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arXiv:1606.09400 · Journal of Physics B Atomic Molecular and Optical Physics

The influence of the interaction between quasiparticles on parametric resonance in Bose–Einstein condensates

Paweł Zin, Maciej Pylak

Published Mar 9, 2017• 3 citations
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Abstract

Abstract We analyse a uniform weakly interacting bosonic gas undergoing a periodic oscillation of the interaction constant. This, within the Bogoliubov approximation, leads to the creation of atomic pairs with well defined opposite velocities. We show how the interaction between quasiparticles, omitted in the Bogoliubov approximation, significantly changes the atom pair creation process and the properties of the scattered atoms.

DOI
10.1088/1361-6455/aa65ad

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Abstract We analyse a uniform weakly interacting bosonic gas undergoing a periodic oscillation of the interaction constant. This, within the Bogoliubov approximation, leads to the creation of atomic pairs with well defined opposite velocities. We show how the interaction between quasiparticles, omitted in the Bogoliubov approximation, significantly changes the atom pair creation process and the properties of the scattered atoms.
We perform a simulation of the experiment [J. C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)] where the temporal modification of the effective one-dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate the huge impact of the interaction between quasiparticles due to finite temperature on the pair production process, explaining the relatively small atomic pair production and the absence of number squeezing in the experiment.
A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, nonequilibrium many-body system. We investigate the quasiparticle (QP) creation and thermalization dynamics of this system by solving the time-dependent Keldysh-Bogoliubov equations. We find avalanchelike QP creation due to a parametric resonance between BEC and QP oscillations, followed by slow, exponential relaxation to a thermal state at an elevated temperature, controlled by the initial excitation energy of the oscillating BEC above its ground state. The crossover between the two regimes occurs because of an effective decoupling of the QP and BEC oscillations. This dynamics is analogous to elementary particle creation in models of the early universe. The thermalization in our setup occurs because the BEC acts as a grand canonical reservoir for the quasiparticle system.
By exciting the transverse breathing mode of an elongated Bose–Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process, also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observations with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.
Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a three-dimensional time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasimomenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression for the adiabatic time, its dependence on the fraction of atoms in each component, and its scaling with the system size.
We study the quasiparticle dispersion relation for a homogeneous Bose gas in a large cubic box with periodic boundary conditions at zero temperature. Inspired by the Bogoliubov method, we rearrange the usual Bose gas Hamiltonian in a form adapted to perturbation theory in the weak-coupling regime, both in the canonical and grand-canonical setting. We compute the first non-trivial corrections to the dispersion relation in both settings. We show that for small momenta they are linear in the absolute value of the momentum. Thus, in this approximation phonons have a well-defined velocity, which we compute.
We investigate strong-coupling superfluidity in a uniform two-component gas of ultracold Fermi atoms attractively interacting via quasimolecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance, becoming large as $2\ensuremath{\nu}$ is decreased (relative to $2{\ensuremath{\varepsilon}}_{\mathrm{F}},$ where ${\ensuremath{\varepsilon}}_{\mathrm{F}}$ is the Fermi energy of one component). In recent work, we showed that the enhancement of this tunable pairing interaction naturally leads to the BCS-BEC (Bose-Einstein condensation) crossover, where the character of the superfluid phase transition changes from the BCS type to a BEC of composite bosons consisting of preformed Cooper-pairs and Feshbach-induced molecules. In this paper, we extend our previous work and study both the quasiparticles and the collective dynamics of the superfluid phase below the phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, limiting ourselves to a uniform gas. We show how the superfluid order parameter changes from the Cooper-pair amplitude $\ensuremath{\Delta}$ to the square root of the number of condensed molecules $({\ensuremath{\varphi}}_{\mathrm{m}})$ associated with the Feshbach resonance, as the threshold energy $2\ensuremath{\nu}$ is lowered. In the intermediate coupling regime, the superfluidity is shown to be characterized by an order parameter consisting of a superposition of $\ensuremath{\Delta}$ and ${\ensuremath{\varphi}}_{\mathrm{m}}.$ We also discuss the Goldstone mode associated with superfluidity, and show how its character smoothly changes from the Anderson-Bogoliubov phonon in the BCS regime to the Bogoliubov phonon in the BEC regime in the BCS-BEC crossover. The velocity of this Goldstone phonon mode is shown to strongly depend on the value of $2\ensuremath{\nu}.$ We also show that this Goldstone mode appears as a resonance in the spectrum of the density-density correlation function, which is experimentally accessible.