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In quantum droplets, the mean-field energy is comparable to the Lee-Huang-Yang (LHY) energy. In the Bogoliubov theory, the LHY energy of the quantum droplet has an imaginary part, but it is neglected for practical purposes. So far, most theoretical studies of quantum droplets have been based on the extended Gross-Pitaevskii (GP) equation obtained by adding the LHY energy to the GP equation. In this article, we present the density-functional theory of quantum droplets. In our approach, the quantum fluctuations in quantum droplets, as described by an effective action, generate the correlation energy which is real and can be determined self-consistently. Our results are consistent with the extended GP equation in the dilute limit, and the implications to current experiments on quantum droplets are discussed.

Lead halide perovskite materials have been emerging as promising candidates for high-performance optoelectronic devices. Significant efforts have sought to realize monocrystalline perovskite films at a large scale. Here, we epitaxially grow monocrystalline methylammonium lead tribromide (MAPbBr3) films on lattice-matched gallium arsenide (GaAs) substrates at a centimeter scale. In particular, a solution-processed lead(II) sulfide (PbS) layer provides a lattice-matched and chemical protective interface for the solid-gas reaction to form MAPbBr3 films on GaAs. Structure characterizations identify the crystal orientations in the trilayer MAPbBr3/PbS/GaAs epi-structure and confirm the monocrystalline nature of MAPbBr3 on PbS/GaAs. The dynamic evolution of surface morphologies during the growth indicates a two-step epitaxial process. These fundamental understandings and practical growth techniques offer a viable guideline to approach high-quality perovskite films for previously inaccessible applications.

In a binary quantum droplet, the interspecies attraction dominates over the intraspecies repulsions and the mean-field energy is unstable. The mechanical stability is restored by the repulsive Lee-Huang-Yang (LHY) energy [1]. In the Bogoliubov theory of the binary quantum droplet, there are two branches of gapless excitations. The lower branch describes the phonon excitation and its energy is imaginary in the long-wavelength limit, implying dynamical instability. Recently it is found that the phonon energy is renormalized by higher-order quantum fluctuations and the dynamical instability is removed [2]. In this work, we study a binary quantum droplet in the path integral formalism to construct an effective model with the correct phonon energy. By integrating out the upper excitation branch, we obtain an effective single-mode model describing density fluctuations, and derive the extended Gross-Pitaevskii equation. In this approach, the LHY energy in the extended-GP equation is purely positive without any assumption of neglecting the imaginary part. This effective single-mode model can be also used outside and close to the quantum droplet region such as in the LHY gas., Comment: 7 pages, 2 figures

Stabilized by quantum fluctuations, dipolar Bose-Einstein condensates can form self-bound liquidlike droplets in the mean-field unstable regime. However in the Bogoliubov theory, some phonon energies are imaginary 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 [1]. In this work, we study the phonon energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations can enhance the phonon stability. We obtain the anisotropic sound velocity which can be tested in experiment.

We study the quantum-droplet state in a 3-dimensional (3D) Bose gas in the presence of 1D spin-orbit-coupling and Raman coupling, especially the stripe phase with density modulation, by numerically computing the ground state energy including the mean-field energy and Lee-HuangYang correction. In this droplet state, the stripe can exist in a wider range of Raman coupling, compared with the BEC-gas state. More intriguingly, both spin-orbit-coupling and Raman coupling strengths can be used to tune the droplet density.

Quantum droplets have been realized in experiments on binary boson mixtures and dipolar Bose gases. In these systems, the mean-field energy of the Bose-Einstein condensation is attractive, and the repulsive Lee-Huang-Yang energy is crucial for stability. The Bogoliubov theory incorrectly predicts that the phonon mode is dynamically unstable in the long-wavelength limit. In this work, we go beyond the Bogoliubov theory to study how the phonon mode is stabilized in the quantum droplet of a binary boson mixture. Similar to Beliaev's approach to a single-component Bose gas, we compute higher-order contributions to the self-energy of the boson propagator. We find that the interaction between spin and phonon excitations is the key for the phonon stability. We obtain the sound velocity which can be tested by measuring the superfluid critical velocity of the droplet in experiments. Beliaev damping of this quantum droplet is also discussed., Comment: 5 pages, 2 figures

In this work, we study two-body bound states in two-component Bose gas with a one-dimensional (1D) spin-orbit coupling (SOC) induced by Raman lasers. The finite Raman coupling strength generates coupling among three spin channels, resulting in the reconstruction of three bound-state bands. In addition, multiple resonances can be induced at finite scattering lengths. By tuning the interaction in one intra-species channel, one bound-state band can be lifted and three resonances can be achieved at different center-of-mass momenta, which can be observable under current experimental conditions in ${}^{87}$Rb atoms., Comment: 5 pages, 4 figures

We study a two-component Bose gas with artificial spin-orbit coupling (SOC) which couples the center-of-mass momentum of atom to its internal states. We show that in this system resonance can be induced by tuning SOC strength. With a two-dimensional SOC, resonances in two scattering channels can be induced by tuning the aspect ratio of SOC strengths. With a three-dimensional SOC, resonance in all scattering channels can be induced by tuning the appropriate SOC strength. Similarly, we also find that in a Fermi gas with two- or three-dimensional SOC resonance can be induced by tuning SOC strength., Comment: 5 pages, 4 figures