Exact results for models of multichannel quantum nonadiabatic transitions

Sinitsyn, N. A.

doi:10.1103/PhysRevA.90.062509

Title: Exact results for models of multichannel quantum nonadiabatic transitions

Journal Article · Thu Dec 11 00:00:00 EST 2014 · Physical Review A - Atomic, Molecular, and Optical Physics

DOI:https://doi.org/10.1103/PhysRevA.90.062509· OSTI ID:1234915

Sinitsyn, N. A. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1234915

Alternate ID(s):: OSTI ID: 1181603

Report Number(s):: LA-UR-14-28887; PLRAAN

Journal Information:: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 90, Issue 6; ISSN 1050-2947

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 16 works

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References (54)

Atomi orientati in campo magnetico variabile Majorana, Ettore Il Nuovo Cimento, Vol. 9, Issue 2 https://doi.org/10.1007/BF02960953	journal	February 1932
Non-Adiabatic Crossing of Energy Levels Zener, C. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 137, Issue 833 https://doi.org/10.1098/rspa.1932.0165	journal	September 1932
Double Stern-Gerlach Experiment and Related Collision Phenomena Rosen, N.; Zener, C. Physical Review, Vol. 40, Issue 4 https://doi.org/10.1103/PhysRev.40.502	journal	May 1932
The Theory of Nonadiabatic Transitions: Recent Development with Exponential Models Nikitin, E. E. Advances in Quantum Chemistry Volume 5 https://doi.org/10.1016/S0065-3276(08)60338-X	book	January 1970
Quantum mechanically exact analytical solutions of a two‐state exponential model Osherov, Vladimir I.; Nakamura, Hiroki The Journal of Chemical Physics, Vol. 105, Issue 7 https://doi.org/10.1063/1.472139	journal	August 1996
Dynamics of a Quantum Phase Transition Zurek, Wojciech H.; Dorner, Uwe; Zoller, Peter Physical Review Letters, Vol. 95, Issue 10 https://doi.org/10.1103/PhysRevLett.95.105701	journal	September 2005
Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again Damski, Bogdan; Zurek, Wojciech H. Physical Review A, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevA.73.063405	journal	June 2006
Critical dynamics of decoherence Damski, Bogdan; Quan, H. T.; Zurek, Wojciech H. Physical Review A, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevA.83.062104	journal	June 2011
Feshbach molecule production in fermionic atomic gases Gurarie, V. Physical Review A, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevA.80.023626	journal	August 2009
Production efficiency of Feshbach molecules in fermion systems Dobrescu, B. E.; Pokrovsky, V. L. Physics Letters A, Vol. 350, Issue 1-2 https://doi.org/10.1016/j.physleta.2005.10.009	journal	January 2006
Forming doublons by a quantum quench Schecter, M.; Kamenev, A. Physical Review A, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevA.85.043623	journal	April 2012
Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms Sun, Deqiang; Abanov, Ar.; Pokrovsky, V. L. EPL (Europhysics Letters), Vol. 83, Issue 1 https://doi.org/10.1209/0295-5075/83/16003	journal	June 2008
Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem Altland, Alexander; Gurarie, V.; Kriecherbauer, T. Physical Review A, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevA.79.042703	journal	April 2009
Dynamics of a many-particle Landau-Zener model: Inverse sweep Itin, A. P.; Törmä, P. Physical Review A, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevA.79.055602	journal	May 2009
Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior Saito, Keiji; Wubs, Martijn; Kohler, Sigmund Physical Review B, Vol. 75, Issue 21 https://doi.org/10.1103/PhysRevB.75.214308	journal	June 2007
Quantum dynamics of a two-state system in a dissipative environment Ao, Ping; Rammer, Jo/rgen Physical Review B, Vol. 43, Issue 7 https://doi.org/10.1103/PhysRevB.43.5397	journal	March 1991
Decoherence in adiabatic quantum computation Amin, M. H. S.; Averin, Dmitri V.; Nesteroff, James A. Physical Review A, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevA.79.022107	journal	February 2009
Landau-Zener transitions in a system of interacting spins: Exact results for demagnetization probability Ostrovsky, V. N.; Volkov, M. V. Physical Review B, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevB.73.060405	journal	February 2006
Coherent Particle Transfer in an On-Demand Single-Electron Source Keeling, J.; Shytov, A. V.; Levitov, L. S. Physical Review Letters, Vol. 101, Issue 19 https://doi.org/10.1103/PhysRevLett.101.196404	journal	November 2008
Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions Wubs, Martijn; Saito, Keiji; Kohler, Sigmund Physical Review Letters, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevLett.97.200404	journal	November 2006
SU(3) Landau-Zener interferometry Kiselev, M. N.; Kikoin, K.; Kenmoe, M. B. EPL (Europhysics Letters), Vol. 104, Issue 5 https://doi.org/10.1209/0295-5075/104/57004	journal	December 2013
Characterization of Qubit Dephasing by Landau-Zener-Stückelberg-Majorana Interferometry Forster, F.; Petersen, G.; Manus, S. Physical Review Letters, Vol. 112, Issue 11 https://doi.org/10.1103/PhysRevLett.112.116803	journal	March 2014
Exact Classification of Landau-Majorana-Stückelberg-Zener Resonances by Floquet Determinants Ganeshan, Sriram; Barnes, Edwin; Das Sarma, S. Physical Review Letters, Vol. 111, Issue 13 https://doi.org/10.1103/PhysRevLett.111.130405	journal	September 2013
Interplay of charge and spin coherence in Landau-Zener-Stückelberg-Majorana interferometry Ribeiro, Hugo; Petta, J. R.; Burkard, Guido Physical Review B, Vol. 87, Issue 23 https://doi.org/10.1103/PhysRevB.87.235318	journal	June 2013
Vibrational Mode Multiplexing of Ultracold Atoms Martínez-Garaot, S.; Torrontegui, E.; Chen, Xi Physical Review Letters, Vol. 111, Issue 21 https://doi.org/10.1103/PhysRevLett.111.213001	journal	November 2013
Cavity-Mediated Entanglement Generation Via Landau-Zener Interferometry Quintana, C. M.; Petersson, K. D.; McFaul, L. W. Physical Review Letters, Vol. 110, Issue 17 https://doi.org/10.1103/PhysRevLett.110.173603	journal	April 2013
High-Fidelity Rapid Ground-State Loading of an Ultracold Gas into an Optical Lattice Masuda, Shumpei; Nakamura, Katsuhiro; del Campo, Adolfo Physical Review Letters, Vol. 113, Issue 6 https://doi.org/10.1103/PhysRevLett.113.063003	journal	August 2014
Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving Deffner, Sebastian; Jarzynski, Christopher; del Campo, Adolfo Physical Review X, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevX.4.021013	journal	April 2014
Assisted Finite-Rate Adiabatic Passage Across a Quantum Critical Point: Exact Solution for the Quantum Ising Model del Campo, Adolfo; Rams, Marek M.; Zurek, Wojciech H. Physical Review Letters, Vol. 109, Issue 11 https://doi.org/10.1103/PhysRevLett.109.115703	journal	September 2012
S-matrix for generalized Landau-Zener problem Brundobler, S.; Elser, Veit Journal of Physics A: Mathematical and General, Vol. 26, Issue 5 https://doi.org/10.1088/0305-4470/26/5/037	journal	March 1993
Landau-Zener transitions in a multilevel system: An exact result Shytov, A. V. Physical Review A, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevA.70.052708	journal	November 2004
Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings Sinitsyn, N. A. Journal of Physics A: Mathematical and General, Vol. 37, Issue 44 https://doi.org/10.1088/0305-4470/37/44/016	journal	October 2004
Comment on ‘Exact results for survival probability in the multistate Landau–Zener model’ Dobrescu, B. E.; Sinitsyn, N. A. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 39, Issue 5 https://doi.org/10.1088/0953-4075/39/5/N01	journal	February 2006
Exact results for survival probability in the multistate Landau–Zener model Volkov, M. V.; Ostrovsky, V. N. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 37, Issue 20 https://doi.org/10.1088/0953-4075/37/20/003	journal	October 2004
No-go theorem for bands of potential curves in multistate Landau–Zener model Volkov, M. V.; Ostrovsky, V. N. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 38, Issue 7 https://doi.org/10.1088/0953-4075/38/7/011	journal	March 2005
Counterintuitive transitions between crossing energy levels Rangelov, A. A.; Piilo, J.; Vitanov, N. V. Physical Review A, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevA.72.053404	journal	November 2005
Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model Dziarmaga, Jacek Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevLett.95.245701	journal	December 2005
Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory Volkov, M. V.; Ostrovsky, V. N. Physical Review A, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevA.75.022105	journal	February 2007
