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

Abstract

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.

Authors:
 [1];  [2]
  1. Texas A & M Univ., College Station, TX (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1344360
Report Number(s):
LA-UR-16-24486
Journal ID: ISSN 2469-9926; PLRAAN; TRN: US1701659
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 94; Journal Issue: 3; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Feshbach Resonance

Citation Formats

Sun, Chen, and Sinitsyn, Nikolai A. Landau-Zener extension of the Tavis-Cummings model: Structure of the solution. United States: N. p., 2016. Web. doi:10.1103/PhysRevA.94.033808.
Sun, Chen, & Sinitsyn, Nikolai A. Landau-Zener extension of the Tavis-Cummings model: Structure of the solution. United States. doi:10.1103/PhysRevA.94.033808.
Sun, Chen, and Sinitsyn, Nikolai A. 2016. "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". United States. doi:10.1103/PhysRevA.94.033808. https://www.osti.gov/servlets/purl/1344360.
@article{osti_1344360,
title = {Landau-Zener extension of the Tavis-Cummings model: Structure of the solution},
author = {Sun, Chen and Sinitsyn, Nikolai A.},
abstractNote = {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.},
doi = {10.1103/PhysRevA.94.033808},
journal = {Physical Review A},
number = 3,
volume = 94,
place = {United States},
year = 2016,
month = 9
}

Journal Article:
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  • The Tavis-Cummings model (the Dicke model treated in the rotating-wave approximation), describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an inverted state, with all two-level systems excited and the bosonic mode is empty. This paper discusses how the quantum dynamics approaches this semiclassical result for large numbers of two-level systems, focusing on how the eigenvalues approach their semiclassical limit. The approach to the semiclassical result is found to be slow, scaling like a power of the logarithm of the system size. Considering also the effect ofmore » weak detuning between the two-level system and the bosonic field, quantum corrections are again found to decay slowly with system size, such that for a fixed detuning, the quantum effects of detuning are greater than the classical effect.« less