Showing papers by "Eugene Demler published in 2012"

Relaxation and Prethermalization in an Isolated Quantum System

Abstract: Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge is the scarcity of experimental tools for the characterization of complex transient states. We used measurements of full quantum mechanical probability distributions of matter-wave interference to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtained comprehensive information about the dynamical states of the system. After an initial rapid evolution, the full distributions reveal the approach toward a thermal-like steady state characterized by an effective temperature that is independent from the initial equilibrium temperature of the system before the splitting process. We conjecture that this state can be described through a generalized Gibbs ensemble and associate it with prethermalization.

Observation of topologically protected bound states in photonic quantum walks

Abstract: Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Abstract: The transport measurements of an interacting fermionic quantum gas in an optical lattice provide a direct experimental realization of the Hubbard model—one of the central models for interacting electrons in solids—and give insights into the transport properties of many-body phases in condensed-matter physics.

The 'Higgs' amplitude mode at the two-dimensional superfluid/Mott insulator transition

Abstract: Spontaneous symmetry breaking plays a key role in our understanding of nature. In relativistic quantum field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitation: massless Nambu–Goldstone modes and a massive ‘Higgs’ amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particle physics, and also appears as a fundamental collective mode in quantum many-body systems. Whether such a mode exists in low-dimensional systems as a resonance-like feature, or whether it becomes overdamped through coupling to Nambu–Goldstone modes, has been a subject of debate. Here we experimentally find and study a Higgs mode in a two-dimensional neutral superfluid close to a quantum phase transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected reduction in frequency of the onset of spectral response when approaching the transition point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum field which constitutes a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations that also addresses the consequences of the reduced dimensionality and confinement of the system. Our work constitutes a step towards exploring emergent relativistic models with ultracold atomic gases.

Measuring entanglement entropy of a generic many-body system with a quantum switch.

Abstract: Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Renyi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Abstract: Expanding the reach of the field of ultracold atoms, a comprehensive and practical proposal describes how a range of new experiments on ultracold fermions can explore impurity-induced quantum dynamics--a classical topic in condensed matter physics that has seen very limited experimental observations

Fermi polarons in two dimensions

Abstract: We theoretically analyze inverse radio-frequency (rf) spectroscopy experiments in two-component Fermi gases. We consider a small number of impurity atoms interacting strongly with a bath of majority atoms. In two-dimensional geometries we find that the main features of the rf spectrum correspond to an attractive polaron and a metastable repulsive polaron. Our results suggest that the attractive polaron has been observed in a recent experiment [B. Fr\"ohlich et al., Phys. Rev. Lett. 106, 105301 (2011)].

Topological flat bands from dipolar spin systems.

Abstract: We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S=1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flips. These gauge fields result in topological band structures, whose band gap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultracold polar molecules or spins in the solid state is considered.

Quantum flutter of supersonic particles in one-dimensional quantum liquids

Abstract: Fast particles propagating through a classical medium give rise to shock waves. Calculations now uncover the surprising behaviour of particles in one-dimensional quantum fluids: a fast particle will never come to a full stop, and a supersonic particle will propagate through the medium undergoing long-lived oscillations.

Dynamics and universality in noise-driven dissipative systems

Abstract: We investigate the dynamical properties of low-dimensional systems, driven by external noise sources Specifically we consider a resistively shunted Josephson junction and a one-dimensional quantum liquid in a commensurate lattice potential, subject to $1/f$ noise In absence of nonlinear coupling, we have shown previously that these systems establish a nonequilibrium critical steady state [Dalla Torre, Demler, Giamarchi, and Altman, Nat Phys 6, 806 (2010)] Here, we use this state as the basis for a controlled renormalization group analysis using the Keldysh path integral formulation to treat the nonlinearities: the Josephson coupling and the commensurate lattice The analysis to first order in the coupling constant indicates transitions between superconducting and localized regimes that are smoothly connected to the respective equilibrium transitions However, at second order, the back action of the mode coupling on the critical state leads to renormalization of dissipation and emergence of an effective temperature In the Josephson junction, the temperature is parametrically small allowing to observe a universal crossover between the superconducting and insulating regimes The I-V characteristics of the junction displays algebraic behavior controlled by the underlying critical state over a wide range In the noisy one-dimensional liquid, the generated dissipation and effective temperature are not small as in the junction We find a crossover between a quasilocalized regime dominated by dissipation and another dominated by temperature However, since in the thermal regime the thermalization rate is parametrically small, signatures of the nonequilibrium critical state may be seen in transient dynamics

Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions

Abstract: We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization. We study the dynamics of a rapidly and coherently split one-dimensional Bose gas. An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves towards a quasi-steady state. This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state. We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model and show that the system dephases to a prethermalized state rather than undergoing thermalization towards a final thermal equilibrium state.

Quantum transport of strongly interacting photons in a one-dimensional nonlinear waveguide

Abstract: We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum nonlinear Schrodinger equation. Although this kind of nonlinearity is quite general, we focus on a realistic implementation involving cold atoms loaded in a hollow-core optical fiber, where the atomic system provides a tunable nonlinearity that can be large even at a single-photon level. In particular, we show that when the interaction between photons is effectively repulsive, the transmission of multiphoton components of the field is suppressed. This leads to antibunching of the transmitted light and indicates that the system acts as a single-photon switch. On the other hand, in the case of attractive interaction, the system can exhibit either antibunching or bunching, which is in stark contrast to semiclassical calculations. We show that the bunching behavior is related to the resonant excitation of bound states of photons inside the system.

Clustered Wigner-crystal phases of cold polar molecules in arrays of one-dimensional tubes

Abstract: We analyze theoretically polar molecules confined in planar arrays of one-dimensional tubes. In the classical limit, if the number of tubes is finite, new types of ``clustered Wigner crystals'' with increasingly many molecules per unit cell can be stabilized by tuning the in-plane angle between the dipolar moments and the tube direction. Quantum mechanically these phases melt into distinct ``clustered Luttinger liquids.'' We calculate the phase diagram of the system and study the quantum melting of the clustered phases. We find that the requirements for exploring these phases are reachable in current experiments and discuss possible experimental signatures.

Resonant soft X-ray scattering, stripe order, and the electron spectral function in cuprates

Abstract: We review the current state of efforts to use resonant soft X-ray scattering (RSXS), which is an elastic, momentum-resolved, valence band probe of strongly correlated electron systems, to study stripe-like phenomena in copper-oxide superconductors and related materials. We review the historical progress including RSXS studies of Wigner crystallization in spin ladder materials, stripe order in 214-phase nickelates, 214-phase cuprates, and other systems. One of the major outstanding issues in RSXS concerns its relationship to more established valence band probes, namely angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). These techniques are widely understood as measuring a one-electron spectral function, yet a relationship between RSXS and a spectral function has so far been unclear. Using physical arguments that apply at the oxygen K edge, we show that RSXS measures the square modulus of an advanced version of the Green’s function measured with STM. This indicates that, despite being a momentum space probe, RSXS is more closely related to STM than to ARPES techniques. Finally, we close with some discussion of the most promising future directions for RSXS. We will argue that the most promising area lies in high magnetic field studies, particularly of edge states in strongly correlated heterostructures, and the vortex state in superconducting cuprates, where RSXS may clarify the anomalous periodicities observed in recent quantum oscillation experiments.

Universal features of the excitation spectrum in a generalized Gibbs distribution ensemble

Abstract: It is shown that excitation spectra of Generalized Gibbs Ensembles (GGE) of one-dimensional integrable models with isotopic symmetry contain universal features insensitive to details of the distribution. Namely, the low energy limit of the subsystem of isotopic (for instance, spin) excitations is described by the effective action of a ferromagnet at thermodynamic equilibrium with a single temperature and with the stiffness determined by the initial conditions. The condition of universality is that the entropy per excited particle is small.

Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps

Abstract: We investigate the equilibrium and dynamical properties of the Bose-Hubbard model and the related particle-hole symmetric spin-1 model in the vicinity of the superfluid to Mott insulator quantum phase transition. We employ the following methods: exact-diagonalization, mean-field (Gutzwiller), cluster mean-field, and mean-field plus Gaussian fluctuations. In the first part of the paper we benchmark the four methods by analyzing the equilibrium problem and give numerical estimates for observables such as the density of double occupancies and their correlation function. In the second part, we study parametric ramps from the superfluid to the Mott insulator and map out the crossover from the regime of fast ramps, which is dominated by local physics, to the regime of slow ramps with a characteristic universal power law scaling, which is dominated by long wavelength excitations. We calculate values of several relevant physical observables, characteristic time scales, and an optimal protocol needed for observing universal scaling.

Collective excitations of quasi-two-dimensional trapped dipolar fermions: Transition from collisionless to hydrodynamic regime

Abstract: We study the collective excitations of polarized single-component quasi-two-dimensional dipolar fermions in an isotropic harmonic trap by solving the collisional Boltzmann-Vlasov (CBV) equation via the method of moments. We study the response to monopole and quadrupole perturbations of the trap potential and investigate the dynamical character of excitations in each case. Simple analytic formulas are found using the linearized scaling ansatz approximation and accurate numerical results are obtained by satisfying the first eight moments of the CBV equation. Except for the lowest-lying monopole mode that is weakly affected by collisions, the quadrupole and the higher-order monopole modes undergo a transition from the collisionless regime to a dissipative crossover regime and finally approach the hydrodynamic regime upon increasing the dipolar interaction strength. For strong transverse confinement (2D limit), we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent. This plateau, which is a direct consequence of dipole-dipole scatterings, persists as long as the scattering energies remain in the near-threshold regime. The predictions of this work are expected to be observable in the current experiments.

