Vibronic Boson Sampling: Generalized Gaussian Boson Sampling for Molecular Vibronic Spectra at Finite Temperature
journal, August 2017
- Huh, Joonsuk; Yung, Man-Hong
- Scientific Reports, Vol. 7, Issue 1
Quantum optical emulation of molecular vibronic spectroscopy using a trapped-ion device
journal, January 2018
- Shen, Yangchao; Lu, Yao; Zhang, Kuan
- Chemical Science, Vol. 9, Issue 4
The diagonal correction to the Born–Oppenheimer approximation: Its effect on the singlet–triplet splitting of CH 2 and other molecular effects
journal, April 1986
- Handy, Nicholas C.; Yamaguchi, Yukio; Schaefer, Henry F.
- The Journal of Chemical Physics, Vol. 84, Issue 8
Corrections to the Born-Oppenheimer approximation by means of perturbation theory
journal, October 1994
- Fernández, Francisco M.
- Physical Review A, Vol. 50, Issue 4
The adiabatic approximation
journal, April 1996
- Handy, Nicholas C.; Lee, Aaron M.
- Chemical Physics Letters, Vol. 252, Issue 5-6
In pursuit of the ab initio limit for conformational energy prototypes
journal, June 1998
- Császár, Attila G.; Allen, Wesley D.; Schaefer, Henry F.
- The Journal of Chemical Physics, Vol. 108, Issue 23
The diagonal Born–Oppenheimer correction beyond the Hartree–Fock approximation
journal, March 2003
- Valeev, Edward F.; Sherrill, C. David
- The Journal of Chemical Physics, Vol. 118, Issue 9
Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory
journal, October 2006
- Gauss, Jürgen; Tajti, Attila; Kállay, Mihály
- The Journal of Chemical Physics, Vol. 125, Issue 14
Quantitative quantum chemistry
journal, August 2008
- Helgaker, Trygve; Klopper, Wim; Tew, David P.
- Molecular Physics, Vol. 106, Issue 16-18
On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods
journal, April 2016
- Gherib, Rami; Ye, Liyuan; Ryabinkin, Ilya G.
- The Journal of Chemical Physics, Vol. 144, Issue 15
A time dependent Born-Oppenheimer approximation
journal, February 1980
- Hagedorn, George A.
- Communications in Mathematical Physics, Vol. 77, Issue 1
Riemannian structure on manifolds of quantum states
journal, September 1980
- Provost, J. P.; Vallee, G.
- Communications in Mathematical Physics, Vol. 76, Issue 3
On the consistency, extremal, and global properties of counterdiabatic fields
journal, October 2008
- Demirplak, Mustafa; Rice, Stuart A.
- The Journal of Chemical Physics, Vol. 129, Issue 15
Conditional probability amplitudes in wave mechanics
journal, March 1975
- Hunter, Geoffrey
- International Journal of Quantum Chemistry, Vol. 9, Issue 2
Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function
journal, September 2010
- Abedi, Ali; Maitra, Neepa T.; Gross, E. K. U.
- Physical Review Letters, Vol. 105, Issue 12
Quantum-Mechanical Description of Two Coupled Harmonic Oscillators
journal, November 1968
- Estes, Lee E.; Keil, Thomas H.; Narducci, Lorenzo M.
- Physical Review, Vol. 175, Issue 1
Illustrative example of Feynman’s rest of the universe
journal, January 1999
- Han, D.; Kim, Y. S.; Noz, Marilyn E.
- American Journal of Physics, Vol. 67, Issue 1
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
journal, January 2004
- Plenio, M. B.; Hartley, J.; Eisert, J.
- New Journal of Physics, Vol. 6
Coupled harmonic oscillators and their quantum entanglement
journal, April 2018
- Makarov, Dmitry N.
- Physical Review E, Vol. 97, Issue 4
Coupled quantized mechanical oscillators
journal, February 2011
- Brown, K. R.; Ospelkaus, C.; Colombe, Y.
- Nature, Vol. 471, Issue 7337
Trapped-ion antennae for the transmission of quantum information
journal, February 2011
- Harlander, M.; Lechner, R.; Brownnutt, M.
- Nature, Vol. 471, Issue 7337
Quantum simulations with trapped ions
journal, April 2012
- Blatt, R.; Roos, C. F.
- Nature Physics, Vol. 8, Issue 4
Experimental quantum simulations of many-body physics with trapped ions
journal, January 2012
- Schneider, Ch; Porras, Diego; Schaetz, Tobias
- Reports on Progress in Physics, Vol. 75, Issue 2
High-Fidelity Rapid Ground-State Loading of an Ultracold Gas into an Optical Lattice
journal, August 2014
- Masuda, Shumpei; Nakamura, Katsuhiro; del Campo, Adolfo
- Physical Review Letters, Vol. 113, Issue 6
Wave Functions for the Hydrogen Atom in Spheroidal Coordinates I: The Derivation and Properties of the Functions
journal, May 1958
- Coulson, C. A.; Robinson, P. D.
- Proceedings of the Physical Society, Vol. 71, Issue 5
Works referencing / citing this record:
Focus on Shortcuts to Adiabaticity
journal, May 2019
- del Campo, Adolfo; Kim, Kihwan
- New Journal of Physics, Vol. 21, Issue 5
Shortcuts to adiabaticity: Concepts, methods, and applications
journal, October 2019
- Guéry-Odelin, D.; Ruschhaupt, A.; Kiely, A.
- Reviews of Modern Physics, Vol. 91, Issue 4
Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions
journal, July 2019
- Urzúa, Alejandro R.; Ramos-Prieto, Irán; Fernández-Guasti, Manuel
- Quantum Reports, Vol. 1, Issue 1
Floquet-engineering counterdiabatic protocols in quantum many-body systems
text, January 2019
- Claeys, Pieter W.; Pandey, Mohit; Sels, Dries
- arXiv