Induced interactions in dilute atomic gases and liquid helium mixtures

In dilute mixtures of two atomic gases, interactions between two minority atoms acquire a contribution due to interaction with the majority component. Using thermodynamic arguments, we derive expressions for this induced interaction for both fermions and bosons for arbitrary strength of the interaction between the two components. Implications of the work for the theory of dilute solutions of $^3$He in liquid $^4$He are discussed.Comment: 7 pages, 1 figure, NORDITA-2012-3

Exchange cotunneling through quantum dots with spin-orbit coupling

We investigate the effects of spin-orbit interaction (SOI) on the exchange cotunneling through a spinful Coulomb blockaded quantum dot. In the case of zero magnetic field, Kondo effect is shown to take place via a Kramers doublet and the SOI will merely affect the Kondo temperature. In contrast, we find that the breaking of time-reversal symmetry in a finite field has a marked influence on the effective Anderson, and Kondo models for a single level. The nonlinear conductance can now be asymmetric in bias voltage and may depend strongly on direction of the magnetic field. A measurement of the angle dependence of finite-field cotunneling spectroscopy thus provides valuable information about orbital, and spin degrees of freedom and their mutual coupling.Comment: 5 pages, 2 figure

One-Particle Anomalous Excitations of Gutzwiller Projected BCS Superconductors and Bogoliubov Quasi-Particle Characteristics

Low-lying one-particle anomalous excitations are studied for Gutzwiller projected strongly correlated BCS states. It is found that the one-particle anomalous excitations are highly coherent, and the numerically calculated spectrum can be reproduced quantitatively by a renormalized BCS theory, thus strongly indicating that the nature of low-lying excitations described by the projected BCS states is essentially understood within a renormalized Bogoliubov quasi-particle picture. This finding resembles a well known fact that a Gutzwiller projected Fermi gas is a Fermi liquid. The present results are consistent with numerically exact calculations of the two-dimensional t-J model as well as recent photoemission experiments on high-T_{\rm C} cuprate superconductors.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. B 74, 180504(R) (2006

Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.Comment: 21 pages, 8 figure

Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.Comment: 21 pages, 10 figure

Probing ultracold Fermi gases with light-induced gauge potentials

We theoretically investigate the response of a two component Fermi gas to vector potentials which couple separately to the two spin components. Such vector potentials may be implemented in ultracold atomic gases using optically dressed states. Our study indicates that light-induced gauge potentials may be used to probe the properies of the interacting ultracold Fermi gas, providing. amongst other things, ways to measure the superfluid density and the strength of pairing.Comment: 8 pages, 3 figure

Strong vs. Weak Coupling Duality and Coupling Dependence of the Kondo Temperature in the Two-Channel Kondo Model

We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo model to obtain the dependence of the Kondo temperature $T_K$ on the dimensionless (bare) spin exchange coupling $g$ over the complete parameter range from $g\ll 1$ to $g\gg 1$. We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\leftrightarrow 3/(2g)$, implying an exponential dependence of $T_K$ on $1/g$ and $g$, respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract $T_K(g)$ over the complete parameter range and obtain a non-monotonous $T_K(g)$ dependence, strongly peaked at the 2CK fixed point coupling $g^*$. These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems, why no broad distribution of $T_K$ is observed in those systems.Comment: 6 pages, 3 figures; PRB published version, shortened, nomenclature clarifie

Kondo effect in a quantum dot coupled to ferromagnetic leads and side-coupled to a nonmagnetic reservoir

Equilibrium transport properties of a single-level quantum dot tunnel-coupled to ferromagnetic leads and exchange-coupled to a side nonmagnetic reservoir are analyzed theoretically in the Kondo regime. The equilibrium spectral functions and conductance through the dot are calculated using the numerical renormalization group (NRG) method. It is shown that in the antiparallel magnetic configuration, the system undergoes a quantum phase transition with increasing exchange coupling $J$, where the conductance drops from its maximum value to zero. In the parallel configuration, on the other hand, the conductance is generally suppressed due to an effective spin splitting of the dot level caused by the presence of ferromagnetic leads, irrespective of the strength of exchange constant. However, for $J$ ranging from J=0 up to the corresponding critical value, the Kondo effect and quantum critical behavior can be restored by applying properly tuned compensating magnetic field.Comment: (8 pages, 8 figs) to appear in PR

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)] that has recently observed this crossover temperature.Comment: 4 pages, 2 figure

Fermi liquid identities for the Infinite U Anderson Model

We show how the electron gas methods of Luttinger, Ward and Nozi\`eres can be applied to the infinite U Anderson impurity model within a Schwinger boson treatment. Working to all orders in a 1/N expansion, we show how the Friedel Langreth relationship, the Yamada-Yosida-Yoshimori and the Shiba-Korringa relations can be derived, under the assumption that the spinon and holon fields are gapped. One of the remarkable features of this treatment, is that the Landau amplitudes depend on the exchange of low energy virtual spinons and holons. We end the paper with a discussion on the extension of our approach to the lattice, where the spinon-holon is expected to close at a quantum critical point.Comment: 18 pages. Version 2 revised after referees comment