Coulomb blockade of the persistent current in a one-dimensional ballistic Luttinger liquid ring

The effect of an electrostatic energy (in the geometrical capacitance approach) on a persistent current is considered. It is shown that at high temperatures the current amplitude shows periodic dips as a function of the potential difference between a ring and a reservoir. These dips correspond to a lift of the Coulomb blockade. In a minimum of a dips a current is periodic in a magnetic flux with a period at any temperatures. Received: 6 April 1998 / Revised: 5 June 1998 / Accepted: 21 July 1998     

Ultracold superstrings in atomic boson-fermion mixtures

We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.     

Temperature-dependent density profiles of trapped boson-fermion mixtures

We present a semiclassical three-fluid model for a Bose-condensed mixture of interacting Bose and Fermi gases confined in harmonic traps at finite temperature. The model is used to characterize the experimentally relevant behaviour of the equilibrium density profile of the fermions with varying composition and temperature across the onset of degeneracy, for coupling strengths relevant to a mixture of ³⁹K and ⁴⁰K atoms. Received: 18 May 1998 / Revised: 24 August 1998 / Accepted: 31 August 1998     

Real space imaging of one-dimensional standing waves: direct evidence for a Luttinger liquid

Electronic standing waves with two different wavelengths were directly mapped near one end of a single-wall carbon nanotube as a function of the tip position and the sample bias voltage with high-resolution position-resolved scanning tunneling spectroscopy. The observed two standing waves caused by separate spin and charge bosonic excitations are found to constitute direct evidence for a Luttinger liquid. The increased group velocity of the charge excitation, the power-law decay of their amplitudes away from the scattering boundary, and the suppression of the density of states near the Fermi level were also directly observed or calculated from the two different standing waves.     

Convective boson-fermion pairing mode in one-dimensional oscillating optical superlattice

A convective pairing mode of a boson-fermion mixture of ultracold atoms confined in an optical superlattice can be induced by the transformation between two optical superlattice configurations. This convective pairing mode only exists in discrete momentum vector zones for pairing energy gaps. The energy spectrum of gapped states is characterized by topological winding numbers. Two neighboring gapped states are bridged by an unstable chiral linear mode, which drives the boson-fermion pair into directional motion for a short period but remains static in the supersymmetric phase with time-reversal symmetry. The phase transition from a gapped mode to a gapless mode occurs at a critical temperature, whose distribution curve for chemical potential demonstrates a similar dome-like trend as that of high $T_c$ superconductor. The boson-fermion pairing may shed light on a possible mechanism of high-$T_c$ superconductivity.     

Density and stability in ultracold dilute boson-fermion mixtures

We analyze in detail recent experiments on ultracold dilute ⁸⁷Rb–⁴⁰K mixtures in Hamburg and in Florence within a mean-field theory. To this end we determine how the stationary bosonic and fermionic density profiles in this mixture depend in the Thomas-Fermi limit on the respective particle numbers. Furthermore, we investigate how the observed stability of the Bose-Fermi mixture with respect to collapse is crucially related to the value of the interspecies s-wave scattering length.     

Narrow-gap Luttinger liquid in carbon nanotubes

Electron interactions reinforce minigaps induced in metallic nanotubes by an external field and turn the gap field dependence into a universal power law. An exactly solvable Gross-Neveau model with an SU(4) symmetry is derived for neutral excitations near half filling. Charge excitations, described by a sine-Gordon perturbation of Luttinger liquid theory, are composite solitons formed by the charged and neutral fields with two separate length scales. Charge compressibility at finite density, evaluated in terms of intersoliton interaction, exhibits a crossover from overlapping to nonoverlapping soliton state. Implications for the Coulomb blockade measurements are discussed.     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

4He Luttinger liquid in nanopores

We study the low-temperature properties of a 4He fluid confined in nanopores, using large-scale quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.     

Transport in a dissipative Luttinger liquid

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is I approximately exp(-E0/eV), where E0 approximately eta/kappa and kappa denotes the compressibility. At nonzero temperature T, the linear conductance is proportional to exp(-sqrt(CE0/kBT)). The decay of Friedel oscillation saturates for a distance larger than L(eta) approximately 1/eta from the impurity.     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.