Shin-Tza Wu

Superfluid stability in the BEC-BCS crossover

We consider a dilute atomic gas of two species of fermions with unequal concentrations under a Feshbach resonance. We find that the system can have distinct properties due to the unbound fermions. The uniform state is stable only when either (a) beyond a critical coupling strength, where it is a gapless superfluid, or (b) when the coupling strength is sufficiently weak, where it is a normal Fermi gas mixture. Phase transition(s) must therefore occur when the resonance is crossed, in contrast to the equal population case where a smooth crossover takes place.

Superfluidity in the interior-gap states

We investigate superfluidity in the interior-gap states proposed by Liu and Wilczek. At weak coupling, we find the gapless interior-gap state unstable in physically accessible regimes of the parameter space, where the superfluid density is shown to be always negative. We therefore conclude that the spatially uniform interior-gap phase is extremely unstable unless it is fully gapped; in this case, however, the state is rather similar to conventional BCS states.

Resonant pairing between fermions with unequal masses

We study via mean-field theory the pairing between fermions of different masses, especially at the unitary limit. At equal populations, the thermodynamic properties are identical with the equal mass case provided an appropriate rescaling is made. At unequal populations, for sufficiently light majority species, the system does not phase separate. For sufficiently heavy majority species, the phase separated normal phase have a density larger than that of the superfluid. For atoms in harmonic traps, the density profiles for unequal mass fermions can be drastically different from their equal-mass counterparts.

Zero-bias conductance peak in tunneling spectroscopy of hybrid superconductor junctions

A generalized method of image, incorporated with the non-equilibrium Keldysh-Greens function formalism, is employed to investigate the tunneling spectroscopy of hybrid systems in the configuration of planar junction. In particular, tunneling spectroscopies of several hybrid systems that exhibit zero-bias conductance peaks (ZBCP) are examined. The well-known metal--d-wave superconductor (ND) junction is first examined in detail. Both the evolution of the ZBCP versus doping and the splitting of the ZBCP in magnetic fields are computed in the framework of the slave-boson mean field theory. Further extension of our method to analyze other states shows that states with particle-hole pairing, such as d-density wave and graphene sheet, are all equivalent to a simple 1D model, which at the same time also describes the polyacetylene. We provide the criteria for the emergence of ZBCP. In particular, broken reflection symmetry at the microscopic level is shown to be a necessary condition for ZBCP to occur.

Generalized method of image and the tunneling spectroscopy in high-T c superconductors

A generalized method of image is developed to investigate the tunneling spectrum from the metal into a class of states, with the tight-binding dispersion fully included. The broken reflection symmetry is shown to be the necessary condition for the appearance of the zero-bias conductance peak ~ZBCP!. Applying this method to the d-wave superconductor yields results in agreement with experiments regarding the splitting of ZBCP’s in magnetic fields. Furthermore, a ZBCP is predicted for tunneling into the~110! direction of the d-density-wave state, providing a signature to look for in experiments. The current transport through a heterojunction consisting of a normal metal and another different material ~X! has been a subject of interest for many years. In this setup, the normal metal with known spectral properties is used as a probe to analyze the electronic states of the material X. 1 Although such measurements have provided useful insights into the bulk spectral properties of X, it has been also realized that the presence of the interface matters. The zero-bias conductance peak ~ZBCP! observed in the tunneling spectra when X is a d-wave superconductor ~ND junction! in the ~110! direction 2 is a well-known example of interface effects. However, the issue of exactly how the tunneling measurements are related to the bulk properties has never been answered satisfactorily. Conventionally, the ND junction is analyzed in the meanfield level, using the Bogoliubov‐de Gennes ~BdG! equations in which continuum and quasiclassical approximations are often invoked. While these approximations are valid for conventional superconductors, they are certainly not justified for high-Tc cuprates where proximity to the Mott insulators entails fully consideration of the tight-binding nature. Previously, 3 this was done by numerically solving the discrete BdG equation for each interface orientation individually without elucidating their relations to the bulk properties. This technical inconvenience makes it difficult to include fluctuations systematically in this approach. In this work, we shall adopt a different approach based on the nonequilibrium Keldysh-Green’s function formalism which enables one to construct systematically higher-order corrections from the mean-field lattice Green’s functions. 4‐6 In this approach, because X extends over a semi-infinite space, one shall need the half-space Green’s functions. For simple configurations such as the ~100! orientation of a d-wave superconductor, it turns out that these half-space Green’s functions only differ from the bulk ones by sinusoidal factors. This relation certainly does not hold for other orientations as it predicts no ZBCP in the ~110! direction. We shall develop a generalized method of image which enables us to construct half-space Green’s functions from the bulk ones. We emphasize the generality of this method and its ability to account for the low-energy features in the tunneling spectrum for a whole class of states . As a demonstration, in this paper we will focus mostly on the study of ND junctions and only briefly mention the applications to other systems. The effects of interactions and fluctuations will be addressed elsewhere. Our results indicate broken reflection symmetry is necessary for the emergence of ZBCP’s. For ND junctions our method can reproduce earlier results on the ZBCP in the continuous-wave approximation. 2,7 In a full tight-binding calculation for ~110! and ~210! directions, we obtain the doping dependence of ZBCP’s which exhibits its sensitivity to the Fermi surface topology. In particular, the splitting of the ZBCP in the current-carrying state is also calculated and is shown to be in agreement with experiments. At the end, we analyze the case when X is the d-density-wave ~DDW! state in ~110! direction and the semi-infinite graphene sheet with a zigzag-type interface. The former state was recently proposed as a possible normal state for high-Tc cuprates. 8 Con

Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space

The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distanceZ from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive indexn. The explicit analytic formulae derived are applicable for arbitrary values ofn. All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. toZ being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/Z3 in the non–retarded regime and as 1/Z4 in the retarded regime, which agrees with the Casimir–Polder result for the limitn→α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distanceZ from the interface.

Quenched decoherence in qubit dynamics due to strong amplitude-damping noise

We study non-perturbatively the time evolution of a qubit subject to amplitude-damping noise. We show that at strong coupling the qubit decoherence can be quenched owing to large environment feedbacks, such that the qubit can evolve coherently even in the long-time limit. As an application, we show that for a quantum channel that consists of two independent qubits subject to uncorrelated local amplitude-damping noises, it can maintain at strong coupling finite entanglement and better than classical teleportation fidelity at long times.

Feedback effects on the current correlations in Y-shaped conductors

We study current fluctuations in a coherent Y-shaped conductor connected to external leads with finite impedances. We show that, due to voltage fluctuations in the circuit, the moments of the transferred charges cannot be obtained from simple rescaling of the zero-impedance expressions already in the second moments. As a consequence, we find the cross correlation between the output terminals can, surprisingly, change from negative to positive for certain combinations of the sample conductance and external impedances.

Exact dynamics for optical coherent-state qubits subject to environmental noise

We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path-integral formulation, we are able to study memory effects on the dynamics of the coherent-state qubits due to strong environment coupling. We apply this formulation to examine the time evolution of a noisy quantum channel formed by two coherent-state qubits that are subject to uncorrelated local environment noises. In particular, we examine the time evolution of entanglement and maximal teleportation fidelity of the noisy quantum channel and show that at strong coupling, due to large feedback effects from the environment noise, it is possible to maintain a robust quantum channel in the long-time limit if an appropriate error-correcting code is applied.

Midgap states and generalized supersymmetry in semi-infinite nanowires

Edge states of semi-infinite nanowires in the tight-binding limit are examined. We argue that understanding these edge states provides a pathway to generic comprehension of surface states in many semi-infinite physical systems. It is shown that the edge states occur within the gaps of the corresponding bulk spectrum (thus also called the midgap states). More importantly, we show that the presence of these midgap states reflects an underlying generalized supersymmetry. This supersymmetric structure is a generalized rotational symmetry among sublattices and results in a universal tendency: all midgap states tend to vanish with periods commensurate with the underlying lattice. Based on our formulation, we propose a structure with superlattice in hopping to control the number of localized electronic states occurring at the ends of the nanowires. Other implications are also discussed. In particular, it is shown that the ordinarily recognized impurity states can be viewed as disguised midgap states.