我们研究了二维旋转偶极费米子维格纳晶体的行为和稳定性。利用只占据最低朗道能级部分的二维旋转偶极费米子的基态的一个近似波函数，研究了Wigner晶体在最低朗道能级的相关能、弹性模量和集体模.然后我们计算了维格纳晶体的位移矢量的均方。在绝对零度下，使用Lindeman准则评估临界填充因子，低于该因子时，预期为结晶状态。我们发现粒子（空穴）晶体在填充因子小于1/15时是局部稳定的（在填充因子14/15和1之间），其中晶体的稳定区域比Baranov，Fehrmann和Lewenstein的结果窄得多，[Phys. Rev. Lett. 100，200402（2008）]。
英文摘要：
We have investigated the behavior and stability of a Wigner crystal of rotating dipolar fermions in two dimensions. Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy, elastic moduli and collective modes of Wigner crystals in the lowest Landau level. We then calculate the mean square of the displacement vector of Wigner crystals. The critical filling factor, below which the crystalline state is expected, is evaluated at absolute zero by use of the Lindeman's criterion. We find that the particle (hole) crystal is locally stable for filling factor is less than 1/15 (between filling factors 14/15 and 1), where the stable regime of the crystal is much narrower than the result from Baranov, Fehrmann and Lewenstein, [Phys. Rev. Lett. 100, 200402 (2008)].
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts. There is growing evidence that quantum liquid crystals play a central role in many electron systems including high temperature superconductors, but a quantitative understanding is lacking due to disorder and other complications. Here, we analyse the quantum phase diagram of a two-dimensional dipolar gas, which exhibits stripe, nematic and supersolid phases.…
We investigate the occurence of Wigner-localization phenomena in bosonic dipolar ultracold few-body systems with Rashba-like spin-orbit coupling. We show that the latter strongly enhances the effects of the dipole-dipole interactions, allowing to reach the Wigner-localized regime for strengths of the dipole moment much smaller than those necessary in the spin-orbit-free case.
Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semi-exactly within the local-density approximation using an empirical fit to Quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to …
The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of a recently proposed density-functional theory [Phys. Rev. A {\bf 92}, 023614 (2015)]. In each two-dimensional layer, the fermions interact via a repulsive, isotropic dipolar interaction. The presence of a second layer introduces an attractive {\em interlayer} interaction, thereby allowing for inhomogeneous density phases which would otherwise be energetically unfavourable. For any fixed layer separation, we find an instability to a commensurate one-dimensional stripe phase in each layer, whi…
A two-dimensional dipolar Fermi gas in harmonic trap under rotation is studied by solving "ab initio" Kohn-Sham equations. The physical parameters used match those of ultracold gas of fermionic $^{23}Na^{40}K$ molecules, a prototype system of strongly interacting dipolar quantum matter, which has been created very recently. We find that, as the critical rotational frequency is approached and the system collapses into the lowest Landau level, an array of tightly packed quantum vortices develops, in spite of the non-superfluid character of the system. In this state the system looses axial symmet…
We study a system of few fermions in a one-dimensional harmonic trap, and focus on the case of dipolar majority particles in contact with a single impurity. The impurity is used both for quenching the system, and for tracking the system evolution after the quench. Employing exact diagonalization, we investigate relaxation and thermalization properties. In the absence of dipolar interactions, the system is near integrability, and the dynamics remains oscillatory even on long time scales. On the other hand, repulsive as well as attractive dipolar interactions lead to quick relaxation to the diag…
Although crystallization is a ubiquitous phenomenon in nature, crystal formation and melting still remain fascinating processes with several open questions yet to be addressed. In this work, we study the emergent crystallization of a laser-driven dipolar Bose-Einstein condensate due to the interplay between long-range magnetic and effectively infinite-range light-induced interactions. The competition between these two interactions results in a collective excitation spectrum with two roton minima that introduce two different length scales at which crystalline order can emerge. In addition to th…
We study the quantum melting of quasi-one-dimensional lattice models in which the dominant energy scale is given by a repulsive dipolar interaction. By constructing an effective low-energy theory, we show that the melting of crystalline phases can occur into two distinct liquid phases, having the same algebraic decay of density-density correlations, but showing a different non-local correlation function expressing string order. We present possible experimental realizations using ultracold atoms and molecules, introducing an implementation based on resonantly driven Rydberg atoms that offers ad…
We study one-dimensional systems of $N$ particles in a one-dimensional harmonic trap with an inverse power law interaction $\sim|x|^{-d}$. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of $N$. A closed form asymptotic expressio…
Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. We map out the phase diagram of this model by computing the ener…
A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational approach based on the Wigner function for the description of ground-state properties of such systems. We show that the stability of dipolar fermions in a general harmonic trap is universal as it only depends on the trap aspect ratios and the dipoles' orientation. We calculate the species-independent stability diagram and the deformation of the Fermi surface (F…
Exploring confinement transitions in $\mathbb{Z}_2$ lattice gauge theories with dipolar atoms beyond one dimension
JILA and Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系及JILA）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学物理系及阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics, Columbia University（哥伦比亚大学物理系）
