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arXiv:1611.07355 · Physical Review A

Properties of strongly dipolar Bose gases beyond the Born approximation

Rafał Ołdziejewski, Krzysztof Jachymski

Published Dec 27, 2016• 27 citations
arXivHTMLPDF

Abstract

Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In a theoretical description of this phenomenon, the low-energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms, corrections with respect to the Born approximation arise, and we derive a modified pseudopotential using a realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagrams. Our results are relevant to recent experiments with erbium and dysprosium atoms.

DOI
10.1103/physreva.94.063638

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Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In a theoretical description of this phenomenon, the low-energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms, corrections with respect to the Born approximation arise, and we derive a modified pseudopotential using a realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagrams. Our results are relevant to recent experiments with erbium and dysprosium atoms.
Ultracold Bose gases of highly magnetic atoms exhibit unique interaction properties that lead to striking many-body behaviors, both at and beyond the mean field. A decade ago, a universal stabilization mechanism driven by quantum fluctuations was discovered in these gases. This mechanism prevents the systems from collapsing and instead allows exotic states of matter to arise, including ultradilute quantum droplets, crystallized quantum states, and especially supersolids. After introducing key features of dipolar quantum Bose gases—including their interactions, ground states, and excitations in a mean-field framework, as well as the onset of quantum-fluctuation stabilization—we review the progress made in understanding the emergence and intriguing properties of these quantum stabilized states. Both theory and experiments are discussed.
Stabilized by quantum fluctuations, dipolar Bose–Einstein condensates can form self-bound liquid-like droplets. However in the Bogoliubov theory, there are imaginary phonon energies in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [Gu Q and Yin L 2020 Phys. Rev. B 102 220503(R)]. We study the excitation energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations significantly enhance the phonon stability. We adopt a self-consistent approach without the problem of complex excitation energy in the Bogoliubov theory, and obtain a stable anisotropic sound velocity which is consistent with the superfluid hydrodynamic theory, but slightly different from the result of the extended Gross–Pitaevskii equation due to quantum depletion. A modified Gross–Pitaevskii equation in agreement with the Beliaev theory is proposed, which takes the effect of quantum fluctuations into account more completely.
Self-bound quantum droplets form when the mean-field tendency of the gas to collapse is stabilized by the effectively repulsive beyond-mean-field fluctuations. The beyond-mean-field effects depend on Rabi frequency ${\ensuremath{\omega}}_{R}$ and quadratic Zeeman effect qqq for the Rabi-coupled Bose mixtures and the spinor gases, respectively. For a quantum droplet, the effects of varying ${\ensuremath{\omega}}_{R}$ and qqq have recently been examined only for unpolarized Rabi-coupled Bose mixtures and unpolarized spinor gases. In this paper, we theoretically explore the stability of the droplet phase for polarized Rabi-coupled Bose mixtures and polarized spinor gases. We calculate the beyond-mean-field corrections for both gases with polarized order parameters and obtain the phase diagram of the droplets on the parameter space of Rabi frequency ${\ensuremath{\omega}}_{R}$ and detuning $\ensuremath{\delta}$ for Rabi-coupled mixtures and quadratic Zeeman energy qqq and linear Zeeman energy ppp for spinor gases. Finally, we highlight the similarities and differences between the two systems and discuss their experimental feasibility.
Abstract The simultaneous presence of two competing inter-particle interactions can lead to the emergence of new phenomena in a many-body system. Among others, such effects are expected in dipolar Bose–Einstein condensates, subject to dipole–dipole interaction and short-range repulsion. Magnetic quantum gases and in particular Dysprosium gases, offering a comparable short-range contact and a long-range dipolar interaction energy, remarkably exhibit such emergent phenomena. In addition an effective cancellation of mean-field effects of the two interactions results in a pronounced importance of quantum-mechanical beyond mean-field effects. For a weakly dominant dipolar interaction the striking consequence is the existence of a new state of matter equilibrated by the balance between weak mean-field attraction and beyond mean-field repulsion. Though exemplified here in the case of dipolar Bose gases, this state of matter should appear also with other microscopic interactions types, provided a competition results in an effective cancellation of the total mean-field. The macroscopic state takes the form of so-called quantum droplets. We present the effects of a long-range dipolar interaction between these droplets.
Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.
Recently, trapped dipolar gases were observed to form high-density droplets in a regime where mean-field theory predicts collapse. These droplets present a form of equilibrium where quantum fluctuations are critical for stability. So far, the effect of quantum fluctuations has only been considered at zero temperature through the local chemical potential arising from the Lee-Huang-Yang correction. Here, we extend the theory of dipolar droplets to nonzero temperatures using Hartree-Fock-Bogoliubov theory (HFBT) and show that the equilibrium is strongly affected by temperature fluctuations. HFBT, together with local density approximation for excitations, reproduces the zero-temperature results and predicts that the condensate density can change dramatically even at low temperatures where the total depletion is small. In particular, we find that typical experimental temperatures ($T\ensuremath{\sim}100$ nK) can significantly modify the transition between low-density and droplet phases.