Quasiuniversal Transient Behavior of a Nonequilibrium Mott Insulator Driven by an Electric Field

We use a self-consistent strong-coupling expansion for the self-energy (perturbation theory in the hopping) to describe the nonequilibrium dynamics of strongly correlated lattice fermions. We study the three-dimensional homogeneous Fermi-Hubbard model driven by an external electric field showing that the damping of the ensuing Bloch oscillations depends on the direction of the field and that for a broad range of field strengths a long-lived transient prethermalized state emerges. This long-lived transient regime implies that thermal equilibrium may be out of reach of the time scales accessible in present cold atom experiments but shows that an interesting new quasiuniversal transient state exists in nonequilibrium governed by a thermalized kinetic energy but not a thermalized potential energy. In addition, when the field strength is equal in magnitude to the interaction between atoms, the system undergoes a rapid thermalization, characterized by a different quasiuniversal behavior of the current and spectral function for different values of the hopping. DOI: 10.1103/PhysRevLett.109.260402

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

Bounds on the spacelike pion electromagnetic form factor from analyticity and unitarity

We use the recently measured accurate BaBaR data on the modulus of the pion electromagnetic form factor,Fπ(t), up to an energy of 3 GeV, the I=1P-wave phase of the π π scattering ampli-tude up to the ω−π threshold, the pion charge radius known from Chiral Perturbation Theory,and the recently measured JLAB value of Fπ in the spacelike region at t=−2.45GeV2 as inputs in a formalism that leads to bounds on Fπ in the intermediate spacelike region. We compare our constraints with experimental data and with perturbative QCD along with the results of several theoretical models for the non-perturbative contribution s proposed in the literature.

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si: P and Ge: P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Fermi-Edge Transmission Resonance in Graphene Driven by a Single Coulomb Impurity

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude approximate to e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Fermions in Synthetic Non-Abelian Gauge Fields

Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.

Frequency-domain stimulated and spontaneous light emission signals at molecular junctions

Using a diagrammatic superoperator formalism we calculate optical signals at molecular junctions where a single molecule is coupled to two metal leads which are held at different chemical potentials. The molecule starts in a nonequilibrium steady state whereby it continuously exchanges electrons with the leads with a constant electron flux. Expressions for frequency domain optical signals measured in response to continuous laser fields are derived by expanding the molecular correlation functions in terms of its many-body states. The nonunitary evolution of molecular states is described by the quantum master equation. (C) 2014 AIP Publishing LLC.

Cooling a Band Insulator with a Metal: Fermionic Superfluid in a Dimerized Holographic Lattice

A cold atomic realization of a quantum correlated state of many fermions on a lattice, eg. superfluid, has eluded experimental realization due to the entropy problem. Here we propose a route to realize such a state using holographic lattice and confining potentials. The potentials are designed to produces aband insulating state (low heat capacity) at the trap center, and a metallic state (high heat capacity) at the periphery. The metal ``cools'' the central band insulator by extracting out the excess entropy. The central band insulator can be turned into a superfluid by tuning an attractive interaction between the fermions. Crucially, the holographic lattice allows the emergent superfluid to have a high transition temperature - even twice that of the effective trap temperature. The scheme provides a promising route to a laboratory realization of a fermionic lattice superfluid, even while being adaptable to simulate other many body states.

Quench dynamics and parity blocking in Majorana wires

We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities-the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term `parity blocking'. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions

The nonlinear optical response of a current-carrying single molecule coupled to two metal leads and driven by a sequence of impulsive optical pulses with controllable phases and time delays is calculated. Coherent (stimulated, heterodyne) detection of photons and incoherent detection of the optically induced current are compared. Using a diagrammatic Liouville space superoperator formalism, the signals are recast in terms of molecular correlation functions which are then expanded in the many-body molecular states. Two dimensional signals in benzene-1,4-dithiol molecule show cross peaks involving charged states. The correlation between optical and charge current signal is also observed. (C) 2015 AIP Publishing LLC.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Spectral intensity distribution of trapped

To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin4 fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.