Crossing of two bands of potential curves Demkov, Yu N.; Ostrovsky, V. N. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 28, Issue 3 https://doi.org/10.1088/0953-4075/28/3/011	journal	February 1995
Exact analytical solution of the N -level Landau - Zener-type bow-tie model Ostrovsky, Valentine N.; Nakamura, Hiroki Journal of Physics A: Mathematical and General, Vol. 30, Issue 19 https://doi.org/10.1088/0305-4470/30/19/028	journal	October 1997
The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model Demkov, Yu N.; Ostrovsky, V. N. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 34, Issue 12 https://doi.org/10.1088/0953-4075/34/12/309	journal	June 2001
Generalisation of the Landau-Zener calculation to three levels Carroll, C. E.; Hioe, F. T. Journal of Physics A: Mathematical and General, Vol. 19, Issue 7 https://doi.org/10.1088/0305-4470/19/7/017	journal	May 1986
Exact transition probabilities in the three-state Landau–Zener–Coulomb model Lin, J.; Sinitsyn, N. A. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 1 https://doi.org/10.1088/1751-8113/47/1/015301	journal	December 2013
The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions Lin, J.; Sinitsyn, N. A. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 17 https://doi.org/10.1088/1751-8113/47/17/175301	journal	April 2014
Manipulation of quantum state transfer in cold Rydberg atom collisions Cabral, J. S.; Kondo, J. M.; Gonçalves, L. F. New Journal of Physics, Vol. 12, Issue 9 https://doi.org/10.1088/1367-2630/12/9/093023	journal	September 2010
Stark Field Control of Nonadiabatic Dynamics in Triatomic Hydrogen Baumgartner, Frank; Helm, Hanspeter Physical Review Letters, Vol. 104, Issue 10 https://doi.org/10.1103/PhysRevLett.104.103002	journal	March 2010
Stark maps and Rydberg transitions in the presence of an electric field for Li, Na, and K. A quantum defect orbital approach Menéndez, J. M.; Martı́n, I.; Velasco, A. M. The Journal of Chemical Physics, Vol. 119, Issue 24 https://doi.org/10.1063/1.1628212	journal	December 2003
Electric Field Effects in the Excitation of Cold Rydberg-Atom Pairs Nascimento, V. A.; Caliri, L. L.; Schwettmann, A. Physical Review Letters, Vol. 102, Issue 21 https://doi.org/10.1103/PhysRevLett.102.213201	journal	May 2009
Selective field ionization in Li and Rb: Theory and experiment Robicheaux, F.; Wesdorp, C.; Noordam, L. D. Physical Review A, Vol. 62, Issue 4 https://doi.org/10.1103/PhysRevA.62.043404	journal	September 2000
A novel method for the calculation of widths for avoided crossings of the highly excited Stark states: detailed implementation for alkali-metal atoms He, Yong-Lin Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 45, Issue 1 https://doi.org/10.1088/0953-4075/45/1/015001	journal	December 2011
Two-state model for top-of-barrier processes Tantawi, R. S.; Sabbah, A. S.; Macek, J. H. Physical Review A, Vol. 62, Issue 4 https://doi.org/10.1103/PhysRevA.62.042710	journal	September 2000
Theory of inelastic collisions between low-lying excited- and ground-state Ne atoms Cohen, James S.; Collins, Lee A.; Lane, Neal F. Physical Review A, Vol. 17, Issue 4 https://doi.org/10.1103/PhysRevA.17.1343	journal	April 1978
Generalization of the Rosen-Zener model of noncrossing interactions. I. Total cross sections Dinterman, T. R.; Delos, J. B. Physical Review A, Vol. 15, Issue 2 https://doi.org/10.1103/PhysRevA.15.463	journal	February 1977
The generalized borel transform and stokes multipliers Gurarii, V. P.; Matsaev, V. I. Theoretical and Mathematical Physics, Vol. 100, Issue 2 https://doi.org/10.1007/BF01016755	journal	August 1994

Cited By (3)

Exact transition probabilities in a 6-state Landau–Zener system with path interference Sinitsyn, N. A. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 19 https://doi.org/10.1088/1751-8113/48/19/195305	journal	April 2015
Counterdiabatic Hamiltonians for multistate Landau-Zener problem Nishimura, Kohji; Takahashi, Kazutaka SciPost Physics, Vol. 5, Issue 3 https://doi.org/10.21468/scipostphys.5.3.029	journal	January 2018
Solvable multistate model of Landau-Zener transitions in cavity QED Sinitsyn, Nikolai A.; Li, Fuxiang arXiv https://doi.org/10.48550/arxiv.1602.03136	text	January 2016

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
quantum nonadiabatic transitions

Title: Exact results for models of multichannel quantum nonadiabatic transitions

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