Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExpanding ring-shaped Bose-Einstein condensates as analogs of cosmological models: Analytical characterization of the inflationary dynamics
365
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We analytically study the expansion of a Bose-Einstein condensate in a ring-shaped trap with an increasing central radius. The evolution of the ground state is described using a scaling transform. Additionally, the dynamics of excited azimuthal modes over the varying ground state is analyzed through a generalization of the Bogoliubov-de Gennes approach. Our results explain some of the features observed in recent experiments focused on testing the applicability of the system as a parallel of cosmological inflationary models. The radial dynamics, which corresponds to the inflaton field of the cosmological counterpart, is analytically characterized: The expansion is found to induce the oscillatory displacement of the condensate as well as the coupled variation of the radial and vertical widths. Our findings account also for the observed redshift and emergence of the Hubble friction in the evolution of initially-prepared azimuthal modes. Our description, which traces the role of the different components of the setup in the expansion, enhances the controllability, and, therefore, the potential of the system as a ground for emulating the inflationary dynamics of cosmological models.
rate research
Read More
Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically symmetric `bubble trap potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states, and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional cross-over to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regards to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion.
We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.
We show that an elliptical obstacle moving through a Bose-Einstein condensate generates wakes of quantum vortices which resemble those of classical viscous flow past a cylinder or sphere. The role of ellipticity is to facilitate the interaction of the vortices nucleated by the obstacle. Initial steady symmetric wakes lose their symmetry and form clusters of like-signed vortices, in analogy to the classical Benard-von Karman vortex street. Our findings, demonstrated numerically in both two and three dimensions, confirm the intuition that a sufficiently large number of quanta of circulation reproduce classical physics.
The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multi-vortex solutions.
An atomic Bose-Einstein condensate (BEC) is often described as a macroscopic object which can be approximated by a coherent state. This, on the surface, would appear to indicate that its behavior should be close to being classical. In this paper, we clarify the extent of how classical a BEC is by exploring the semiclassical equations for BECs under the mean field Gaussian approximation. Such equations describe the dynamics of a condensate in the classical limit in terms of the variables < x > and < p > as well as their respective variances. We compare the semiclassical solution with the full quantum solution based on the Gross-Pitaevskii Equation (GPE) and find that the interatomic interactions which generate nonlinearity make the system less classical. On the other hand, many qualitative features are captured by the semiclassical equations, and the equations to be solved are far less computationally intensive than solving the GPE which make them ideal for providing quick diagnostics, and for obtaining new intuitive insight.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
