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arXiv:2302.00349 · Journal of Low Temperature Physics

Collective Excitations of Bose–Einstein Condensate in a Rydberg Atom

Avra Banerjee, Dwipesh Majumder

Published Mar 19, 2024• 6 citations
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Abstract

Abstract In this work, we investigated a Bose-Einstein condensate (BEC) inside a Rydberg atom. We first observed the system’s density profile using the Gross-Pitaevskii equation, and then we used the Bogoliubov theory to examine the collective excitation spectra. We have also extended our study by taking into account a hybrid of two BEC species. Again, for this new system, the density profile and the collective excitation are investigated in a similar manner. The results of the BEC for one species reveal that the Rydberg atom can trap the BEC and that the excitation curve moves upward with increasing Rydberg atom interaction. We have seen roton minima for two species of BEC, and the depth of the minima shifts with the Rydberg interaction.

DOI
10.1007/s10909-024-03063-8

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Abstract In this work, we investigated a Bose-Einstein condensate (BEC) inside a Rydberg atom. We first observed the system’s density profile using the Gross-Pitaevskii equation, and then we used the Bogoliubov theory to examine the collective excitation spectra. We have also extended our study by taking into account a hybrid of two BEC species. Again, for this new system, the density profile and the collective excitation are investigated in a similar manner. The results of the BEC for one species reveal that the Rydberg atom can trap the BEC and that the excitation curve moves upward with increasing Rydberg atom interaction. We have seen roton minima for two species of BEC, and the depth of the minima shifts with the Rydberg interaction.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.
Superfluidity and Bose-Einstein condensation (BEC) in ultracold atomic gases represent macroscopic quantum phenomena arising from collective particle behavior at near-zero temperatures. Experimental realizations of BEC in alkali gases have enabled the observation of quantized vortices, matter-wave interference, and nonclassical excitations. This article reviews theoretical frameworks including Gross-Pitaevskii and Bogoliubov models, experimental techniques such as evaporative cooling and optical trapping, and computational approaches for simulating condensate dynamics. Two graphical analyses illustrate the condensate density profile and vortex lattice formation. Understanding these phenomena has implications for quantum simulation, atom interferometry, and exploration of quantum hydrodynamics.
Abstract We have studied the collective excitation of Bose–Einstein condensate of short-range weak interacting atoms with spin–orbit coupling (SOC) in two dimensions in the liquid phase. In our study, we have included Rashba, Dresselhaus, as well as Raman SOC. The study of Bogoliubov excitation shows that in small interactions, only phonon modes are present, and for higher interactions, roton modes start to appear. Energy spectra contain two roton modes in relatively strong interacting atomic systems.
We present the collective excitation spectrum analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a quasi-two-dimensional system. In particular, we investigate the role of SO and Rabi coupling strengths in determining the dynamical stability of the coupled BECs using Bogoliubov--de Gennes (BdG) theory. Using the eigenenergy of the BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and interspecies contact interactions. The depth of the minimum corresponding to the roton mode strongly depends on the coupling strength. We find that the increase of the SO coupling leads to instability, while the increase in the Rabi coupling stabilizes the system. Also, the eigenvectors of the BdG spectrum indicate the presence of a densitylike mode in the stable regime and spinlike modes in the unstable regimes. A phase diagram demonstrating the stability regime in the plane of SO and Rabi coupling strengths is obtained. Finally, we complement the observation of the excitation spectrum with the direct numerical simulation results of coupled Gross-Pitaevskii equations.
Abstract Recent experiments with Bose–Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross–Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron–atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics. Combining all these insights, our results suggest Bose–Einstein condensates as a viable platform for the in situ and real time interrogation of ultra-cold chemistry dynamics involving Rydberg states.
We investigate the low-energy excitations of the spherically and axially trapped atomic Bose-Einstein condensate coupled to a molecular Bose gas by coherent Raman transitions. We apply the sum-rule approach of many-body response theory to derive the low-lying collective excitation frequencies of the hybrid atom-molecular system. The atomic and molecular ground-state densities obtained in Gross-Pitaevskii and modified Gross-Pitaevskii (including the higher order Lee-Huang-Yang term in interatomic interaction) approaches are used to find out the individual energy components and hence the excitation frequencies. We obtain different excitation energies for different angular momenta and study their characteristic dependence on the effective Raman detuning, the scattering length for atom-atom interaction, and the intensities of the coupling lasers. We show that the inclusion of the higher-order nonlinear interatomic interaction in modified Gross-Pitaevskii approach introduces significant corrections to the ground-state properties and the excitation frequencies both for axially and spherically trapped coupled 87Rb^{87}\mathrm{Rb}87Rb condensate system with the increase in the sss-wave scattering length (for peak gas-parameter $\ensuremath{\geqslant}{10}^{\ensuremath{-}3}$). It has been shown that the excitation frequencies decrease with the increase in the effective Raman detuning as well as the sss-wave scattering length, whereas excitation frequencies increase with the increase in the atom-molecular coupling strength. The frequencies in modified Gross-Pitaevskii approximation exhibit an upward trend after a certain value of scattering length and also largely deviate from the Gross-Pitaevskii results with the increase in sss-wave scattering length. The strong dependence of excitation frequencies on the laser intensities used for Raman transitions manifests the role of atom-molecular coupling strength on the control of collective excitations. The collective excitation frequencies for the hybrid atom-molecular BEC differ significantly from the excitation frequencies of a pure atomic BEC system when the atom-to-molecule conversion efficiency increases due to the decrease in the effective Raman detuning and increase in the atom-molecule coupling strength.