Extending our previous work, we explore the breathing mode---the (uniform) radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from weak to moderate couplings and confirm that its frequency is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show that the breathing frequency has a minimum for a small particle number. We validate the accuracy of our results, comparing them to exact configuration interaction results for up to eight particles.
Extending our previous work, we explore the breathing mode---the (uniform) radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from weak to moderate couplings and confirm that its frequency is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show that the breathing frequency has a minimum for a small particle number. We validate the accuracy of our results, comparing them to exact configuration interaction results for up to eight particles.
The breathing mode – the uniform radial expansion and contraction of a system of interacting particles – is analyzed. Extending our previous work [Bauch et al 2009 Phys. Rev. B. 80 054515] we present a systematic analysis of the breathing mode for fermions with an inverse power law interaction potential w ( r ) ~ r −d with d = 1,2,3 in the whole range of coupling parameters. The results thus cover the range from the ideal "gas" to the Wigner crystal-like state. In addition to exact results for two particles obtained from a solution of the time-dependent Schrödinger equation we present results for N = 4,6 from multiconfiguration time-dependent Hartree-Fock simulations.
We investigate the quantum breathing mode (monopole oscillation) of trapped fermionic particles with Coulomb and dipole interaction in one and two dimensions. This collective oscillation has been shown to reveal detailed information on the many-particle state of interacting trapped systems and is thus a sensitive diagnostics for a variety of finite systems, including cold atomic and molecular gases in traps and optical lattices, electrons in metal clusters and in quantum confined semiconductor structures or nanoplasmas. An improved sum rule formalism allows us to accurately determine the breathing frequencies from the ground state of the system, avoiding complicated time-dependent simulations. In combination with the Hartree–Fock and the Thomas–Fermi approximations this enables us to extend the calculations to large particle numbers N on the order of several million. Tracing the breathing frequency to large N as a function of the coupling parameter of the system reveals a surprising difference of the asymptotic behavior of one-dimensional and two-dimensional harmonically trapped Coulomb systems.
Interacting particles in a harmonic trap are known to possess a radial collective oscillation---the breathing mode (BM). We show that a quantum system has two BMs and analyze their properties by exactly solving the time-dependent Schr\"odinger equation. We report that the frequency of one BM changes with system dimensionality, the particle spin and the strength of the pair interaction and propose a scheme that gives direct access to key properties of trapped particles, including their many-body effects.
Following a ``bottom-up approach'' in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a one-dimensional (1D) harmonic trap on the number of bosons ranging from few to many. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for bosons (ML-MCTDHB) which has been developed very recently [Kr\"onke, Cao, Vendrell, and Schmelcher, New J. Phys. 15, 063018 (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region where the mean-field description provides a valid approximation.
We calculate the breathing mode frequency ω in a one-dimensional Bose gas confined to a harmonic trap of frequency ωz. We predict a smooth crossover from Thomas-Fermi Bose-Einstein condensate (BEC) regime (ω=3ωz) to Gaussian BEC regime (ω=2ωz) using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau (ω=2ωz) to Thomas-Fermi BEC (ω=3ωz) regimes. Predictions from local density and Hartree approximations can be continuously matched for N>25 particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from N=2 to N=25) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbruck group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas-Fermi - Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.
We theoretically investigate the ground-state properties and breathing-mode collective excitations of three-dimensional dipolar Bose gases in anisotropic harmonic traps incorporating quantum fluctuations. Combining a Gaussian variational ansatz with a non-perturbative sum-rule analysis, we derive explicit analytical expressions for both axial and radial breathing-mode frequencies, which are validated by numerical solutions of the time-dependent extended Gross-Pitaevskii equation. Our theoretical predictions show excellent agreement with existing experimental data for 166Er and 162Dy gases. By constructing comprehensive phase diagrams across the parameter space of the s-wave scattering length, atom number, and trap aspect ratio, we reveal both discontinuous first-order phase transitions and smooth crossovers between the dilute Bose-Einstein condensate and dense quantum droplet phases. We confirm that the enhanced incompressibility induced by quantum fluctuations significantly elevates the breathing-mode frequencies in the droplet phase compared to conventional weakly interacting Bose gases. Furthermore, the system undergoes a phase transition and a crossover over the scattering length under the quasi-two-dimensional and quasi-one-dimensional confinements, characterized by discontinuous jumps and continuous crossovers in peak density and atomic cloud sizes, respectively. Our work offers a rigorous and highly accurate framework to characterize collective excitations in dipolar quantum gases, providing quantitative insights for forthcoming ultracold atom experiments in lanthanide atoms and polar molecules.