Marco Schiro

Localization and Glassy Dynamics Of Many-Body Quantum Systems

When classical systems fail to explore their entire configurational space, intriguing macroscopic phenomena like aging and glass formation may emerge. Also closed quanto-mechanical systems may stop wandering freely around the whole Hilbert space, even if they are initially prepared into a macroscopically large combination of eigenstates. Here, we report numerical evidences that the dynamics of strongly interacting lattice bosons driven sufficiently far from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon. We argue that the resulting long-lived inhomogeneities are responsible for the lack of thermalization observed in large systems. Such a rich phenomenology could be experimentally uncovered upon probing the out-of-equilibrium dynamics of conveniently prepared quantum states of trapped cold atoms which we hereby suggest.

Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems

A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wave function. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean-field level an extremely rich behavior. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein, Phys. Rev. Lett. 103, 056403 (2009)10.1103/PhysRevLett.103.056403, obtained by dynamical mean-field theory, that turns into a crossover at any finite doping.

Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations

We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary Quantum Ising Model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include gaussian fluctuations around the non equilibrium mean field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean field dynamical critical line, which suggests they could even alter qualitatively the mean field scenario.

Transient Dynamics of d-Wave Superconductors after a Sudden Excitation.

Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.

Transient orthogonality catastrophe in a time-dependent nonequilibrium environment.

We study the response of a highly excited time-dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient nonequilibrium environment. To this extent we consider, as a key quantity, the overlap between time-dependent wave functions, which we write in terms of a novel two-time correlator generalizing the standard Loschmidt echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through nonequilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one-dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power-law structure even in the presence of a large nonequilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of nonlinearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.

Tunable hybrid quantum electrodynamics from nonlinear electron transport

Recent advances in quantum electronics have allowed to engineer hybrid nano-devices comprising on chip a microwave electromagnetic resonator coupled to an artificial atom, a quantum dot. These systems realize novel platforms to explore non-equilibrium quantum impurity physics with light and matter. Coupling the quantum dot system to reservoir leads (source and drain) produces an electronic current as well as dissipation when applying a bias voltage across the system. Focusing on a standard model of biased quantum dot coupled to a photon mode we elucidate the signatures of the electronic correlations in the phase of the transmitted microwave signal. In addition, we illustrate the effect of the electronic degrees of freedom on the photon field, giving rise to non-linearities, damping and dissipation, and discuss how to control these effects by means of gate and bias voltages.

Quantum phase transition of light in the Rabi?Hubbard model

We discuss the physics of the Rabi?Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi nonlinearity. We show that the inclusion of counter-rotating terms in the light?matter interaction, often neglected in theoretical descriptions based on Jaynes?Cumming models, is crucial to stabilize finite-density quantum phases of correlated photons with no need for an artificially engineered chemical potential. We?show that the physical properties of these phases and the quantum phase transition occurring between them is remarkably different from those of interacting bosonic massive quantum particles. The competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z2 parity symmetry-breaking quantum phase transition between two gapped phases, a Rabi insulator and a delocalized super-radiant phase.

Nonequilibrium dynamics across an impurity quantum critical point due to quantum quenches

Whether a small quantum mechanical system is able to equilibrate with its environment once an external local perturbation drives it out of thermal equilibrium is a central question which cuts across many different fields of science. Here we consider such a problem for a correlated quantum impurity coupled to a fermionic reservoir and driven out of equilibrium by local quantum quenches such as those recently realized in optical absorption experiments on single quantum dots. We argue that equilibration in this problem is deeply connected to the occurrence of Kondo Effect at low energy and that a highly non trivial dynamical behavior may emerge whenever a local quantum critical point intrudes between a conventional Kondo screened phase and a Kondo unscreened one. We discuss this issue in the context of the Anderson Impurity model coupled to a pseudo-gap reservoir by using a correlated time dependent variational wave function that is able to qualitatively describe this physics.