Showing papers by "Eugene Demler published in 2009"
TL;DR: This analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially and the corresponding relaxation time exhibits a minimum at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.
Abstract: We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or nonoscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a minimum at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.
192 citations
TL;DR: In this paper, the authors investigated the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement.
Abstract: We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of ``density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.
101 citations
Abstract: Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties usually relevant in solid-state many-body systems. In this paper we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. This reveals which aspects of non-equilibrium dynamics can as in equilibrium be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.
87 citations
TL;DR: In this paper, the form-factor approach was combined with the method of intertwining operator, which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions.
Abstract: In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.
84 citations
Journal Article•
55 citations
TL;DR: In this paper, an experimental scheme was proposed to detect ultracold-atom d-wave Cooper pairs in superconductors by combining optical lattices and superlattices.
Abstract: d-wave Cooper pairs are believed to be the key for understanding the phenomenon of high-temperature superconductivity in cuprates. These superconductors are an example of the emergence of strong pairing in systems with purely repulsive interactions, similar to superfluid helium 3 and the newly discovered iron oxypnictides. Despite intense studies, there is currently no consensus as to what causes the formation of d-wave Cooper pairs in these materials. Here we propose a novel experimental scheme in which recently demonstrated methods for realizing optical lattices and superlattices are combined to create and to detect, in a controlled way, ultracold-atom d-wave Cooper pairs. Our scheme starts from arrays of isolated plaquettes which incorporate the required d-wave correlations on a short length scale. By tuning the parameters of the potentials, these plaquettes can be coupled to achieve long-range d-wave superfluid correlations, finally arriving at the generic Hubbard model.
44 citations
TL;DR: It is shown how the generic many-body phenomena of antibunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.
Abstract: Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of antibunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.
32 citations
TL;DR: It is shown that optical lattice modulation spectroscopy can be used to detect antiferromagnetic order and probe the nature of quasiparticle excitations in a fermionic Mott insulator.
Abstract: Observing antiferromagnetic correlations in ultracold fermions on optical lattices is an important step towards quantum simulation of the repulsive Hubbard model. We show that optical lattice modulation spectroscopy can be used to detect antiferromagnetic order and probe the nature of quasiparticle excitations in a fermionic Mott insulator. At high temperatures, the rate of creation of double occupancies shows a broad peak at frequency of the on-site repulsion U, reflecting the incoherent nature of the hole excitations. At low temperatures, antiferromagnetic order leads to fine structure in the response consisting of a sharp absorption edge reflecting coherent propagation of holes and oscillations as a function of modulation frequency representing spin-wave shake-off processes.
23 citations
TL;DR: In this paper, the interplay of quantum fluctuations and dissipation in uniform superconducting nanowires is discussed. And the authors find that phase-slip dipoles proliferate in the wire and decouple the two fluids within its bulk, and that the normal fluid only couples to the superconductor fluid through the leads at the edges of the wire.
Abstract: In this paper we discuss the interplay of quantum fluctuations and dissipation in uniform superconducting nanowires. We consider a phenomenological model with superconducting and normal components and a finite equilibration rate between these two fluids. We find that phase-slip dipoles proliferate in the wire and decouple the two fluids within its bulk. This implies that the normal fluid only couples to the superconductor fluid through the leads at the edges of the wire, and the local dissipation is unimportant. Therefore, while long wires have a superconductor-metal transition tuned by local properties of the superconducting fluid, short wires have a transition when the total resistance is R_(tot)=R_Q=h/4e^2.
18 citations
TL;DR: It is shown that magnetoroton softening occurs in 87Rb spinor condensates and a rich variety of dynamical instabilities emerges as a function of the magnetic field orientation and strength of the quadratic Zeeman shift.
Abstract: Superfluids with a tendency towards periodic order have both phonon- and rotonlike spectra. We show that magnetoroton softening occurs in $^{87}\mathrm{Rb}$ spinor condensates. A rich variety of dynamical instabilities emerges as a function of the magnetic field orientation and strength of the quadratic Zeeman shift. These instabilities are driven by an effective dipolar interaction modified dramatically by quasi-two-dimensionality and rapid Larmor precession.
16 citations
TL;DR: In this article, the spin-resolved noise correlations of two-dimensional and three-dimensional optical lattices were used to detect antiferromagnetic correlations of fermionic atoms.
