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Register a new userTransient ordering in the Gross-Pitaevskii lattice subject to an energy quench within the disordered phase
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Using the discrete Gross-Pitaevskii equation on a three-dimensional cubic lattice, we numerically investigate energy quench dynamics in the vicinity of the continuous U(1) ordering transition. The post-quench relaxation is accompanied by a transient order revival: during non-equilibrium stages, the order parameter temporarily exceeds its vanishing equilibrium pre-quench value. The revival is associated with slowly relaxing population of lattice sites aggregating large portions of the potential energy. To observe the revival, no preliminary fine-tuning of the model parameters is necessary. Our findings suggest that the order revival may be a robust feature of a broad class of models. This premise is consistent with the experimental observations of the revival in dissimilar classes of condensed matter systems.
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We review the stochastic Gross-Pitaevskii approach for non-equilibrium finite temperature Bose gases, focussing on the formulation of Stoof; this method provides a unified description of condensed and thermal atoms, and can thus describe the physics of the critical fluctuation regime. We discuss simplifications of the full theory, which facilitate straightforward numerical implementation, and how the results of such stochastic simulations can be interpreted, including the procedure for extracting phase-coherent (`condensate) and density-coherent (`quasi-condensate) fractions. The power of this methodology is demonstrated by successful ab initio modelling of several recent atom chip experiments, with the important information contained in each individual realisation highlighted by analysing dark soliton decay within a phase-fluctuating condensate.
Among the various numerical techniques to study the physics of strongly correlated quantum many-body systems, the self-energy functional approach (SFA) has become increasingly important. In its previous form, however, SFA is not applicable to Bose-Einstein condensation or superfluidity. In this paper we show how to overcome this shortcoming. To this end we identify an appropriate quantity, which we term $D$, that represents the correlation correction of the condensate order parameter, as it does the self-energy for the Greens function. An appropriate functional is derived, which is stationary at the exact physical realizations of $D$ and of the self-energy. Its derivation is based on a functional-integral representation of the grand potential followed by an appropriate sequence of Legendre transformations. The approach is not perturbative and therefore applicable to a wide range of models with local interactions. We show that the variational cluster approach based on the extended self-energy functional is equivalent to the pseudoparticle approach introduced in Phys. Rev. B, 83, 134507 (2011). We present results for the superfluid density in the two-dimensional Bose-Hubbard model, which show a remarkable agreement with those of Quantum-Monte-Carlo calculations.
We show that a Wilson-type discretization of the Gross-Neveu model, a fermionic N-flavor quantum field theory displaying asymptotic freedom and chiral symmetry breaking, can serve as a playground to explore correlated symmetry-protected phases of matter using techniques borrowed from high-energy physics. A large- N study, both in the Hamiltonian and Euclidean formalisms, yields a phase diagram with trivial, topological, and symmetry-broken phases separated by critical lines that meet at a tri-critical point. We benchmark these predictions using tools from condensed matter and quantum information science, which show that the large-N method captures the essence of the phase diagram even at N = 1. Moreover, we describe a cold-atom scheme for the quantum simulation of this lattice model, which would allow to explore the single-flavor phase diagram.
Atom interferometers using Bose-Einstein condensates are fundamentally limited by a phase diffusion process that arises from atomic interactions. The Gross-Pitaevskii equation is here used to accurately calculate the diffusion rate for a Bragg interferometer. It is seen to agree with a Thomas-Fermi approximation at large atom numbers and a perturbative approximation at low atom numbers. The diffusion times obtained are generally longer than the coherence times observed in experiments to date.
We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite life time of the condensed particles and energy relaxation. The coupling between the reservoir and the condensate is described with semi-classical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyse the main properties of a condensate described by this hybrid Boltzmann Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first order coherence, dynamic and energetic stability, drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfils the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs it moves at a velocity smaller than the speed of excitations. First order spatial coherence of the condensate is found to decay exponentially in 1D and with a power law in 2D, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite life time of the condensate excitations. We compare these properties with the ones of a condensate described by the popular diffusive models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.
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