Exact transition probabilities in a 6-state Landau–Zener system with path interference

Sinitsyn, Nikolai A.

doi:10.1088/1751-8113/48/19/195305

Exact transition probabilities in a 6-state Landau–Zener system with path interference

Journal Article · Thu Apr 23 00:00:00 EDT 2015 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8113/48/19/195305· OSTI ID:1325633

Sinitsyn, Nikolai A. ^[1]

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

In this paper, we identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. Finally, we discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Advanced Research Projects Agency - Energy (ARPA-E); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1325633

Alternate ID(s):: OSTI ID: 22498362
OSTI ID: 1239016

Report Number(s):: LA-UR--15-20432

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 19 Vol. 48; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (46)

Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids Chen, Yu-Ao; Huber, Sebastian D.; Trotzky, Stefan Nature Physics, Vol. 7, Issue 1 https://doi.org/10.1038/nphys1801	journal	October 2010
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
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
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
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
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
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
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
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
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
Multipath interference in a multistate Landau-Zener-type model Demkov, Yu. N.; Ostrovsky, V. N. Physical Review A, Vol. 61, Issue 3 https://doi.org/10.1103/PhysRevA.61.032705	journal	February 2000
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 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
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
Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids Caballero-Benítez, Santiago F.; Paredes, Rosario Physical Review A, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevA.85.023605	journal	February 2012
Nonequilibrium dynamics in Bose-Hubbard ladders Tschischik, Wladimir; Haque, Masudul; Moessner, Roderich Physical Review A, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevA.86.063633	journal	December 2012
Landau-Zener transitions in chains Sinitsyn, N. A. Physical Review A, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevA.87.032701	journal	March 2013
Exact results for models of multichannel quantum nonadiabatic transitions Sinitsyn, N. A. Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.062509	journal	December 2014
Landau-Zener transitions in a linear chain Pokrovsky, V. L.; Sinitsyn, N. A. Physical Review B, Vol. 65, Issue 15 https://doi.org/10.1103/PhysRevB.65.153105	journal	April 2002
Multiparticle Landau-Zener problem: Application to quantum dots Sinitsyn, N. A. Physical Review B, Vol. 66, Issue 20 https://doi.org/10.1103/PhysRevB.66.205303	journal	November 2002
Landau-Zener Sweeps and Sudden Quenches in Coupled Bose-Hubbard Chains Kasztelan, C.; Trotzky, S.; Chen, Y. -A. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/PhysRevLett.106.155302	journal	April 2011
Nonadiabatic Transitions in Exactly Solvable Quantum Mechanical Multichannel Model: Role of Level Curvature and Counterintuitive Behavior Sinitsyn, N. A. Physical Review Letters, Vol. 110, Issue 15 https://doi.org/10.1103/PhysRevLett.110.150603	journal	April 2013
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
Multipath interference in a multistate Landau-Zener-type model Demkov, Yu. N.; Ostrovsky, V. N. Physical Review A, Vol. 61, Issue 3 https://doi.org/10.1103/physreva.61.032705	journal	February 2000
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 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
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
Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids Caballero-Benítez, Santiago F.; Paredes, Rosario Physical Review A, Vol. 85, Issue 2 https://doi.org/10.1103/physreva.85.023605	journal	February 2012
Nonequilibrium dynamics in Bose-Hubbard ladders Tschischik, Wladimir; Haque, Masudul; Moessner, Roderich Physical Review A, Vol. 86, Issue 6 https://doi.org/10.1103/physreva.86.063633	journal	December 2012
Landau-Zener transitions in chains Sinitsyn, N. A. Physical Review A, Vol. 87, Issue 3 https://doi.org/10.1103/physreva.87.032701	journal	March 2013
Exact results for models of multichannel quantum nonadiabatic transitions Sinitsyn, N. A. Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/physreva.90.062509	journal	December 2014
Landau-Zener transitions in a linear chain Pokrovsky, V. L.; Sinitsyn, N. A. Physical Review B, Vol. 65, Issue 15 https://doi.org/10.1103/physrevb.65.153105	journal	April 2002
Multiparticle Landau-Zener problem: Application to quantum dots Sinitsyn, N. A. Physical Review B, Vol. 66, Issue 20 https://doi.org/10.1103/physrevb.66.205303	journal	November 2002
Landau-Zener Sweeps and Sudden Quenches in Coupled Bose-Hubbard Chains Kasztelan, C.; Trotzky, S.; Chen, Y. -A. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/physrevlett.106.155302	journal	April 2011
Nonadiabatic Transitions in Exactly Solvable Quantum Mechanical Multichannel Model: Role of Level Curvature and Counterintuitive Behavior Sinitsyn, N. A. Physical Review Letters, Vol. 110, Issue 15 https://doi.org/10.1103/physrevlett.110.150603	journal	April 2013
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
Nonadiabatic Transition Nakamura, Hiroki World Scientific https://doi.org/10.1142/8009	book	January 2012
Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains Kasztelan, Christian; Trotzky, Stefan; Chen, Yu-Ao arXiv https://doi.org/10.48550/arxiv.1102.5301	text	January 2011
Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids Caballero-Benitez, Santiago F.; Paredes, Rosario arXiv https://doi.org/10.48550/arxiv.1106.6179	text	January 2011
Non-equilibrium dynamics in Bose-Hubbard ladders Tschischik, Wladimir; Haque, Masudul; Moessner, Roderich arXiv https://doi.org/10.48550/arxiv.1209.5534	text	January 2012
Landau-Zener transitions in a linear chain Pokrovsky, V. L.; Sinitsyn, N. A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0112419	text	January 2001
Landau-Zener transition in a multilevel system. An exact result Shytov, A. V. arXiv https://doi.org/10.48550/arxiv.cond-mat/0312011	text	January 2003
Dynamics of quantum phase transition: exact solution in quantum Ising model Dziarmaga, Jacek arXiv https://doi.org/10.48550/arxiv.cond-mat/0509490	text	January 2005
Exact results for state-to-state transition probabilities in the multistate Landau-Zener model by non-stationary perturbation theory Volkov, M. V.; Ostrovsky, V. N. arXiv https://doi.org/10.48550/arxiv.cond-mat/0611046	text	January 2006
Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings Sinitsyn, N. A. arXiv https://doi.org/10.48550/arxiv.quant-ph/0403113	text	January 2004

