Abnormal Superfluid Fraction of Harmonically Trapped Few-Fermion Systems

Abstract

Superfluidity is a fascinating phenomenon that, at the macroscopic scale, leads to dissipationless flow and the emergence of vortices. While these macroscopic manifestations of superfluidity are well described by theories that have their origin in Landau's two-fluid model, our microscopic understanding of superfluidity is far from complete. Using analytical and numerical ab initio approaches, this paper determines the superfluid fraction and local superfluid density of small harmonically trapped two-component Fermi gases as a function of the interaction strength and temperature. At low temperature, we find that the superfluid fraction is, in certain regions of the parameter space, negative. This counterintuitive finding is traced back to the symmetry of the system's ground state wave function, which gives rise to a diverging quantum moment of inertia Iq. Analogous abnormal behavior of Iq has been observed in even-odd nuclei at low temperature. Our predictions can be tested in modern cold atom experiments.Superfluidity plays a crucial role in various areas of physics. The core of neutron stars is thought to be superfluid, giving rise to modifications of the specific heat and rapid cooling [1,2]. In laboratory settings, the superfluidity of bosonic liquid helium-4 below 2.17K and fermionic liquid helium-3 below 3mK leads to dissipationless flow and the formation of vortices [3]. More recently, superfluidity has been demonstrated in various dilute atomic Bose and Fermi gas experiments [4][5][6][7].Over the past 20 years or so, non-classical rotations in small doped bosonic helium-4 and molecular parahydrogen clusters have been, through combined theoretical and experimental studies [8][9][10][11][12][13], interpreted within the framework of microscopic superfluidity. Some elements of this framework date back to 1959 when Migdal introduced a moments of inertia based method for the study of superfluidity in finite-sized nuclei [14]. In nuclei, superfluidity is tied to the pairing of nucleons [15,16]. As a consequence of pairing, the quantum moment of inertia of even-even nuclei, i.e., nuclei with an even number of protons and an even number of neutrons, tends to go to zero in the zero temperature limit while that of evenodd nuclei tends to increase sharply as the temperature approaches zero [17].The present work investigates the superfluid fraction and local superfluid density of small dilute atomic Fermi gases over a wide range of interaction strengths. In the low temperature region, we identify parameter combinations where the quantum moment of inertia is abnormally large, i.e., larger than the classical moment of inertia, implying a negative superfluid fraction. The negative superfluid fraction is linked to the topology of the density matrix. Specifically, the superfluid fraction takes on negative values in the low temperature regime when one of the energetically low-lying eigen states supports a Pauli vortex with finite circulation [18][19][20] at the center of the trap. Intuitively, this can be understood as foll...

Temperature dependence of small harmonically trapped atom systems with Bose, Fermi, and Boltzmann statistics

“…IV A that the superfluid fraction of the N boson system is, for certain parameter combinations, approximated well by that of a single particle. The superfluid fraction reflects symmetry properties of the system [30,64,65]. The connection between superfluidity and angular momentum decoupling mechanisms, e.g., has been discussed in some detail in the context of small doped bosonic helium droplets [66,67].…”

“…Selected results were presented in our earlier work [65]. We anticipate that the analysis of the superfluid properties presented in the previous paragraphs for two noninteracting fermions will inspire other studies, for bosons or fermions, that are concerned with understanding the distribution of the superfluid properties in finite-sized systems or systems with interfaces [ …”

“…Our calculations go down to k B T = 0.6E ho . Based on our earlier work [65], we expect that the superfluid fraction for the system with Fermi statistics will take on negative values as the temperature approaches zero. At high temperature, the perturbative analysis, introduced earlier for the energy, can be applied to the superfluid fraction.…”

Abnormal superfluid fraction and structural properties of electrons in 2D and 3D quantum dots: an ab initio path-integral Monte Carlo study

“…Therefore, our simulations are afflicted with the notorious fermion sign problem (FSP) [42,43,44], but are exact within the given Monte Carlo error bars, which allows for a rigorous treatment of the intriguing interplay between the effects i)-iv) mentioned above. From a practical perspective, the PIMC method gives us direct access to the superfluid fraction of the system [45,46], which exhibits a remarkable abnormal divergence towards negative infinity in the case of fermions for some conditions [47,48]. This effect was first reported by Yan and Blume [47] for a short-range pair potential and subsequently found by Dornheim [48] for quantumdipole systems, and has been explained in terms of the symmetry of the thermal density matrix.…”

Are smooth pseudopotentials a good choice for representing short-range interactions?

“…Specifically we consider what the requirements are for the basis set to reach the regime of exponential convergence and whether this approach is feasible for multiparticle simulations. Examples of finite-range pseudopotentials used in the literature are the Troullier-Martins [43,44], Pöschl-Teller [45,46], and Gaussian potentials [26,36,[47][48][49][50][51][52][53][54][55][56][57], in addition to the square well popular in diffusion Monte Carlo simulations [48].…”