Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>scaling behavior of the ground-state energy, fidelity, and the order parameter in the Dicke model

Liu, Tao; Zhang, Yuyu; Chen, Qing-Hu; Wang, Kelin

doi:10.1103/physreva.80.023810

Cited by 70 publications

(20 citation statements)

References 40 publications

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“…9(c) we show the scaling of the QFI with N (16) which is characterized by an exponent γ = 2/3. The same scaling has been provided for the the QFI (or equivalently fidelity susceptibility) in the Lipkin-Meshkow-Glick [44], Dicke [45] and bosonic Josephson junction [8] models [55]. Consequently, it suggests that the antiferromagnetic spinor condensate hosts a second-order quantum phase transition in the same universal class of these systems.…”

Section: Discussionmentioning

confidence: 58%

Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

2020

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We consider an antiferromagnetic Bose-Einstein condensate in a traverse magnetic field with a fixed macroscopic magnetization. The system exhibits two different critical behaviors corresponding to transitions from polar to broken-axisymmetry and from antiferromagnetic to broken-axisymmetry phases depending on the value of magnetization. We exploit both types of system criticality as a resource in the precise estimation of control parameter value. We quantify the achievable precision by the quantum Fisher information. We demonstrate the super-sub-shot noise sensitivity and show that the precision scales with the number of atoms up to N 4 around critically. In addition, we study the precision based on the error-propagation formula providing the simple-to-measure signal which coincides its scaling with the quantum Fisher information. Finally, we take into account the effect of non-zero temperature and show that the sub-shot noise sensitivity in the estimation of the control parameter is achievable in the low-temperature limit.

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Section: Discussionmentioning

confidence: 58%

Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

2020

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“…In the realm of traditional quantum mechanics, the geometric phase has been introduced to analyze the quantum phase transitions of the XY model [15][16][17] and much effort has been devoted to various Hermitian many-body systems [18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Geometric phase and phase diagram for a non-Hermitian quantumXYmodel

Zhang

Song

2013

Phys. Rev. A

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We study the geometric phase for the ground state of a generalized one-dimensional non-Hermitian quantum XY model, which has transverse-field-dependent intrinsic rotation-time reversal symmetry. Based on the exact solution, this model is shown to have a full real spectrum in multiple regions for the finite-size system. The result indicates that the phase diagram or exceptional boundary which separates the unbroken-and broken-symmetry regions corresponds to the divergence of the Berry curvature. The scaling behaviors of the ground-state energy and Berry curvature are obtained in an analytical manner for a concrete system.

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“…In fact, the Dicke model with j ≥ 1 for nonzero energy splitting between the two levels of the single atom is formally not integrable when λ/ω 0 → ∞, though the model is exactly solvable and integrable when j = 1/2, as recently pointed out by Braak [16,20]. Braak's exact solution to the Dicke model with j = 1/2 was also recovered [50,51] by using the Bogoliubov operators and the method proposed in [22], respectively, while the finite size Dicke model was also studied within the shifted boson basis in [52], which confirms Braak's observations on the exact solvability of the Dicke model, though the model is not integrable in general. However, the Poissonian limit is reached as λ/ω 0 → ∞ at the resonance point, which is also demonstrated in [10].…”

Section: Level Statistical Propertiesmentioning

confidence: 85%

“…As a remedy, instead of the Dicke basis, the Dicke Hamiltonian can be diagonalized in a shifted boson basis where convergence is reached with a smaller number of shifted boson states across the whole coupling regime [21]. This approach was also used to study the quantum criticality, the finite size effects, fidelity and the order parameter in the Dicke model [22].…”

Section: Introductionmentioning

confidence: 99%

The Critical Point Entanglement and Chaos in the Dicke Model

Bao

Pan

et al. 2015

Entropy

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Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.

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Large-Nscaling behavior of the ground-state energy, fidelity, and the order parameter in the Dicke model

Cited by 70 publications

References 40 publications

Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

Geometric phase and phase diagram for a non-Hermitian quantumXYmodel

The Critical Point Entanglement and Chaos in the Dicke Model

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