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Register a new userPeres Lattices and chaos in the Dicke model
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Added by
Miguel Bastarrachea-Magnani
Publication date
2013
fields
Physics
and research's language is
English
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Peres lattices are employed as a visual method to identify the presence of chaos in different regions of the energy spectra in the Dicke model. The coexistence of regular and chaotic regions can be clearly observed for certain energy regions, even if the coupling constant is smaller than the critical value to reach superradiance. It also exhibits the presence of two Excited-State Quantum Phase Transitions, a static and a dynamic one. The diagonalization is performed in a extended bosonic coherent basis which enable us to reach a large number of excited states with good numerical convergence.
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We have studied entanglement entropy and Husimi $Q$ distribution as a tool to explore chaos in the quantum two-photon Dicke model. With the increase of the energy of system, the linear entanglement entropy of coherent state prepared in the classical chaotic and regular regions become more distinguishable, and the correspondence relationship between the distribution of time-averaged entanglement entropy and the classical Poincar{e} section has been improved obviously. Moreover, Husimi $Q$ distribution for the initial states corresponded to the points in the chaotic region in the higher energy system disperses more quickly than that in the lower energy system. Our result imply that higher system energy has contributed to distinguish the chaotic and regular behavior in the quantum two-photon Dicke model.
We calculate numerically the fidelity and its susceptibility for the ground state of the Dicke model. A minimum in the fidelity identifies the critical value of the interaction where a quantum phase crossover, the precursor of a phase transition for finite number of atoms N, takes place. The evolution of these observables is studied as a function of N, and their critical exponents evaluated. Using the critical exponents the universal curve for the specific susceptibility is recovered. An estimate to the precision to which the ground state wave function is numerically calculated is given, and found to have its lowest value, for a fixed truncation, in a vicinity of the critical coupling.
We study the ergodic -- non-ergodic transition in a generalized Dicke model with independent co- and counter rotating light-matter coupling terms. By studying level statistics, the average ratio of consecutive level spacings, and the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we show that the ergodic -- non-ergodic transition in the Dicke model is a consequence of the proximity to the integrable limit of the model when one of the couplings is set to zero. This can be interpreted as a hint for the existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser theorem. Besides, we show that there is no intrinsic relation between the ergodic -- non-ergodic transition and the precursors of the normal -- superradiant quantum phase transition.
The symmetry operators generating the hidden $mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) at bias $epsilon in frac{1}{2}mathbb{Z}$ have recently been constructed by V. V. Mangazeev et al. [J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to determine symmetry operators for the $N$-qubit generalisation of the AQRM, also known as the biased Dicke model, at special biases. We also prove for general $N$ that the symmetry operators, which commute with the Hamiltonian of the biased Dicke model, generate a $mathbb{Z}_2$ symmetry.
We consider an important generalization of the Dicke model in which multi-level atoms, instead of two-level atoms as in conventional Dicke model, interact with a single photonic mode. We explore the phase diagram of a broad class of atom-photon coupling schemes and show that, under this generalization, the Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. We also calculate the atom-photon entanglement entropy for both critical and non-critical cases. We find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.
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