Browsing by Subject "Hartree-Fock-Bogoliubov theory"

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Open Access
Temperature dependence of the density and excitations of dipolar droplets
(American Physical Society, 2020) Öztürk, S. F.; Enes, Aybar; Oktel, M. Özgür
Droplet states of ultracold gases which are stabilized by fluctuations have recently been observed in dipolar and two-component Bose gases. These systems present an alternate form of equilibrium where an instability at the mean-field level is arrested by higher-order correlations, making the droplet states sensitive probes of fluctuations. In a recent paper, we argued that thermal fluctuations can play an important role for droplets even at low temperatures where the noncondensed density is much smaller than the condensate density. We used the Hartree-Fock-Bogoliubov theory together with the local density approximation for fluctuations to obtain a generalized Gross-Pitaevskii (GP) equation and solved it with a Gaussian variational ansatz to show that the transition between the low density and droplet states can be significantly modified by the temperature. In this paper, we first solve the same GP equation numerically with a time-splitting spectral method to check the validity of the Gaussian variational ansatz. Our numerical results are in good agreement with the Gaussian ansatz for a large parameter regime and show that the density of the gas is most strongly modified by temperature near the abrupt transition between a pancake-shaped cloud and the droplet. For cigar-shaped condensates, as in the recent Er experiments, the dependence of the density on temperature remains quite small throughout the smooth transition. We then consider the effect of temperature on the collective oscillation frequencies of the droplet using both a time-dependent Gaussian variational ansatz and real-time numerical evolution. We find that the oscillation frequencies depend significantly on the temperature close to the transition for the experimentally relevant temperature regime (≃100nK).
Open Access
Temperature dependent density profiles and collective oscillations of dipolar droplets
(2019-09) Aybar, Enes
Dipolar droplets are a novel form of Bose gas that form in a regime where the mean field theory predicts collapse. In the literature, the beyond mean field e ects in the form of the Lee-Huang-Yang correction to the local chemical potential are used to explain the stability of these droplets. We employ the Hartree-Fock- Bogoliubov theory to include the beyond mean field terms in a systematic manner that also allows finite temperature calculations. In this thesis, we derive the modified Gross-Pitaevskii equation and the Bogoliubov-de Gennes equations, then solve the latter with a local density approximation and the former with a Gaussian variational anzats. We show that Hartree-Fock-Bogoliubov theory reproduces the zero temperature results found in the literature, and indicates that the density profile and the collective oscillation of dipolar droplets depend on the temperature. We find that experimentally relevant temperatures (T 100nK) may significantly alter the transition between low and high density phases, and change the collective oscillation frequencies of the system.