论文

2024

1. arXiv

   Fate of thermalization of ultracold fermions with two-body dissipation

   Xin-Yuan Gao, and Yangqian Yan

   arXiv:2410.12204

   arXiv
2. arXiv

   Thermodynamics of Spin-Imbalanced Fermi Gases with SU(N) Symmetric Interaction

   Chengdong He, Xin-Yuan Gao, Ka Kwan Pak, Yu-Jun Liu, Peng Ren, Mengbo Guo, Entong Zhao, Yangqian Yan, and Gyu-Boong Jo

   arXiv:2409.04960

   arXiv
3. PRR

   Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves

   Xin-Yuan Gao, D. Blume, and Yangqian Yan

   Phys. Rev. Res. 6, 033173 (2024)

   Abs arXiv PDF DOI

   While the thermodynamics for bosonic systems with weak s-wave interactions has been known for decades, a general and systematic extension to higher partial-waves has not yet been reported. We provide closed-form expressions for the equations of state for weakly-interacting systems with arbitrary partial-waves in the normal phase. Thermodynamics, including contact, loss rate, and compressibility, are derived over the entire temperature regime. Our results offer an improved thermometer for ultracold atoms and molecules with weak high-partial wave interactions.

4. arXiv

   Interaction induced splitting of Dirac monopoles in the topological Thouless pumping of strongly interacting Bosons and SU(N) Fermions

   Hei Lam, and Yangqian Yan

   arXiv:2405.10291

   Abs arXiv

   Motivated by the observation of the breakdown of quantization for the Thouless pump in the presence of strong interaction by ETH [Walter et. al. Nat. Phys. 19, 1471 (2023), Viebahn et. al. arXiv:2308.03756], we study the interplay of strong interaction and topology in the (1+1)-dimensional interacting Rice-Mele model. We point out that the quantization of the interacting Thouless pump is dictated by the Chern number, i.e., the Dirac monopoles enclosed by the generalized Brillouin zone of the many-body wave function. By analyzing the change of location monopoles due to interaction, we predict the Thouless charge pump for strongly interacting Bose and SU(N) Fermi gases in optical lattices and explain the ETH experiment.

2023

1. PRL

   Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules

   Xin-Yuan Gao, D. Blume, and Yangqian Yan

   Phys. Rev. Lett. 131, 043401 (2023)

   Abs arXiv PDF Supp DOI

   Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state \mathrmKRb molecules with intrinsic two-body losses [L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules,Science 363, 853 (2019)], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the p-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using p-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally—in agreement with the Bethe-Wigner threshold law—linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular p-wave gases but also to atomic single-component Fermi gases, such as ^40\textK and ^6\textLi.

2022

1. PRL

   Expansion Dynamics of a Shell-Shaped Bose-Einstein Condensate

   Fan Jia, Zerong Huang, Liyuan Qiu, Rongzi Zhou, Yangqian Yan, and Dajun Wang

   Phys. Rev. Lett. 129, 243402 (2022)

   Abs arXiv PDF DOI

   We report the creation of a shell BEC in the presence of Earth’s gravity with immiscible dual-species BECs of sodium and rubidium atoms. After minimizing the displacement between the centers of mass of the two BECs with a magic-wavelength optical dipole trap, the interspecies repulsive interaction ensures the formation of a closed shell of sodium atoms with its center filled by rubidium atoms. Releasing the double BEC together from the trap, we observe explosion of the filled shell accompanied by energy transfer from the inner BEC to the shell BEC. With the inner BEC removed, we obtain a hollow shell BEC that shows self-interference as a manifestation of implosion. Our results pave an alternative way for investigating many of the intriguing physics offered by shell BECs.

2. NJP

   Abnormal Quantum Moment of Inertia and Structural Properties of Electrons in 2D and 3D Quantum Dots: An Ab Initio Path-Integral Monte Carlo Study

   Tobias Dornheim, and Yangqian Yan

   New J. Phys. 24, 113024 (2022)

   Abs arXiv PDF DOI

   We present extensive new direct path-integral Monte Carlo results for electrons in quantum dots in two and three dimensions. This allows us to investigate the nonclassical rotational inertia (NCRI) of the system, and we find an abnormal negative quantum moment of inertia (2014 Phys. Rev. Lett. 112 235301) under some conditions. In addition, we study the structural properties by computing a re-normalized, angular-resolved center-two particle correlation function. Remarkably, we find no connection between the spatial structure and the NCRI, since the former can be nearly identical for Fermi- and Bose-statistics for parameters where the superfluid fraction is diverging towards negative infinity.

