Field-induced decay dynamics in square-lattice antiferromagnet

Dynamical properties of the square-lattice Heisenberg antiferromagnet in applied magnetic field are studied for arbitrary value S of the spin. Above the threshold field for two-particle decays, the standard spin-wave theory yields singular corrections to the excitation spectrum with logarithmic divergences for certain momenta. We develop a self-consistent approximation applicable for S >= 1, which avoids such singularities and provides regularized magnon decay rates. Results for the dynamical structure factor obtained in this approach are presented for S = 1 and S = 5/2.Comment: 12 pages, 11 figures, final versio

Collapse and revival of excitations in Bose-Einstein condensates

We study the energies and decay of elementary excitations in weakly interacting Bose-Einstein condensates within a finite-temperature gapless second-order theory. The energy shifts for the high-lying collective modes turn out to be systematically negative compared with the Hartree-Fock-Bogoliubov-Popov approximation and the decay of the low-lying modes is found to exhibit collapse and revival effects. In addition, perturbation theory is used to qualitatively explain the experimentally observed Beliaev decay process of the scissors mode.Comment: 9 pages, 5 figure

Controlling quasiparticle excitations in a trapped Bose-Einstein condensate

We describe an approach to quantum control of the quasiparticle excitations in a trapped Bose-Einstein condensate based on adiabatic and diabatic changes in the trap anisotropy. We describe our approach in the context of Landau-Zener transition at the avoided crossings in the quasiparticle excitation spectrum. We show that there can be population oscillation between different modes at the specific aspect ratios of the trapping potential at which the mode energies are almost degenerate. These effects may have implications in the expansion of an excited condensate as well as the dynamics of a moving condensate in an atomic wave guide with a varying width

Functional renormalization for Bose-Einstein Condensation

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.Comment: 21 pages, 16 figures. Reference adde

Coherence time of a Bose-Einstein condensate

Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an "open" quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with non-condensed modes gradually smears out the condensate phase, with a variance growing as A t^2+B t+C at long times t, and we give a quantitative prediction for A, B and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.Comment: 17 pages, 8 figures; typos correcte

Optically-Induced Polarons in Bose-Einstein Condensates: Monitoring Composite Quasiparticle Decay

Nonresonant light-scattering off atomic Bose-Einstein condensates (BECs) is predicted to give rise to hitherto unexplored composite quasiparticles: unstable polarons, i.e., local ``impurities'' dressed by virtual phonons. Optical monitoring of their spontaneous decay can display either Zeno or anti-Zeno deviations from the Golden Rule, and thereby probe the temporal correlations of elementary excitations in BECs.Comment: 4 pages, 3 figure

Spectral function and quasi-particle damping of interacting bosons in two dimensions

We employ the functional renormalization group to study dynamical properties of the two-dimensional Bose gas. Our approach is free of infrared divergences, which plague the usual diagrammatic approaches, and is consistent with the exact Nepomnyashchy identity, which states that the anomalous self-energy vanishes at zero frequency and momentum. We recover the correct infrared behavior of the propagators and present explicit results for the spectral line-shape, from which we extract the quasi-particle dispersion and damping.Comment: 4 pages, 3 figures, revisited version, to appear as Phys. Rev. Lette

Commensurate and incommensurate ground states of Cs_2CuCl_4 in a magnetic field

We present calculations of the magnetic ground state of Cs_2CuCl_4 in an applied magnetic field, with the aim of understanding the commensurately ordered state that has been discovered in recent experiments. This layered material is a realization of a Heisenberg antiferromagnet on an anisotropic triangular lattice. Its behavior in a magnetic field depends on field orientation, because of weak Dzyaloshinskii-Moriya interactions.We study the system by mapping the spin-1/2 Heisenberg Hamiltonian onto a Bose gas with hard core repulsion. This Bose gas is dilute, and calculations are controlled, close to the saturation field. We find a zero-temperature transition between incommensurate and commensurate phases as longitudinal field strength is varied, but only incommensurate order in a transverse field. Results for both field orientations are consistent with experiment.Comment: 5 Pages, 3 Figure

Condensate Oscillations, Kinetic Equations and Two-Fluid Hydrodynamics in a Bose Gas

This is based on 4 lectures given at the 13th Australian Physics Summer School, Australia National University, Canberra, Jan 17-28, 2000. The main topic is the theory of collective modes in a trapped Bose gas at finite temperatures. A generalized Gross-Pitaevskii equation is derived at finite temperatures, which is used to discuss a new mechanism for damping in the collisionless region arising from interactions with a static thermal cloud of non-condensate atoms. Next, introducing a kinetic equation for the thermal cloud, we derive two-fluid equations of motion for the condensate and non-condensate components in the collision-dominated hydrodynamic region. We show that these are precisely the equivalent of the Landau two-fluid equations in the limit that the two components are in diffusive local equilibrium. However, our equations also predict the existence of a new zero frequency relaxational mode, in addition to the usual Landau hydrodynamic modes (such as first and second sound). The special importance and simplicity of two-fluid hydrodynamics is stressed.Comment: 50 pages, 7 figures; To appear in "Proceedings of the 13th Physics Summer S chool: Bose-Einstein Condensation", eds. C.M.Savage and M.Das (World Scientific, 2000

Quantum Fluctuations in Dipolar Bose Gases

We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the condensate and the excited particles. This allows to obtain the Bogoliubov spectrum analytically in the limit of large particle numbers. After discussing the condensate depletion and the ground-state energy correction, we derive quantum corrected equations of motion for harmonically trapped dipolar Bose gases by using superfluid hydrodynamics. These equations are subsequently applied to analyze the equilibrium configuration, the low-lying oscillation frequencies, and the time-of-flight dynamics. We find that both atomic magnetic and molecular electric dipolar systems offer promising scenarios for detecting beyond mean-field effects.Comment: Published in PR