Decoherence due to an excited-state quantum phase transition in a two-level boson model

Abstract

The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuousexcited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor ͑or the fidelity͒ goes to zero with a finite-size scaling power law.

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

“…Typical examples are the U(5)-SO(6) ESQPT [9][10][11] in the IBM and the U(2)-SO(3) ESQPT [15,16] in the two dimensional limit of the VM. ESQPTs in other many-body quantum systems have also been investigated, such as those in the Lipkin-Meshkov-Glick (LMG) model [20,21], the Jaynes-Cummings model [22,23], the Dicke model [22][23][24], and the kicked-top model [25]. Generally, ESQPTs emerge in the systems with a large number of particles.…”

Structure of eigenstates and quench dynamics at an excited-state quantum phase transition

“…This critical point can be reached either for a constant excited energy by varying the control parameter(s) or by fixing the latter and increasing the energy. ESQPTs have been investigated for a broad class of many-body quantum systems, such as the Lipkin-Meshkov-Glick (LMG) [17][18][19], the molecular vibron [15,20] In terms of dynamics, it has been shown that an ESQPT leads to random oscillations of the survival probability in isolated systems [21], to singularities in the evolution of observables [32], and to maximal decoherence in open systems [18,33]. Despite these works, studies of the effects of ESQPTs on systems' evolutions are still scarce.…”

“…In terms of dynamics, it has been shown that an ESQPT leads to random oscillations of the survival probability in isolated systems [21], to singularities in the evolution of observables [32], and to maximal decoherence in open systems [18,33]. Despite these works, studies of the effects of ESQPTs on systems' evolutions are still scarce.…”

“…One of the systems considered was described by the Ising spin-1/2 Hamiltonian with a transverse field, which in the limit of infinite-range interaction corresponds to the LMG model [17][18][19]. Thus, the experimental setup to compare the speed of the evolution for different basis vectors is already available.…”

Excited-state quantum phase transitions studied from a non-Hermitian perspective

“…This divergence in the density states at the lowest energy moves to higher energies as the control parameter increases above the QPT critical point. The energy value where the density of states peaks marks the point of the ESQPT.ESQPTs have been analyzed in various theoretical models [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and have also been observed experimentally [22][23][24][25][26][27]. They have been linked with the bifurcation phenomenon [20] and with the exceedingly slow evolution of initial states with energy close to the ESQPT critical point [18][19][20].…”