Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of N − 1 non-interacting identical heavy bosons, which interact with a light impurity through a large s-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies E (n,1) 4 and E (n,2) 4, which are universally linked to the energy E 3 ) 1/2 ≈ 1.51 and (E (1,2) 4 /E3 ) 1/2 ≈ 1.01. The 133 Li scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for N > 4 are also discussed. Possible implications of our results for ongoing cold atom experiments are presented. PACS numbers:Continuous and discrete scale invariances underlie many phenomena in physics. The possibly most aesthetically appealing examples are fractals [1], where a given pattern repeats itself as one zooms in. Scale invariance phenomena also emerge in quantum mechanics. A prominent example is the three-body Efimov effect [2, 3]. If there exists an Efimov trimer of size l 3 . Here, λ (λ > 1) is a scaling factor that depends on the masses and particle statistics of the constituents.The experimental observation of consecutive threebody resonances is extremely challenging as it requires working in the universal Efimov window. To be in this window, the absolute values of at least two of the three two-body s-wave scattering lengths [5] have to be larger than the other length scales of the underlying two-body potentials and the temperature has to be lower than the energy scale set by the s-wave scattering length. Thus, to observe two consecutive three-atom resonances, exquisite control over the scattering lengths and ultralow temperatures are required. For three identical bosons, λ is approximately equal to 22.7 and two consecutive threeatom resonances in a bosonic system have only been observed recently in 133 Cs [6, 7].It is well known that the scaling factor λ takes smaller, and hence more favorable, values for heteronuclear mixtures with infinitely large interspecies s-wave scattering length [3,[8][9][10][11][12][13] [15] groups independently reported the experimental observation of, respectively, two and three consecutive Cs-Cs-Li three-atom resonances. The analysis shows that the Cs-Cs interactions play a negligible role at the present precision of the experiments, indicating that the observation of Efimov physics in these heavylight mixtures is due to the large magnitude of the Cs-Li s-wave scattering length.The extended Efimov scenario has been studied predominantly for four identical bosons with large in absolute value two-body s-wave scattering length [16][17][18][19][20][21][22]. In this case, there exist two four-body states with energies E (n,1) 4 and E (n,2) 4 that are universally tied to the nth Efimov trimer with energy E (n) 3 . These four-body states lead to measurable four-atom resonance...

The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astro physics. This work determines the fourth-order virial coefficient b4 of such a strongly-interacting Fermi gas using a customized ab initio path integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4, our b4 agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly anti-symmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions. [8,9], which can nowadays be produced routinely in table-top experiments, are ideal for studying strongly-interacting systems since (i) the van der Waals interaction is short-ranged, which means that it can be approximated by a contact potential that introduces a single length scale, i.e., the s-wave scattering length a s ; and (ii) a s can be tuned at will utilizing Feshbach resonance techniques [10]. When a s diverges, i.e., becomes infinitely large, the two-body contact potential does not define a length scale [11]. Just like the non-interacting Fermi gas, the properties of the unitary Fermi gas (Fermi gas with infinite a s ) are determined by two length scales, the de Broglie wavelength λ and interparticle spacingr [12].At high temperature, λ is much smaller thanr and the grand canonical thermodynamic potential Ω can be expanded in terms of the fugacity [13,14]. The n thorder expansion or virial coefficient b n is determined by the partition functions of clusters containing n or fewer fermions. Since all thermodynamic properties at high temperature can be derived from the virial coefficients b n [15], the b n 's are essential to understanding the normal state of strongly-interacting Fermi gases.While the second-and third-order virial coefficients are well understood [13,[15][16][17][18][19][20][21], none of the theoretical calculations for b 4 [22][23][24][25] agree with the experimental data [19,26]. This letter rectifies this situation: our theoretically determined b 4 agrees with the experimentally determined value. Our approach uses a trap regulator [27,28] and employs the path integral Monte Carlo

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...

arXiv:1508.00081v1 [cond-mat.quant-gas] 1 Aug 2015Energy and structural properties of N-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator The low-energy spectrum of N -boson clusters with pairwise zero-range interactions is believed to be governed by a three-body parameter. We study the ground state of N -boson clusters with infinite two-body s-wave scattering length by performing ab initio Monte Carlo simulations. To prevent Thomas collapse, different finite-range three-body regulators are used. The energy and structural properties for the three-body Hamiltonian with two-body zero-range interactions and three-body regulator are in much better agreement with the "ideal zero-range Efimov theory" results than those for Hamiltonian with two-body finite-range interactions. For larger clusters we find that the ground state energy and structural properties of the Hamiltonian with two-body zero-range interactions and finite-range three-body regulators are not universally determined by the three-body parameter, i.e., dependences on the specific form of the three-body regulator are observed. For comparison, we consider Hamiltonian with two-body van der Waals interactions and no three-body regulator. For the interactions considered, the ground state energy of the N -body clusters is-if scaled by the three-body ground state energy-fairly universal, i.e., the dependence on the short-range details of the two-body van der Waals potentials is small. Our results are compared with the literature.

The transition from "few to many" has recently been probed experimentally in an ultracold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz et al., Science 342, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and found to converge toward the corresponding expression for an infinitely large Fermi gas. Motivated by these experimental results, we apply perturbative techniques to determine the interaction energy for weak and strong coupling strengths and derive approximate descriptions for the interaction energy for repulsive interactions with varying strength between the impurity and the majority atoms and any number of majority atoms.PACS numbers: