本文研究了囚禁在一维谐振势中的3个费米子向强关联区间的转变。这个有趣但鲜有研究的系统使我们能够识别出该区间的特征特性，其中一些也存在于与工业相关的强关联材料中。此外，我们的发现描述了量子点中的电子、Paul阱中的离子，甚至一维光学晶格中的费米原子的行为。在基态附近，所有这些平台都可以描述为囚禁在谐振势中的费米子。关联区间可以通过改变囚禁势的自然频率来控制，为了探测它，我们提出使用扭曲光。我们在一维3费米子阱中识别出强关联的4个特征，这些特征很可能存在于任意数量N的囚禁费米子中：i) 基态密度强烈局域化，具有N个最大间距的峰（Wigner Crystal）；ii) 对称和反对称基态波函数变得简并（玻色化）；iii) von Neumann熵增长；iv) 能谱完全由N个或更少的简正模表征。
英文摘要：
The transition into a strongly-correlated regime of 3 fermions trapped in a one-dimensional harmonic potential is investigated. This interesting, but little-studied system, allows us to identify characteristic features of the regime, some of which are also present in strongly-correlated materials relevant to the industry. Furthermore, our findings describe the behavior of electrons in quantum dots, ions in Paul traps, and even fermionic atoms in one-dimensional optical lattices. Near the ground state, all these platforms can be described as fermions trapped in a harmonic potential. The correlation regime can be controlled by varying the natural frequency of the trapping potential, and to probe it, we propose to use twisted light. We identify 4 signatures of strong correlation in the one-dimensional 3-fermion trap, which are likely to be present for any number N of trapped fermions: i) the ground state density is strongly localized with N maximally separated peaks (Wigner Crystal) ii) the symmetric and antisymmetric ground state wavefunctions become degenerate (bosonization) iii) the von Neumann entropy grows, iv) the energy spectrum is fully characterized by N normal modes or less.
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a renormalization method for the interparticle interactions. The procedure is benchmarked with state-of-the-art numerical results for three and four symmetric fermions.
System of a two-flavor mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied in the frame of the center of mass. We present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which enable one to determine an eigenstate of the Hamiltonian and to label excitations of the center of mass. The tool presented may be particularly useful in experimental analysis of the interparticle interactions which do not affect the center of mass excitati…
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of "shortcuts to adiabaticity", we design inversely the time-dependent trap position and spin-orbit coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The non-adiabatic transport and relevant spin dynamics are illustrated with numerical examples, and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of …
Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtaine…
We show that the presence of a harmonic trap may in itself lead to many-body localization for cold atoms confined in that trap in a quasi-one-dimensional geometry. Specifically, the coexistence of delocalized phase in the center of the trap with localized region closer to the edges is predicted with the borderline dependent on the curvature of the trap. The phenomenon, similar in its origin to Stark localization, should be directly observed with cold atomic species. We discuss both the spinless and the spinful fermions, for the latter we address Stark localization at the same time as it has no…
Standard lattice formulations of non-relativistic Fermi gases with two spin components suffer from a sign problem in the cases of repulsive contact interactions and attractive contact interactions with spin imbalance. We discuss the nature of this sign problem and the applicability of stochastic quantisation with complex Langevin evolution in both cases. For repulsive interactions, we find that the results converge, using adaptive step size scaling and a Gaussian regulator to modify the lattice action. We present results on density profiles and correlations of a harmonically trapped system in …
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance a…
Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency and coupling strength. Our simple, analytic results for the interaction-induced changes $Δb_3$ and $Δb_4$ agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of three-dimensional Fermi gases.
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the v…
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could b…
We directly compare the mean-field and the many-body approach in a one-dimensional Bose system in a harmonic trap. Both contact and dipolar interactions are considered. We propose a multi-atom version of the phase imprinting method to generate dark solitons in the system. We begin with a general analysis of system dynamics and observe the emergence of a dark soliton and a shock wave. Center of mass and soliton motion become decoupled because the shock wave oscillates with the trap frequency and soliton does not. A detailed investigation of frequencies reveals significant differences between re…
Attractive Bose-Einstein Condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps
我们研究谐波捕获超冷玻色气体与有吸引力的粒子间相互作用下的外部旋转在三维空间，并确定的吸引力强度的临界值，气体崩溃作为一个函数的旋转频率。为此，我们研究的定态的共转框架与多体的方法，以及在Gross-Pitaevskii理论的陷阱中的系统具有不同的各向异性。与最近报道的结果相反[N。A. Jamaludin，N. G. Parker和A. M. Martin，Phys.Rev.A \textbf{77}，051603（R）（2008）]，我们发现在存在旋转的情况下，塌缩不会推迟。与排斥性气体不同，吸引系统的性质在各向同性和略微各向异性的陷阱中旋转时几乎保持不变。
We propose a numerically exact method for a mixture with a single impurity immersed in several majority fermions, confined in a harmonic potential. We separate one of the degrees of freedom through an appropriately tailored canonical transformation and perform exact diagonalization on the simplified Hamiltonian. This method is especially effective for a heavy impurity, where it outmatches the typical exact diagonalization approach. We used our method to calculate energy and density profiles of the first few eigenstates for the mixture with up to ten majority fermions.
