Quantum phase diagrams of matter-field Hamiltonians II: Wigner function analysis

López‐Peña, R.; Cordero, Sergio; Nahmad-Achar, Eduardo; Castaños, Octavio

doi:10.1088/1402-4896/abd654

Cited by 13 publications

(19 citation statements)

References 44 publications

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“…gapped. The Goldstone mode also appear in the so called SU (3) Dicke model [912][913][914]. Here the two boson modes couple to SU (3) pseudo-spins, e.g.…”

Section: The Dicke and Tavis-cummings Modelsmentioning

confidence: 99%

The Jaynes-Cummings model and its descendants

Larson,

Mavrogordatos

2022

Preprint

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The Jaynes-Cummings (JC) model has been at the forefront of quantum optics for almost six decades to date, providing one of the simplest yet intricately nonlinear formulations of light-matter interaction in modern physics. Laying most of the emphasis to the omnipresence of the model across a range of disciplines, this monograph brings up the fundamental generality of its formalism, looking at a wide gamut of applications in specific physical systems among several realms, including atomic physics, quantum optics, solid-state physics and quantum information science. When bringing the various pieces together to assemble our narrative, we have primarily targeted researchers in quantum physics and quantum optics. The monograph also comprises an accessible introduction for graduate students engaged with non-equilibrium quantum phase transitions, quantum computing and simulation, and quantum many-body physics. In that framework, we aim to reveal the common ground between physics and applications scattered across literature and different technological advancements. The exposition guides the reader through a vibrant field interlacing quantum optics and condensed-matter physics. All sections are devoted to the strong interconnection between theory and experiment, historically linked to the development of the various modern research directions stemming from JC physics. This is accompanied by a comprehensive list of references to the key publications that have shaped its evolution since the early 1960s. Finally, we have endeavoured to keep the presentation of such a multi-sided material as concise as possible, interspersing continuous text with various illustrations alongside an economical use of mathematical expressions.

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“…gapped. The Goldstone mode also appear in the so called SU (3) Dicke model [912][913][914]. Here the two boson modes couple to SU (3) pseudo-spins, e.g.…”

Section: The Dicke and Tavis-cummings Modelsmentioning

confidence: 99%

The Jaynes-Cummings model and its descendants

Larson,

Mavrogordatos

2022

Preprint

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“…Another criterion that we have proposed [1,2] in order to find transitions not detectable through the Ehrenfest classification, is to use the Bures distance in the total product space of n-level atoms and -mode radiation field, defined by [20,21]…”

Section: Three-level Atomsmentioning

confidence: 99%

“…As a general procedure, one selects various points around a circumference of radius ε about each point p in parameter space, in order to find the state with maximum distance to p (cf. [1,2] for details). In our case, it was sufficient to calculate it for four points about each p in order to get a qualitative behavior of the surface of maximum Bures distance.…”

Section: Three-level Atomsmentioning

confidence: 99%

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Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of Field-Matter Interactions I: Variational procedure

Cordero,

Castaños,

López-Peña

et al. 2021

Preprint

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We establish, within the second quantization method, the general dipole-dipole Hamiltonian interaction of a system of n-level atoms. The variational energy surface of the n-level atoms interacting with -mode fields and under the Van Der Waals forces is calculated with respect the tensorial product of matter and electromagnetic field coherent states. This is used to determine the quantum phase diagram associated to the ground state of the system and quantify the effect of the dipole-dipole Hamiltonian interaction. By considering real induced electric dipole moments, we find the quantum phase transitions for 2-and 3-level atomic systems interacting with 1-and 2-modes of the electromagnetic field, respectively. The corresponding order of the transitions is established by means of Ehrenfest classification; for some undetermined cases, we propose two procedures: the difference of the expectation value of the Casimir operators of the 2-level subsystems, and by maximizing the Bures distance between neighbor variational solutions.

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“…As an alternative formulation of quantum mechanics, phase space methods have numerous applications in many areas of physics, e.g., quantum optics [18], atomic physics [19,20], quantum chaos [21,22], condensed matter physics [23,24], and quantum thermodynamics [25][26][27]. In particular, recent studies have shown that phase space methods are a powerful tool for the understanding of quantum phase transitions in many-body systems [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Wang

Pérez‐Bernal

2021

Phys. Rev. E

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Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.

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Quantum phase diagrams of matter-field Hamiltonians II: Wigner function analysis

Cited by 13 publications

References 44 publications

The Jaynes-Cummings model and its descendants

The Jaynes-Cummings model and its descendants

Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of Field-Matter Interactions I: Variational procedure

Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

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