Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

Sun, Chen; Sinitsyn, Nikolai A.

doi:10.1103/PhysRevA.94.033808

Title: Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

Journal Article · Wed Sep 07 00:00:00 EDT 2016 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.94.033808· OSTI ID:1344360

Sun, Chen ^[1]; Sinitsyn, Nikolai A. ^[2]

Texas A & M Univ., College Station, TX (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and _q-deformed binomial statistics.

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1344360

Alternate ID(s):: OSTI ID: 1321041

Report Number(s):: LA-UR-16-24486; PLRAAN; TRN: US1701659

Journal Information:: Physical Review A, Vol. 94, Issue 3; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 26 works

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References (33)

Quantum Painlevé-Calogero correspondence Zabrodin, A.; Zotov, A. Journal of Mathematical Physics, Vol. 53, Issue 7 https://doi.org/10.1063/1.4732532	journal	July 2012
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
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
Atomi orientati in campo magnetico variabile Majorana, Ettore Il Nuovo Cimento, Vol. 9, Issue 2 https://doi.org/10.1007/BF02960953	journal	February 1932
A survey of results on the q-Bernstein polynomials Phillips, G. M. IMA Journal of Numerical Analysis, Vol. 30, Issue 1 https://doi.org/10.1093/imanum/drn088	journal	June 2009
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
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
Quantum effects on curve crossing in a Bose-Einstein condensate Yurovsky, V. A.; Ben-Reuven, A.; Julienne, P. S. Physical Review A, Vol. 65, Issue 4 https://doi.org/10.1103/PhysRevA.65.043607	journal	March 2002
The q-deformed binomial distribution and its asymptotic behaviour Sicong, Jing Journal of Physics A: Mathematical and General, Vol. 27, Issue 2 https://doi.org/10.1088/0305-4470/27/2/031	journal	January 1994
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 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
Bose–Einstein condensation, fluctuations, and recurrence relations in statistical mechanics Mullin, W. J.; Fernández, J. P. American Journal of Physics, Vol. 71, Issue 7 https://doi.org/10.1119/1.1544520	journal	July 2003
Convergence properties of the q-deformed binomial distribution Martin, Zeiner Applicable Analysis and Discrete Mathematics, Vol. 4, Issue 1 https://doi.org/10.2298/AADM100217016Z	journal	January 2010
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
Solvable four-state Landau-Zener model of two interacting qubits with path interference Sinitsyn, N. A. Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.205431	journal	November 2015
q-deformed probability and binomial distribution Chung, Won-Sang; Chung, Ki-Soo; Kang, Hye-Jung International Journal of Theoretical Physics, Vol. 34, Issue 11 https://doi.org/10.1007/BF00673832	journal	November 1995
Quantum integrability in the multistate Landau–Zener problem Patra, A.; Yuzbashyan, E. A. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 24 https://doi.org/10.1088/1751-8113/48/24/245303	journal	May 2015
Formation of a two-component Bose condensate during the chemical-potential curve crossing Kayali, M. A.; Sinitsyn, N. A. Physical Review A, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevA.67.045603	journal	April 2003
The q-Bernstein basis as a q-binomial distribution Charalambides, Charalambos A. Journal of Statistical Planning and Inference, Vol. 140, Issue 8 https://doi.org/10.1016/j.jspi.2010.01.014	journal	August 2010
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
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
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
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
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
Heine-euler extensions of the poisson distribution Kemp, Adrienne W. Communications in Statistics - Theory and Methods, Vol. 21, Issue 3 https://doi.org/10.1080/03610929208830799	journal	January 1992
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
Many Body Generalization of the Landau-Zener Problem Altland, Alexander; Gurarie, V. Physical Review Letters, Vol. 100, Issue 6 https://doi.org/10.1103/PhysRevLett.100.063602	journal	February 2008
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
Algebraic bethe anzatz and the tavis-cummings model Bogolyubov, N. M. Journal of Mathematical Sciences, Vol. 100, Issue 2 https://doi.org/10.1007/BF02675727	journal	June 2000
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
A q-deformation of the harmonic oscillator Lorek, A.; Ruffing, A.; Wess, J. Zeitschrift f�r Physik C Particles and Fields, Vol. 74, Issue 2 https://doi.org/10.1007/s002880050399	journal	April 1997
Transitionless quantum driving Berry, M. V. Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 36 https://doi.org/10.1088/1751-8113/42/36/365303	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

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Berry phase of the Tavis-Cummings model with three modes of oscillation Choreño, E.; Ojeda-Guillén, D.; Valencia, R. Journal of Mathematical Physics, Vol. 60, Issue 11 https://doi.org/10.1063/1.5123624	journal	November 2019
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
Landau-Zener-Stückelberg interferometry in $PT$ -symmetric non-Hermitian models Shen, Xin; Wang, Fudong; Li, Zhi Physical Review A, Vol. 100, Issue 6 https://doi.org/10.1103/physreva.100.062514	journal	December 2019
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
Landau-Zener transition in a two-level system coupled to a single highly excited oscillator Malla, Rajesh K.; Raikh, M. E. Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/physrevb.97.035428	journal	January 2018
Cooperative Light Emission in the Presence of Strong Inhomogeneous Broadening Sun, Chen; Chernyak, Vladimir Y.; Piryatinski, Andrei Physical Review Letters, Vol. 123, Issue 12 https://doi.org/10.1103/physrevlett.123.123605	journal	September 2019
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
Berry phase of the Tavis-Cummings model with three modes of oscillation Choreño, E.; Ojeda-Guillén, D.; Valencia, R. arXiv https://doi.org/10.48550/arxiv.1908.00190	text	January 2019

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