Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.     

Effects of pairing potential scattering on Fourier-transformed inelastic tunneling spectra of high-Tc cuprate superconductors with bosonic modes

Recent scanning tunneling microscopy (STM) experimentally observed strong gap inhomogeneity in Bi2Sr2CaCu2O(8+delta) (BSCCO). We argue that disorder in the pair potential underlies the gap inhomogeneity, and investigate its role in the Fourier-transformed inelastic tunneling spectra as revealed in the STM. We find that the random pair potential induces unique q-space patterns in the local density of states (LDOS) of a d-wave superconductor. We consider the effects of electron coupling to various bosonic modes and find the pattern of LDOS modulation due to coupling to the B(1g) phonon mode to be consistent with the one observed in the inelastic electron tunnneling STM experiment in BSCCO. These results suggest strong electron-lattice coupling as an essential part of the superconducting state in high-Tc materials.     

Mixed state of a dirty two-band superconductor: application to MgB2

We investigate the vortex state in a two-band superconductor with strong intraband and weak interband electronic scattering rates. Coupled Usadel equations are solved numerically, and the distributions of the pair potentials and local densities of states are calculated for two bands at different values of magnetic fields. The existence of two distinct length scales corresponding to different bands is demonstrated. The results provide qualitative interpretation of recent scanning tunneling microscopy experiments on vortex structure imaging in MgB2.     

Effect of measurement on the periodicity of the Coulomb staircase of a superconducting box

We report on the effect of the backaction of a single Cooper pair transistor electrometer (E) on the charge state of a superconducting box (B). The charge is e periodic in the gate bias of B when E is operated near voltages 2 Delta/e or 4 Delta/e. We show that this is due to quasiparticle poisoning of B at a rate proportional to the number of quasiparticle tunneling events in E per second. We are able to eliminate this backaction and recover 2e-charge periodicity using a new measurement method based on switching-current modulation of E.     

Theory of tunneling conductance of STS around magnetic impurity in superconductors

Local density of states of quasiparticles around the magnetic impurity in superconductors are calculated on the basis of a pair potential the spatial dependence of which is determined self-consistently using negative Hubbard model. The spatial dependence of the tunneling conductance observed by Scanning tunneling spectroscopy (STS) strongly depends on the magnitude of the impurity potentials.     

Atomic Landau-Zener tunneling in Fourier-synthesized optical lattices

We report on an experimental study of quantum transport of atoms in variable periodic optical potentials. The band structure of both ratchet-type asymmetric and symmetric lattice potentials is explored. The variable atom potential is realized by superimposing a conventional standing wave potential of lambda/2 spatial periodicity with a fourth-order multiphoton potential of lambda/4 periodicity. We find that the Landau-Zener tunneling rate between the first and the second excited Bloch band depends critically on the relative phase between the two spatial lattice harmonics.     

Limit Gibbs state for some classes of one-dimensional systems of quantum statistical mechanics

We prove the existence of the limit Gibbs state for one-dimensional continuous quantum fermion systems with non-hard-core, non-negative, rapidly decreasing pair interaction potentials. Existence of the limit Gibbs state is also established for one-dimensional continuous quantum boson systems with pair interaction potentials as above which, in addition, increase sufficiently fast at small distances.This work is partially performed with the support of the National Council of Researches of Italy     

Probing superconducting phase fluctuations from the current noise spectrum of pseudogapped metal-superconductor tunnel junctions

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency omega(J) = 2eV when omega(J) is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an ac voltage, the tunneling current noise shows a series of characteristic peaks with increasing dc voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high- T(c) superconductors and the pair decay rate can be estimated from the half width of the peaks.     

Quantum antidot as an electrometer:Observation of fractional charge

In experiments on resonant tunneling through a quantum antidot in the quantum Hall (QH) regime, we observe periodic conductance peaks both versus magnetic field and a global gate voltage, i.e., electric field. Each conductance peak can be attributed to tunneling through a quantized antidot-bound state. The fact that the variation of the uniform electric field produces conductance peaks implies that the deficiency of the electrical charge on the antidot is quantized in units of charge of quasiparticles of surrounding QH condensate. The period in magnetic field gives the effective area of the antidot state through which tunneling occurs, the period in electric field (obtained from the global gate voltage) then constitutes a direct measurement of the charge of the tunneling particles. We obtain electron charge C in the integer QH regime, and quasiparticle charge C for the QH state.     

Path Integral Method for Tunneling of Spin Systems and the Macroscopic Quantum Effect of Magnetization

The quantum tunneling effect in a ferromagnetic particle which can be evaluated only for the ground state previously is extended to excited states within the framework of instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration with which a formula of level-splitting valid for entire energy region is derived. In low energy region periodic instanton results coincide exactly with those derived through the LSZ reduction procedure. The tunneling effect increases at excited states. These results should be useful in further investigation of phase transition problem in ferromagnetic particles.     

