Aníbal Iucci

Quantum quench dynamics of the Luttinger model

The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one- and two-point correlation functions for two types of quenches: from a noninteracting to an interacting Luttinger model and vice versa. In the former case, the noninteracting Fermi gas features in the momentum distribution and other correlation functions are destroyed as time evolves. In the infinite-time limit, equal-time correlations are power laws but the critical exponents are found to differ from their equilibrium values. In all cases, we find that these correlations are well described by a generalized Gibbs ensemble [M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)], which assigns a momentum-dependent temperature to each eigenmode.The dynamics of the Luttinger model and the sine-Gordon model (at the Luther-Emery point and in the semiclassical approximation) after a quantum quench is studied. We compute in detail one and two-point correlation functions for different types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa, and from the gapped to the gapless phase of the sine-Gordon model and vice-versa. A progressive destruction of the Fermi gas features in the momentum distribution is found in the case of a quench into an interacting state in the Luttinger model. The critical exponents for spatial correlations are also found to be different from their equilibrium values. Correlations following a quench of the sine-Gordon model from the gapped to the gapless phase are found in agreement with the predictions of Calabrese and Cardy [Phys. Rev. Lett. {\bf 96} 136801 (2006)]. However, correlations following a quench from the gapped to the gapless phase at the Luther-Emery and the semi-classical limit exhibit a somewhat different behavior, which may indicate a break-down of the semiclassical approximation or a qualitative change in the behavior of correlations as one moves away from the Luther-Emergy point. In all cases, we find that the correlations at infinite times after the quench are well described by a generalized Gibbs ensemble [M. Rigol \emph{et al.} Phys. Rev. Lett. {\bf 98}, 050405 (2007)], which assigns a momentum dependent temperature to each eigenmode.

Spectroscopy of Ultracold Atoms by Periodic Lattice Modulations

We present a nonperturbative analysis of a new experimental technique for probing ultracold bosons in an optical lattice by periodic lattice depth modulations. This is done using the time-dependent density-matrix renormalization group method. We find that sharp energy absorption peaks are not unique to the Mott insulating phase at commensurate filling but also exist for superfluids at incommensurate filling. For strong interactions, the peak structure provides an experimental measure of the interaction strength. Moreover, the peak height of the peaks at Plancks omega > or approximately 2U can be employed as a measure of the incommensurability of the system.

Modulation spectroscopy with ultracold fermions in an optical lattice

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time-dependent density-matrix renormalization-group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott insulator, respectively. In the Mott insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations.

Energy absorption of a Bose gas in a periodically modulated optical lattice

We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.

Dissipation-driven phase transitions in superconducting wires

We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization group and a self-consistent variational approach to obtain the critical points and phases at T=0. We predict a quantum phase transition toward a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the dc resistivity of the wire.

Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasiperiodic optical lattices

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasiperiodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the noncommensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly, we find that a perturbative treatment in both cases, weak and strong disorders, gives a good description at all frequencies. In particular, we find that the infrared-absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected since for other quantities, like the conductivity in one-dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems and, in particular, the effect of the harmonic trap.

Transient and finite-size effects in transport properties of a quantum wire

We study the time-dependent backscattered current produced in a quantum wire when a local barrier is suddenly switched on. Previous investigations are improved by taking into account the finite length of the device. We establish two different regimes in terms of the relationship between the energy scales associated to the voltage and the length of the system. We show how previous results, valid for wires of infinite length, are modified by the finite size of the system. In particular our study reveals a rich pattern of temporal steps within which the current suffers an initial relaxation followed by temporary revivals. By employing both analytical and numerical methods we describe peculiar features of this structure. From this analysis one concludes that our results render a recently proposed approach to the determination of the Luttinger parameter K, more realistic.

Competition between Vortex Unbinding and Tunneling in an Optical Lattice

We study a system of two-dimensional Bose gases trapped in minima of a deep one-dimensional optical lattice potential. Increasing the tunneling amplitude between adjacent gases drives a deconfinement transition to a phase where coherence is established between neighboring two-dimensional gases. We compute the signature of this transition in the interference pattern of the system as well as in its rotational response, which provides a direct measurement of the superfluidity in the system

Bosonization approach to the mixed-valence two-channel Kondo problem

We present in detail the bosonization-refermionization solution of the anisotropic version of the two-channel Anderson model at a particular manifold in the space of parameters of the theory, where we establish an equivalence with a Fermi-Majorana biresonant-level model. The correspondence is rigorously proved by explicitly constructing the new fermionic fields and Klein factors in terms of the original ones and showing that the commutation properties between original and new Klein factors are of semionic type. We also demonstrate that the fixed points associated with the solvable manifold are renormalization-group stable and generic, and therefore representative of the physics of the original model. The simplicity of the solution found allows for the computation of the full set of thermodynamic quantities. In particular, we compute the entropy, occupation, and magnetization of the impurity as functions of temperature, and identify the different physical energy scales. In the absence of external fields, two energy scales appear and, as the temperature goes to zero, a nontrivial residual entropy indicates that the model approaches a universal line of fixed points of non-Fermi-liquid type. An external field, even if small, introduces a third energy scale and causes the quenching of the impurity entropy to zero, taking the system to a corresponding Fermi-liquid fixed point.

Fourier transform of the 2kF Luttinger liquid density correlation function with different spin and charge velocities

We obtain a closed-form analytical expression for the zero-temperature Fourier transform of the 2kF component of the density-density correlation function in a Luttinger liquid with different spin and charge velocities. For frequencies near the spin and charge singularities, approximate analytical forms are given and compared with the exact result. We find power-law-like singularities leading to either divergence or cusps, depending on the values of the Luttinger parameters, and compute the corresponding exponents. Exact integral expressions and numerical results are given for the finite-temperature case as well. We show, in particular, how the temperature rounds the singularities in the correlation function.