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

Hall effect in strongly correlated low dimensional systems

We investigate the Hall effect in a quasi one-dimensional system made of weakly coupled Luttinger Liquids at half filling. Using a memory function approach, we compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter $K_{\rho}$. At high enough temperature or frequency the Hall coefficient approaches the band value.Comment: 7 pages, 3 figure

Hall effect in quasi one-dimensional organic conductors

We study the Hall effect in a system of weakly coupled Luttinger Liquid chains, using a Memory function approach to compute the Hall constant in the presence of umklapp scattering along the chains. In this approximation, the Hall constant decomposes into two terms: a high-frequency term and a Memory function term. For the case of zero umklapp scattering, where the Memory function vanishes, the Hall constant is simply the band value, in agreement with former results in a similar model with no dissipation along the chains. With umklapp scattering along the chains, we find a power-law temperature dependance of the Hall constant. We discuss the applications to quasi 1D organic conductors at high temperatures.Comment: Proceedings of the ISCOM conference "Sixth International Symposium on Crystalline Organic Metals, Superconductors, and Ferromagnets", Key West, Florida, USA (Sept. 2005), to be plublished in the Journal of Low Temperature Physic

No quasi-long-range order in strongly disordered vortex glasses: a rigorous proof

The paper contains a rigorous proof of the absence of quasi-long-range order in the random-field O(N) model for strong disorder in the space of an arbitrary dimensionality. This result implies that quasi-long-range order inherent to the Bragg glass phase of the vortex system in disordered superconductors is absent as the disorder or external magnetic field is strong.Comment: 3 pages, Revte

Rectification in Y-junctions of Luttinger liquid wires

We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. The rectification effect is the strongest in the absence of the time-reversal symmetry. In that case, the maximal rectification current can be comparable with the total current $\sim e^2V/h$ even for low voltages, weak scatterers and modest interaction strength. In a certain range of low voltages, the rectification current can grow as the voltage decreases. This leads to a bump in the $I$-$V$ curve.Comment: 14 pages, 4 figures; The latest versio

Disorder Effects in Fluctuating One-Dimensional Interacting Systems

The zero temperature localization of interacting electrons coupled to a two-dimensional quenched random potential, and constrained to move on a fluctuating one-dimensional string embedded in the disordered plane, is studied using a perturbative renormalization group approach. In the reference frame of the electrons the impurities are dynamical and their localizing effect is expected to decrease. We consider several models for the string dynamics and find that while the extent of the delocalized regime indeed grows with the degree of string fluctuations, the critical interaction strength, which determines the localization-delocalization transition for infinitesimal disorder,does not change unless the fluctuations are softer than those of a simple elastic string.Comment: 15 page

Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond

We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a new direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements

Multiple Particle Scattering in Quantum Point Contacts

Recent experiments performed on weakly pinched quantum point contacts, have shown a resistance that tend to decrease at low source drain voltage. We show that enhanced Coulomb interactions, prompt by the presence of the point contact, may lead to anomalously large multiple-particle scattering at finite bias voltage. These processes tend to decrease at low voltage, and thus may account for the observed reduction of the resistance. We concentrate on the case of a normal point contact, and model it by a spinfull interacting Tomonaga-Luttinger liquid, with a single impurity, connected to non interacting leads. We find that sufficiently strong Coulomb interactions enhance two-electron scattering, so as these dominate the conductance. Our calculation shows that the effective charge, probed by the shot noise of such a system, approaches a value proportional to e* = 2e at sufficiently large backscattering current. This distinctive hallmark may be tested experimentally. We discuss possible applications of this model to experiments conducted on Hall bars.Comment: 5 pages, 2 figure

Competing effects of interactions and spin-orbit coupling in a quantum wire

We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.Comment: 4 pages, 2 figure

Coulomb blockade in a quantum wire with long-range Coulomb interactions

We study the transport through two impurities or ``barriers'' in a one-dimensional quantum wire, taking into account the long-range $\frac1r$ Coulomb interactions. We compute the temperature-dependent conductance $G(T)$ of this system. Long-range forces lead to a dramatic increase of weak barrier potentials with decreasing temperature, even in the ``resonant'' case. The system thus always reaches a ``strong barrier'' regime in which only charge is pinned, contrary to the standard LL case. $G(T)$ vanishes faster than any power as $T$ goes to zero. In particular, resonant tunneling is suppressed at zero temperature.Comment: 11 pages,1 figure, uses epsfi