Tunneling control and localization for Bose-Einstein condensates in a frequency modulated optical lattice

The similarity between matter waves in periodic potential and solid-state physics processes has triggered the interest in quantum simulation using Bose-Fermi ultracold gases in optical lattices. The present work evidences the similarity between electrons moving under the application of oscillating electromagnetic fields and matter waves experiencing an optical lattice modulated by a frequency difference, equivalent to a spatially shaken periodic potential. We demonstrate that the tunneling properties of a Bose-Einstein condensate in shaken periodic potentials can be precisely controlled. We take additional crucial steps towards future applications of this method by proving that the strong shaking of the optical lattice preserves the coherence of the matter wavefunction and that the shaking parameters can be changed adiabatically, even in the presence of interactions. We induce reversibly the quantum phase transition to the Mott insulator in a driven periodic potential.     

Inter-Well Coupling and Resonant Tunneling Modes of MultipleGraphene Quantum Wells

We investigate the inter-well coupling of multiple graphene quantum well structures consisting of graphene superlattices with different periodic potentials. The general form of the eigenlevel equation for the bound states of the quantum well is expressed in terms of the transfer matrix elements. It is found that the electronic transmission exhibits resonant tunneling peaks at the eigenlevels of the bound states and shifts to the higher energy with increasing the incident angle. If there are N coupled quantum wells, the resonant modes have N-fold splitting. The peaks of resonant tunneling can be controlled by modulating the graphene barriers.     

Cold atoms in non-Abelian gauge potentials: from the Hofstadter "moth" to lattice gauge theory

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.     

Bound state resonances in atom-solid scattering

Theoretical studies and numerical calculations of bound state resonances (selective adsorption) in the elastic scattering of low-energy light atoms from a perfect crystalline surface are made. The surface-atom potential used is the sum of Yukawa-6 pair potentials with the pair potential parameters fixed to yield the correct bound state energies for the HeLiF system. The scattering equation is numerically integrated using basis sets of open and closed channels of varying number. It is found that numerically accurate solutions are obtained only if the basis set includes the bound state in resonance, all diffracted channels coupled strongly to it by the periodic surface potential, and the specular and other low-order diffracted channels. The calculations yield specular minimum and (11) and (21) diffraction maximum under (01) selective adsorption conditions in agreement with experimental observations for the HeLiF and HeNaF systems. These results appear independent of the potential model. The atomic band structure due to the surface periodic potential is found to yield splitting of the specular minima and/or broadening of the minima. It is suggested that studying such splittings will yield information on the periodic surface potential.     

Unusual band structure and exotic electrical conduction for electrons in incommensurate lattice potentials

Electrons in crystals with incommensurate periodic potentials are shown to exhibit a band structure with many very narrow bands separated by narrow band gaps. This makes such systems ideal candidates for observing such exotic electrical conduction phenomena in d.c. fields as Zener tunneling and Stark oscillations. Estimates are made of the conditions under which such phenomena should be observable experimentally.     

铁磁-p波超导结中的自旋极化隧道谱与散粒噪声

考虑到界面的势垒散射和铁磁层中的磁交换作用，依照Sr2RuO4超导体具有自旋三重配对态的p波对称结构，研究铁磁-p波超导结中的自旋极化隧道谱与散粒噪声，研究表明：1.对于幺正配对态，随着铁磁层中磁交换劈裂增强，隧道谱与散粒噪声都减少；2.对于非幺正配对态，隧道谱与散粒噪声都依赖于铁磁层的磁化轴方向，当磁化轴平行于非幺正配对态的自旋轴时，在低偏压下磁交换作用能使隧谱与散粒噪声增强，而当磁化轴反平行于自旋转轴时，其结果相反。     

Tunneling into clean heavy fermion compounds: origin of the Fano line shape

Recently observed tunneling spectra on clean heavy-fermion compounds show a lattice periodic Fano line shape similar to what is observed in the case of tunneling to a Kondo ion adsorbed at the surface. We show that the translation symmetry of a clean surface in the case of weakly correlated metals leads to a tunneling spectrum which shows a hybridization gap but does not have a Fano line shape. By contrast, in a strongly correlated heavy-fermion metal the heavy quasiparticle states will be broadened by interaction effects. The hybridization gap is completely filled in this way, and an ideal Fano line shape of width ～2TK results. In addition, we discuss the possible influence of the tunneling tip on the surface, in (i) leading to additional broadening of the Fano line and (ii) enhancing the hybridization locally, hence adding to the impurity type behavior. The latter effects depend on the tip-surface distance.     

Tuning the Mott transition in a Bose-Einstein condensate by multiple photon absorption

We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how applying a periodic driving field can induce coherent destruction of tunneling. In the low-frequency regime, we obtain the novel result that the destruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with the depth of the trapping potential ("multi-photon resonances"), which allows the quantum phase transition between the Mott insulator and the superfluid state to be controlled with high precision. We further show how the waveform of the field can be chosen to maximize this effect.     

Coherent Cooper pair tunneling in systems of Josephson junctions: Effects of quasiparticle tunneling and of the electromagnetic environment

Small capacitance tunnel junctions show single electron effects and, in the superconducting state, the coherent tunneling of Cooper pairs. We study these effects in a system of two Josephson junctions, driven by a voltage source with a finite impedance. Novel features show up in theI?V characteristics, in particular pronounced structures at subgap voltages. These are due to Cooper pair tunneling, combined with tunneling of quasiparticles or with excitation of the electromagnetic environment.     

Dynamics of a cold quantum gas in a δ-split one-dimensional potential well

Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.