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arXiv:1804.03278 · Physical Review A

Spin-orbit-coupling-induced quantum droplet in ultracold Bose-Fermi mixtures

Xiaoling Cui

Published Aug 27, 2018• 55 citations
arXivHTMLPDF

Abstract

Quantum droplets have aroused much attention recently in view of their successful observations in ultracold homonuclear atoms. In this paper, we demonstrate an alternative mechanism for the formation of quantum droplets in heteronuclear atomic systems, i.e., by applying synthetic spin-orbit coupling (SOC). Taking the Bose-Fermi mixture, for example, we show that by imposing a Rashba SOC between the spin states of fermions such that all fermions occupy the lower helicity branch, the greatly suppressed Fermi pressure can enable the formation of Bose-Fermi droplets even for very weak boson-fermion attractions, which are insufficient to bound a droplet if without SOC. In such SOC-induced quantum droplets, the boson-fermion density ratio universally depends on the SOC strength, and they occur in the mean-field collapsing regime but with a negative fluctuation energy, distinct from the interaction-induced droplets found in literature. The accessibility of these Bose-Fermi droplets in ultracold Cs-Li and Rb-K mixtures is also discussed. Our results shed light on the droplet formation in a vast class of heteronuclear atomic systems through the manipulation of single-particle physics.

DOI
10.1103/physreva.98.023630

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We study the formation of quantum droplets in the mixture of a single-component Bose–Einstein condensate (BEC), and a two-species Fermi superfluid across a wide Feshbach resonance. With repulsive boson-boson and attractive boson-fermion interactions, we show that quantum droplets can be stabilized by attractive fermion-fermion interactions on the Bardeen–Cooper–Schrieffer (BCS) side of the resonance, and can also exist in the deep BEC regime under weak boson-fermion interactions. We map out the phase diagram for stable droplets with respect to the boson-boson and boson-fermion interactions, and discuss the role of different types of quantum fluctuations in the relevant regions of the BCS-BEC crossover. Our work reveals the impact of fermion pairing on the formation of quantum droplets in Bose–Fermi mixtures, and provides a useful guide for future experiments.
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We present an analytical description for ultracold collisions between two spin-12\frac{1}{2}21​ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-12\frac{1}{2}21​ fermions such as electrons in condensed matter and to ultracold pseudo-spin-12\frac{1}{2}21​ atoms such as 6{}^{6}6Li in its ground hyperfine state.
We study formation of a Bose–Fermi droplet in realistic experimental setting. We start with a typical experimental arrangement of two atomic species—bosons and fermions in a harmonic axially symmetric confinement. The variational analysis shows that the system exhibits bistability. For weak repulsion between bosons, one of the equilibrium states, smaller in size, spherically symmetric, and with negative energy, corresponds to quantum droplet; the other with always positive energy represents the elongated droplet-like state immersed in the sea of a fermionic cloud. For stronger repulsion between bosons the bifurcation is seized and only the former state is left. Now it represents an elongated object which, for strong enough boson–fermion attraction, gets negative energy. It becomes an excited Bose–Fermi droplet when the trap is released, what is demonstrated by solving the quantum hydrodynamics equations for the Bose–Fermi system. To depict our ideas we consider the 133 Cs– 6 Li mixture under ideal conditions, i.e. we assume no losses.