Some experimental tests of Tomonaga-Luttinger liquids

The Tomonaga-Luttinger-Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.Comment: Part of the special issue on "Luttinger liquids", Vieri Mastropietro e

Relaxation dynamics of two coherently coupled one-dimensional bosonic gases

In this work we consider the non-equilibrium dynamics of two tunnel coupled bosonic gases which are created from the coherent splitting of a one-dimensional gas. The consequences of the tunneling both in the non-stationary regime as well as at large time are investigated and compared with equilibrium results. In particular, within a semiclassical approximation, we compute correlation functions for the relative phase which are experimentally measurable and we observe a transient regime displaying oscillations as a function of the distance. The steady regime is very well approximated by a thermal state with a temperature independent of the tunneling strength.Comment: 12 pages, 4 figure

Finite temperature dynamical properties of SU(NN) fermionic Hubbard models in the spin-incoherent regime

We study strongly correlated Hubbard systems extended to symmetric $N$-component fermions. We focus on the intermediate-temperature regime between magnetic superexchange and interaction energy, which is relevant to current ultracold fermionic atom experiments. The $N$-component fermions are represented by slave particles, and, by using a diagrammatic technique based on the atomic limit, spectral functions are analytically obtained as a function of temperature, filling factor and the component number $N$. We also apply this analytical technique to the calculation of lattice modulation experiments. We compute the production rate of double occupancy induced by modulation of an optical lattice potential. Furthermore, we extend the analysis to take into account the trapping potential by use of the local density approximation. We find an excellent agreement with recent experiments on $^{173}$Yb atoms.Comment: 15 pages, 13 figures, published versio

X-ray diffraction of a disordered charge density wave

We study the X-ray diffraction spectrum produced by a collectively pinned charge density wave (CDW), for which one can expect a Bragg glass phase. The spectrum consists of two asymmetric divergent peaks. We compute the shape of the peaks, and discuss the experimental consequences.Comment: 5 pages, 2 figure

Mode coupling induced dissipative and thermal effects at long times after a quantum quench

An interaction quench in a Luttinger liquid can drive it into an athermal steady state. We analyze the effects on such an out of equilibrium state of a mode coupling term due to a periodic potential. Employing a perturbative renormalization group approach we show that even when the periodic potential is an irrelevant perturbation in equilibrium, it has important consequences on the athermal steady state as it generates a temperature as well as a dissipation and hence a finite life-time for the bosonic modes.Comment: 4+ pages and 2 figure

Strongly correlated bosons and fermions in optical lattices

These lectures are an introduction to the physics of strongly correlated fermions and bosons. They are specially targeted for the experimental realizations that have been provided by cold atomic gases in optical lattices.Comment: Lectures presented at the Les Houches summer school 2010: "Many-Body Physics with Ultracold Gases", organized by C. Salomon and G. V. Shlyapniko

Spectroscopy for cold atom gases in periodically phase-modulated optical lattices

The response of cold atom gases to small periodic phase modulation of an optical lattice is discussed. For bosonic gases, the energy absorption rate is given, within linear response theory, by imaginary part of the current correlation function. For fermionic gases in a strong lattice potential, the same correlation function can be probed via the production rate double occupancy. The phase modulation gives thus direct access to the conductivity of the system, as function of the modulation frequency. We give an example of application in the case of one dimensional bosons at zero temperature and discuss the link between the phase- and amplitude-modulation.Comment: 4 pages, 2 figures, final versio

Time dependent local potential in a Tomonaga-Luttinger liquid

We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $\omega$. We use bosonization, renormalization group and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the system, a crossover between week and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale $\omega_\ast$, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponent for $K>1$ and $K<1$. We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.Comment: 13 pages, 3 figure