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Register a new userMany-body physics in the classical-field description of a degenerate Bose gas
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The classical-field formalism has been widely applied in the calculation of normal correlation functions, and the characterization of condensation, in finite-temperature Bose gases. Here we discuss the extension of this method to the calculation of more general correlations, including the so-called anomalous correlations of the field, without recourse to symmetry-breaking assumptions. Our method is based on the introduction of U(1)-symmetric classical-field variables analogous to the modified quantum ladder operators of number-conserving approaches to the degenerate Bose gas, and allows us to rigorously quantify the anomalous and non-Gaussian character of the field fluctuations. We compare our results for anomalous correlation functions with the predictions of mean-field theories, and demonstrate that the nonlinear classical-field dynamics incorporate a full description of many-body processes which modify the effective mean-field potentials experienced by condensate and noncondensate atoms. We discuss the role of these processes in shaping the condensate mode, and thereby demonstrate the consistency of the Penrose-Onsager definition of the condensate orbital in the classical-field equilibrium. We consider the contribution of various noncondensate-field correlations to the overall suppression of density fluctuations and interactions in the field, and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase.
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The coherence properties of degenerate Bose gases have usually been expressed in terms of spatial correlation functions, neglecting the rich information encoded in their temporal behavior. In this paper we show, using a Hamiltonian classical-field formalism, that temporal correlations can be used to characterize familiar properties of a finite-temperature degenerate Bose gas. The temporal coherence of a Bose-Einstein condensate is limited only by the slow diffusion of its phase, and thus the presence of a condensate is indicated by a sharp feature in the temporal power spectrum of the field. We show that the condensate mode can be obtained by averaging the field for a short time in an appropriate phase-rotating frame, and that for a wide range of temperatures, the condensate obtained in this approach agrees well with that defined by the Penrose-Onsager criterion based on one-body (spatial) correlations. For time periods long compared to the phase diffusion time, the field will average to zero, as we would expect from the overall U(1) symmetry of the Hamiltonian. We identify the emergence of the first moment on short time scales with the concept of U(1) symmetry breaking that is central to traditional mean-field theories of Bose condensation. We demonstrate that the short-time averaging procedure constitutes a general analog of the anomalous averaging operation of symmetry-broken theories by calculating the anomalous thermal density of the field, which we find to have form and temperature dependence consistent with the results of mean-field theories.
Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This is accomplished by extracting the one-particle irreducible (1PI) vertices from which one can construct all observables. To match the capabilities of experimental techniques used in quantum simulation experiments, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate our procedure by applying it to the quantum sine-Gordon model in thermal equilibrium. The theoretical foundations are illustrated by estimating the irreducible vertices at equal times both analytically and using numerical simulations. We then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract the full two-point function and the interaction vertex (four-point function) and their variation with momentum, encoding the `running of the couplings. The measured 1PI vertices are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing fundamental questions in quantum field theory, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology.
We observe the condensation of magnon excitations within an $F=1$ $^{87}$Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a longitudinally spin-polarized gas, allowed to equilibrate to a non-degenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization whereupon they condense. We find magnon condensation to be described quantitatively as the condensation of free particles in an effective potential that is uniform within the ferromagnetic condensate volume, evidenced by the number and distribution of magnons at the condensation transition. Transverse magnetization images reveal directly the spontaneous, inhomogeneous symmetry breaking by the magnon quasi-condensate, including signatures of Mermin-Ho spin textures that appear as phase singularities in the magnon condensate wavefunction.
We investigate the problem of $N$ identical bosons that are coupled to an impurity particle with infinite mass. For non-interacting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce an effective boson-boson repulsion which strongly modifies the bound states consisting of the impurity and $N$ bosons. In particular, we demonstrate the existence of two universal multi-body resonances, where all multi-body bound states involving any $N$ emerge and disappear. The first multi-body resonance corresponds to infinite impurity-boson scattering length, $ato +infty$, while the second corresponds to the critical scattering length $a^*>0$ beyond which the trimer ($N=2$ bound state) ceases to exist. Crucially, we show that the existence of $a^*$ ensures that the ground-state energy in the multi-body bound-state region, $infty>a> a^*$, is bounded from below, with a bound that is independent of $N$. Thus, even though the impurity can support multi-body bound states, they become increasingly fragile beyond the dimer state. This has implications for the nature of the Bose polaron currently being studied in cold-atom experiments.
We provide evidence that a clean kicked Bose-Hubbard model exhibits a many-body dynamically localized phase. This phase shows ergodicity breaking up to the largest sizes we were able to consider. We argue that this property persists in the limit of large size. The Floquet states violate eigenstate thermalization and then the asymptotic value of local observables depends on the initial state and is not thermal. This implies that the system does not generically heat up to infinite temperature, for almost all the initial states. Differently from many-body localization here the entanglement entropy linearly increases in time. This increase corresponds to space-delocalized Floquet states which are nevertheless localized across specific subsectors of the Hilbert space: In this way the system is prevented from randomly exploring all the Hilbert space and does not thermalize.
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