Dynamics of Loschmidt echoes and fidelity decay

In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves a time-reversal procedure to assess the effect of perturbations in a quantum excitation dynamics. However, when addressing macroscopic systems one is repeatedly confronted with limitations that seem insurmountable. This led to formulate the...

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value beca...

We study fidelity decay by a uniform semiclassical approach, in the three perturbation regimes, namely, the perturbative regime, the Fermi-golden-rule (FGR) regime, and the Lyapunov regime. A semiclassical expression is derived for fidelity of initial Gaussian wave packets with width of the order $\sqrt{\hbar}$ ($\hbar$ being the effective Planck constant). Short time decay of fidelity of initial Gaussian wave packets is also studied, with respect to two time scales int...

We study the transition of a quantum system $S $ from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system $E$ coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of $E$ modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of $E$ strongly affects its capa...

In Echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity, the Boltzmann echo, where only part of the system's degrees of freedom can be time-reversed. We present a semiclassical calculation of the Boltzmann echo. We show that, as the time-reversal operation is performed more and more accurately, the decay rate of the Boltzmann echo s...

We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_g where F_g scales as F_g(\alpha, \epsilon, \eta)= f_cl(\chi_cl equiv\eta^{3-\alpha}/\epsilon); \alpha is the order of singularity of the potential, \eta is the spread of the initial phase space density and \epsilon is the perturbation strength. Instead, the ...

We analyze the fidelity decay for a system of interacting bosons described by a Bose-Hubbard Hamiltonian. We find echoes associated with "non-universal" structures that dominate the energy landscape of the perturbation operator. Despite their classical origin, these echoes persist deep into the quantum (perturbative) regime and can be described by an improved random matrix modeling. In the opposite limit of strong perturbations (and high enough energies), classical considerat...

We employ the Loschmidt Echo, i.e. the signal recovered after the reversal of an evolution, to identify and quantify the processes contributing to decoherence. This procedure, which has been extensively used in single particle physics, is here employed in a spin ladder. The isolated chains have 1/2 spins with XY interaction and their excitations would sustain a one-body like propagation. One of them constitutes the controlled system S whose reversible dynamics is degraded by ...

We study the dynamical fidelity $\mathcal{F} (t)$ and the Loschmidt echo $\mathcal{L} (t)$, following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after $n$ periods $\tau$. We show that $\log{\mathcal{F}}(n\tau)/L$ (the logarithm of the fidelity per-site) reaches a steady value in the asymptotic limit $n\to \infty...

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not...