Abstract: We analyze how noise correlations probed by time-of-flight experiments reveal antiferromagnetic (AF) correlations of fermionic atoms in two-dimensional and three-dimensional optical lattices. Combining analytical and quantum Monte Carlo calculations using experimentally realistic parameters, we show that AF correlations can be detected for temperatures above and below the critical temperature for AF ordering. It is demonstrated that spin-resolved noise correlations yield important information about the spin ordering. Finally, we show how to extract the spin correlation length and the related critical exponent of the AF transition from the noise.
Posted Content•
TL;DR: In this article, the dynamics of two component non-interacting ultracold Fermions which are initially in thermal equilibrium and undergo a rapid quench to either the repulsive or attractive side of a Feshbach resonance are described.
Abstract: We describe the dynamics of two component non-interacting ultracold Fermions which are initially in thermal equilibrium and undergo a rapid quench to either the repulsive or attractive side of a Feshbach resonance. The short time dynamics is dominated by the exponentially growing collective modes. We study the Stoner instability and formation of ferromagnetic textures on the repulsive side, and the pairing instability towards BCS or FFLO-like states (determined by the population imbalance) on the attractive side. In each case, we evaluate the growth rate of unstable modes and predict the typical lengthscale of textures to be formed.
TL;DR: In this article, a cyclic spin-2 condensate is placed in a small magnetic field that breaks the spin symmetry, these vortices may form bound states, and it is shown that some configurations that are stable at zero temperature can decay at finite temperatures by crossing over energy barriers.
Abstract: Condensates of atoms with spins can have vortices of several types; these are related to the symmetry group of the atoms' ground state. We discuss how, when a condensate is placed in a small magnetic field that breaks the spin symmetry, these vortices may form bound states. Using symmetry classification of vortex charge and rough estimates for vortex interactions, one can show that some configurations that are stable at zero temperature can decay at finite temperatures by crossing over energy barriers. Our focus is cyclic spin-2 condensates which have tetrahedral symmetry.
TL;DR: In this article, a controllable method for observing interaction induced ferromagnetism in ultracold fermionic atoms loaded in optical superlattices is proposed. But the method is limited to the case of four lattice sites arranged in a square.
Abstract: We propose a controllable method for observing interaction induced ferromagnetism in ultracold fermionic atoms loaded in optical superlattices. We first discuss how to probe and control Nagaoka ferromagnetism in an array of isolated plaquettes (four lattice sites arranged in a square). Next, we show that introducing a weak interplaquette coupling destroys the ferromagnetic correlations. To overcome this instability we propose to mediate long-range ferromagnetic correlations among the plaquettes via double-exchange processes. Conditions for experimental realization and techniques to detect such states are discussed.
TL;DR: In this article, a general approach to investigate non-equilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-core optical fiber.
Abstract: We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate non-equilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-core optical fiber. We show that when the interaction between photons is effectively repulsive, the system acts as a single-photon switch. In the case of attractive interaction, the system can exhibit either anti-bunching or bunching, associated with the resonant excitation of bound states of photons by the input field. These effects can be observed by probing statistics of photons transmitted through the nonlinear fiber.
Journal Article•
TL;DR: In this article, the authors construct phase diagrams showing a variety of instabilities as a function of the direction of the magnetic field and the strength of the quadratic Zeeman shift.
Abstract: Rb spinor condensates once dipolar interactions and spindynamics are taken into account. By including the effects of a quasi-two-dimensional geometry andrapid Larmor precession, we show a dynamical instability develops in the collective mode spectrumat finite wavevectors. We construct phase diagrams showing a variety of instabilities as a function ofthe direction of the magnetic field and strength of the quadratic Zeeman shift. Our results providea possible explanation of current experiments in the Berkeley group Phys. Rev. Lett. 100:170403(2008).
TL;DR: In this article, a broad class of time-dependent interacting systems subject to external linear and parabolic potentials is discussed, for which the many-body Schr\"{o}dinger equation can be solved using a scaling transformation.
Abstract: Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems, which allow reliable theoretical analysis, are few and far between. In this paper we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schr\"{o}dinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and nonlocal interactions and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result we find that weakly and strongly interacting Bose-gases expanding from a parabolic trap can exhibit very similar dynamics.