Cited By (6)

A large class of solvable multistate Landau–Zener models and quantum integrability Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 24 https://doi.org/10.1088/1751-8121/aac3b2	journal	May 2018
Solvable multistate model of Landau-Zener transitions in cavity QED Sinitsyn, Nikolai A.; Li, Fuxiang Physical Review A, Vol. 93, Issue 6 https://doi.org/10.1103/physreva.93.063859	journal	June 2016
Detuning-induced robustness of a three-state Landau-Zener model against dissipation Militello, Benedetto Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/physreva.99.063412	journal	June 2019
Integrable Time-Dependent Quantum Hamiltonians Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y. Physical Review Letters, Vol. 120, Issue 19 https://doi.org/10.1103/physrevlett.120.190402	journal	May 2018
Degenerate Landau–Zener model in the presence of quantum noise Militello, Benedetto International Journal of Quantum Information, Vol. 17, Issue 05 https://doi.org/10.1142/s0219749919500497	journal	August 2019
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

Similar Records

Solvable four-state Landau-Zener model of two interacting qubits with path interference

Journal Article · Sun Nov 29 19:00:00 EST 2015 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1335604

Four-state nonstationary models in multistate Landau-Zener theory

Journal Article · Sun Dec 31 23:00:00 EST 2006 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:20976640

Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory

Journal Article · Wed Feb 14 23:00:00 EST 2007 · Physical Review. A · OSTI ID:20982064

Related Subjects

97 MATHEMATICS AND COMPUTING
Landau-Zener
exactly solvable model
nonadiabatic transitions
quantum integrability

Exact transition probabilities in a 6-state Landau–Zener system with path interference

Citation Formats

References (46)

Cited By (6)

Similar Records

Related Subjects