Comment on ``Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids''

In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.Comment: 1 page, Revte

Commensurate mixtures of ultra-cold atoms in one dimension

We study binary mixtures of ultra-cold atoms, confined to one dimension in an optical lattice, with commensurate densities. Within a Luttinger liquid description, which treats various mixtures on equal footing, we derive a system of renormalization group equations at second order, from which we determine the rich phase diagrams of these mixtures. These phases include charge/spin density wave order, singlet and triplet pairing, polaron pairing, and a supersolid phase. Various methods to detect our results experimentally are discussed.Comment: 7 pages, 4 figures, v4: extended versio

Crystal Distortion and the Two-Channel Kondo Effect

We study a simple model of the two-channel Kondo effect in a distorted crystal. This model is then used to investigate the interplay of the Kondo and Jahn-Teller effects, and also the Kondo effect in an impure crystal. We find that the Jahn-Teller interaction modifies the characteristic energy scale of the system below which non-Fermi-liquid properties of the model become apparent. The modified energy scale tends to zero as the limit of a purely static Jahn-Teller effect is approached. We find also that the non-Fermi-liquid properties of the quadrupolar Kondo effect are not stable against crystal distortion caused by impurities.Comment: 11 page

Reliable quantum certification for photonic quantum technologies

A major roadblock for large-scale photonic quantum technologies is the lack of practical reliable certification tools. We introduce an experimentally friendly - yet mathematically rigorous - certification test for experimental preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states generated by linear-optical circuits with n-boson Fock-basis states as inputs, and states of these two classes subsequently post-selected with local measurements on ancillary modes. The protocol is efficient in m and the inverse post-selection success probability for all Gaussian states and all mentioned non-Gaussian states with constant n. We follow the mindset of an untrusted prover, who prepares the state, and a skeptic certifier, with classical computing and single-mode homodyne-detection capabilities only. No assumptions are made on the type of noise or capabilities of the prover. Our technique exploits an extremality-based fidelity bound whose estimation relies on non-Gaussian state nullifiers, which we introduce on the way as a byproduct result. The certification of many-mode photonic networks, as those used for photonic quantum simulations, boson samplers, and quantum metrology, is now within reach.Comment: 8 pages + 20 pages appendix, 2 figures, results generalized to scenarios with post-selection, presentation improve

Full counting statistics of spin transfer through ultrasmall quantum dots

We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modelling the setup by the Anderson Hamiltonian, we explicitly take into account the onsite Coulomb repulsion $U$. We calculate the cumulant generating function for the probability to transfer a certain number of electrons with a preselected spin orientation during a fixed time interval. With the cumulant generating function at hand we are then able to calculate the spin current correlations which are of outmost importance in the emerging field of spintronics. We confirm the existing results for the charge statistics and report the discovery of the new type of correlation between the spin-up and -down polarized electrons flows, which has a potential to become a powerful new instrument for the investigation of the Kondo effect in nanostructures.Comment: 5 pages, 1 figur

Threshold Singularities in the One Dimensional Hubbard Model

We consider excitations with the quantum numbers of a hole in the one dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with delta-function interactions).Comment: 26 pages, 12 figures version to appear in Phys Rev

Localization of a matter wave packet in a disordered potential

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis

Correlation functions of one-dimensional Bose-Fermi mixtures

We calculate the asymptotic behaviour of correlation functions as a function of the microscopic parameters for a Bose-Fermi mixture with repulsive interaction in one dimension. For two cases, namely polarized and unpolarized fermions the singularities of the momentum distribution functions are characterized as a function of the coupling constant and the relative density of bosons.Comment: RevTeX 4, 10 pages, 2 figure

Full counting statistics for the Kondo dot in the unitary limit

We calculate the charge transfer probability distribution function $\chi(\lambda)$ for the Kondo dot in the strong coupling limit within the framework of the Nozi\`{e}res--Fermi--liquid theory of the Kondo effect. At zero temperature, the ratio of the moments $C_n$ of the charge distribution to the backscattering current $I_{{\rm bs}}$ follows a universal law $C_n/2I_{{\rm bs}}=(-1)^n(1+2^n)/6$. The functional form of $\chi(\lambda)$ is consistent with tunnelling of electrons and, possibly, electron pairs. We then discuss the cross-over behaviour of $\chi(\lambda)$ from weak to strong Coulomb repulsion in the underlying Anderson impurity model and relate this to the existing results. Finally, we extend our analysis to the case of finite temperatures.Comment: 5 pages, 1 eps figur