Pairing instabilities in quasi-two-dimensional Fermi gases

Abstract: We study nonequilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from a weakly interacting to a strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules.

Relaxation Dynamics and Pre-thermalization in an Isolated Quantum System

Abstract: Understanding non-equilibrium dynamics of many-body quantum systems is crucial for many fundamental and applied physics problems ranging from de-coherence and equilibration to the development of future quantum technologies such as quantum computers which are inherently non-equilibrium quantum systems. One of the biggest challenges is that there is no general approach to characterize the resulting quantum states.

Two-dimensional coupled resonator optical waveguide arrangements and systems, devices, and methods thereof

Abstract: Two-dimensional coupled resonator optical waveguide arrangements and systems, devices, and methods thereof. Networks of coupled resonator optical waveguides are arranged so as to exploit topological properties of these optical networks. Such arrangement affords topological protection against disorders or perturbations in the network that may hinder or block photon flow. As a result of a disorder, photons traversing along edge states of the array are rerouted based on the disorder or perturbation. Photon routing in the network is accordingly protected against disorder or defects.

Quantum flutter of supersonic particles in one-dimensional quantum liquids

Abstract: Fast particles propagating through a classical medium give rise to shock waves. Calculations now uncover the surprising behaviour of particles in one-dimensional quantum fluids: a fast particle will never come to a full stop, and a supersonic particle will propagate through the medium undergoing long-lived oscillations.

Photo control of transport properties in disorderd wire; average conductance, conductance statistics, and time-reversal symmetry

Abstract: In this paper, we study the full conductance statistics of disordered one dimensional wire under the application of light. We develop the transfer matrix method for periodically driven systems to analyze the conductance of large system with small frequency of light, where coherent photon absorptions play important role to determine not only the average but also the shape of conductance distributions. The average conductance under the application of light results from the competition between dynamic localization and effective dimension increase, and shows non-monotonic behavior as a function of driving amplitude. On the other hand, the shape of conductance distribution displays crossover phenomena in the intermediate disorder strength; the application of light dramatically changes the distribution from log-normal to normal distributions. Furthermore, we propose that conductance of disordered systems can be controlled by engineering the shape, frequency and amplitude of light. Change of the shape of driving field controls the time-reversals symmetry and the disordered system shows analogous behavior as negative magneto-resistance known in static weak localization. A small change of frequency and amplitude of light leads to a large change of conductance, displaying giant-opto response. Our work advances the perspective to control the mean as well as the full conductance statistics by coherently driving disordered systems.

Doublon production rate in modulated optical lattices

Abstract: We theoretically study lattice modulation experiments with ultracold fermions in optical lattices. We focus on the regime relevant to current experiments when interaction strength is larger than the bandwidth and temperature is higher than magnetic superexchange energy. We obtain analytical expressions for the rate of doublon production as a function of modulation frequency, filling factor, and temperature. We use local density approximation to average over inhomogeneous density for atoms in a parabolic trap and find excellent agreement with experimentally measured values. Our results suggest that lattice modulation experiments can be used for thermometry of strongly interacting fermionic ensembles in optical lattices.

Triplet pair correlations in s-wave superfluids as a signature of the Fulde-Ferrell-Larkin-Ovchinnikov state.

Abstract: We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states

Mott criticality and pseudogap in Bose-Fermi mixtures.

Abstract: We study the Mott transition of a mixed Bose-Fermi system of ultracold atoms in an optical lattice, where the number of (spinless) fermions and bosons adds up to one atom per lattice, n(F)+n(B)=1. For weak interactions, a Fermi surface coexists with a Bose-Einstein condensate while for strong interaction the system is incompressible but still characterized by a Fermi surface of composite fermions. At the critical point, the spectral function of the fermions A(k,ω) exhibits a pseudogapped behavior, rising as |ω| at the Fermi momentum, while in the Mott phase it is fully gapped. Taking into account the interaction between the critical modes leads at very low temperatures either to p-wave pairing or the transition is driven weakly first order. The same mechanism should also be important in antiferromagnetic metals with a small Fermi surface.

Noisy quantum phase transitions: an intuitive approach

Abstract: Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by $1/f$ charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.

Pairing instabilities in quasi-two-dimensional Fermi gases

Abstract: We study nonequilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from a weakly interacting to a strongly interacting regime. We develop a $T$-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules.

Noisy quantum phase transitions: an intuitive approach

Abstract: Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers, we have considered the specific case of a resistively shunted Josephson junction driven by 1/f charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group approach, we found that the noise has three main effects: it shifts the phase transition, renormalizes the resistance and generates an effective temperature. In this paper, we explain how to understand these effects using simpler arguments based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current–voltage characteristic of the junction. In the appendix, we describe two possible realizations of the model with ultracold atoms confined to one dimension.