Steady-states of out-of-equlibrium inhomogeneous Richardson–Gaudin quantum integrable models in quantum optics
| Autor: | Hugo Tschirhart, Alexandre Faribault, Thierry Platini |
|---|---|
| Přispěvatelé: | Physics and Materials Science Research Unit, University of Luxembourg [Luxembourg], Applied Mathematics Research Center, Coventry University (AMRC), Coventry University, Laboratoire de Physique et Chimie Théoriques (LPCT), Institut de Chimie du CNRS (INC)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Integrable system [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas] [PHYS.NUCL]Physics [physics]/Nuclear Theory [nucl-th] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Superposition principle symbols.namesake Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 010306 general physics Quantum ComputingMilieux_MISCELLANEOUS [PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] Spin-½ Mathematical physics Quantum optics Physics Quantum Physics Condensed Matter - Mesoscale and Nanoscale Physics Statistical and Nonlinear Physics Coupling (probability) Conserved quantity [PHYS.COND.CM-S]Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con] symbols Statistics Probability and Uncertainty Quantum Physics (quant-ph) Hamiltonian (quantum mechanics) |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2018, 2018 (8), pp.083102. ⟨10.1088/1742-5468/aad6b8⟩ |
| ISSN: | 1742-5468 |
| DOI: | 10.1088/1742-5468/aad6b8⟩ |
| Popis: | In this work we present numerical results for physical quantities in the steady-state obtained after a variety of product-states initial conditions are evolved unitarily, driven by the dynamics of quantum integrable models of the rational (XXX) Richardson-Gaudin family, which includes notably Tavis-Cummings models. The problem of interest here is one where a completely inhomogeneous ensemble of two-level systems (spins-1/2) are coupled to a single bosonic mode. The long-time averaged magnetisation along the z-axis as well as the bosonic occupation are evaluated in the diagonal ensemble by performing the complete sum over the full Hilbert space for small system sizes. These numerically exact results are independent of any particular choice of Hamiltonian and therefore describe general results valid for any member of this class of quantum integrable models built out of the same underlying conserved quantities. The collection of numerical results obtained can be qualitatively understood by a relaxation process for which, at infinitely strong coupling, every initial state will relax to a common state where each spin is in a maximally coherent superposition of its $\left|\uparrow\right>$ and $\left|\downarrow\right>$ states, i.e. they are in-plane polarised, and consequently the bosonic mode is also in a maximally coherent superposition of different occupation number states. This bosonic coherence being a feature of a superradiant state, we shall loosely use the term superradiant steady-state to describe it. A finite value of the coupling between the spins and the bosonic mode then leads to a long-time limit steady-state whose properties are qualitatively captured by a simple "dynamical" vision in which the coupling strength $V$ plays the role of a time $t_V$ at which this "relaxation process" towards the common strong coupling superradiant steady-state is interrupted. 27 pages, 13 figures |
| Databáze: | OpenAIRE |
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