Quantum quench influenced by an excited-state phase transition

Fernández, Pedro Pérez; Cejnar, Pavel; Arias, J. M.; Dukelsky, J.; García‐Ramos, J. E.; Relaño, Armando

doi:10.1103/physreva.83.033802

Cited by 116 publications

(193 citation statements)

References 57 publications

(218 reference statements)

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“…Another important feature in the Hamiltonian is the excited-state quantum phase transitions (ESQPT) [31,32], manifested as a singularity in the level density, order parameters, and wave function properties [33,34]. They could have important effects in decoherence [35] and in the temporal evolution for quantum quenches [36]. It is strongly suggested that the relation between the ESQPT and chaos is dependent on the system [37].…”

Section: Arxiv:150905918v1 [Quant-ph] 19 Sep 2015mentioning

confidence: 99%

Delocalization and quantum chaos in atom-field systems

et al. 2016

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Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions, and with its square root in the regular ones.

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Section: Arxiv:150905918v1 [Quant-ph] 19 Sep 2015mentioning

confidence: 99%

Delocalization and quantum chaos in atom-field systems

et al. 2016

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“…In this way, we obtain the critical energy in the thermodinamical limit E c /J = −1, which is independent of λ . This critical energy is valid for all λ > λ c and represent the border between two phases with different properties, where the ESQPT's take place, supporting previous results [5]. Properties of this two phases can be explored analyzing the dynamical behavior of certain observables [4].…”

mentioning

confidence: 50%

Quantum phase transitions and spontaneous symmetry-breaking in Dicke model

Puebla¹,

Relaño²,

Retamosa³

2013

AIP Conference Proceedings

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Abstract.A method to find the Excited-States Quantum Phase Transitions (ESQPT's) from paritysymmetry in the Dicke model is studied and presented. This method allows us to stablish a critical energy where ESQPT's take places, and divides the whole energy spectrum in two regions with different properties.Keywords: Quantum phase transition, Spontaneous symmetry-breaking PACS: 42.50.Nn, 05.30.Rt, 11.30.Qc, 64.70.Tg The Dicke model describes the interaction between an ensemble of two-level atoms and a single electromagnetic field mode, as a function of the radiation-matter coupling [1]. Its main property is a second order Quantum Phase Transition (QPT) which produces a macroscopic population of the upper atomic level. The Hamiltonian can be written as follows:where the N atoms are represented by J, the angular momentum operator with a pseudospin lenght J = N/2. Photons are represented by the usual annihilation and creation operators, and ω and ω 0 represent the frecuency of the cavity mode and the transition frecuency respectively. The system is governed by λ , the intensity of radiation-matter coupling, and its critical value for QPT is λ c = √ ωω 0 /2. We consider thath = 1 and ω = ω 0 = 1. The parity of the system is Π = e iπ(J+J z +a † a) , which is a conserved quantity since [H, Π] = 0. The symmetry-parity is given by the invariance of H under J x → −J x and a → −a [2]. This symmetry is spontaneously broken when the critical point of QPT is crossed [3]. Since the parity Π is a conserved quantity, we can label the eigenstates of H with a certain value of the parity, positive or negative. Hence, we obtain two sets of eigenstates, for a i-th eigenstate we have another with opposite parity. Fixing he number of atoms N, we analyze the relative difference of the energy between two i-th eigenstates with opposite parity. We have shown that for λ > λ c every couple of eigenstates with opposite parity are degenerated below a certain critical energy [4]. This critical energy E N c (λ ) separates two regions in the spectrum and is a function of λ and the number of atoms N. Here we show how to find the E c in the thermodinamical limit by fitting the finite precursor E N c (λ ) to a linear function E N c (λ )/J = A N + B N λ , and studying the finite-size scaling of coefficients A N and B N .

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“…In some collective many-body quantum systems, QPTs are accompanied by ESQPTs, giving rise to a critical energy E c for certain values of the system control parameter [9][10][11][12][13][14][15][16][17]. Traditionally, ESQPTs have been linked to singularities in the density of states or in one of its derivatives, depending on the number of system's degrees of freedom in the semiclassical limit [37].…”

Section: Excited-state Quantum Phase Transitionsmentioning

confidence: 99%

“…They appear in models pertaining to different branches of physics, like the interacting boson model (IBM) [12,13], Lipkin-Meshkov-Glick model [14], vibron model [15], Dicke and Jaynes-Cummings models [10,16,17], kicked top [18], and microwave Dirac billiards [19]. It is worth mentioning that, despite the fact that the excitation energy is linked to the temperature of an isolated system, ESQPTs are qualitatively different from thermal phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

et al. 2014

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The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

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Quantum quench influenced by an excited-state phase transition

Cited by 116 publications

References 57 publications

Delocalization and quantum chaos in atom-field systems

Delocalization and quantum chaos in atom-field systems

Quantum phase transitions and spontaneous symmetry-breaking in Dicke model

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

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