3. PRXQ

   Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder

   Chuan-Hsun Li, Yangqian Yan, Shih-Wen Feng, Sayan Choudhury, David B. Blasing, Qi Zhou, and Yong P. Chen

   PRX Quantum 3, 010316 (2022)

   Abs arXiv PDF DOI

   The interplay between matter particles and gauge fields in physical spaces with nontrivial geometries can lead to novel topological quantum matter. However, detailed microscopic mechanisms are often obscure, and unconventional spaces are generally challenging to construct in solids. Highly controllable atomic systems can quantum simulate such physics, even those inaccessible in other platforms. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux. We observe a symmetry-protected topological band structure emerging on this Hall cylinder but disappearing in the planar counterpart. BEC’s transport observed as Bloch oscillations in the band structure is analogous to traveling on a Möbius strip in the momentum space, revealing topological band crossings protected by a nonsymmorphic symmetry. We demonstrate that breaking this symmetry induces a topological transition manifested as gap opening at band crossings, and further manipulate the band structure and BEC’s transport by controlling the axial synthetic magnetic flux. Our work opens the door for using atomic quantum simulators to explore intriguing topological phenomena intrinsic in unconventional spaces.

2021

1. PRL

   Localization on a Synthetic Hall Cylinder

   Ren Zhang, Yangqian Yan, and Qi Zhou

   Phys. Rev. Lett. 126, 193001 (2021)

   Abs arXiv PDF DOI

   By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, the dependence of physical observables on the axial magnetic flux allows us to tackle a fundamental question of determining the accuracy of rational approximation of irrational numbers. In the irrational limit, physical observables are no longer affected by fluctuations of the axial flux.

2. SciBul

   Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces

   Ren Zhang, Chenwei Lv, Yangqian Yan, and Qi Zhou

   Science Bulletin 66, 1967–1972 (2021)

   Abs arXiv DOI

   Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincaré half-planes and Poincaré disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincaré half-plane or its equivalent on the Poincaré disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.

2020

1. PRX

   Evidence for bosonization in a three-dimensional gas of SU (N) fermions

   Bo Song, Yangqian Yan, Chengdong He, Zejian Ren, Qi Zhou, and Gyu-Boong Jo

   Phys. Rev. X 10, 041053 (2020)

   Abs PDF DOI

   Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics. One such example is a multicomponent Fermi gas with SU(N) symmetry that is expected to behave like spinless bosons in the large-N limit, where the large number of internal states weakens constraints from the Pauli exclusion principle. However, bosonization in SU(N) fermions has never been established in high dimensions where exact solutions are absent. Here, we report direct evidence for bosonization in a SU(N) fermionic ytterbium gas with tunable N in three dimensions (3D). We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a 1/N scaling in the low-fugacity regime consistent with our theoretical prediction. This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity. Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions. It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.

2. PRR

   Eternal discrete time crystal beating the Heisenberg limit

   Changyuan Lyu, Sayan Choudhury, Chenwei Lv, Yangqian Yan, and Qi Zhou

   Phys. Rev. Res. 2, 033070 (2020)

   Abs PDF DOI

   A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. Discrete time crystals promise profound applications in precision timekeeping and other quantum techniques. However, it has been facing a grand challenge of thermalization. The periodic driving supplying the power may ultimately bring DTCs to thermal equilibrium and destroy their coherence. Here we show that an all-to-all interaction delivers a DTC that evades thermalization and maintains quantum coherence and quantum synchronization regardless of spatial inhomogeneities in the driving field and the environment. Moreover, the sensitivity of this DTC scales with the total particle number to the power of 3/2, realizing a quantum device of measuring the driving frequency or the interaction strength beyond the Heisenberg limit. Our work paves the way for designing nonequilibrium phases with long coherence time to advance quantum metrology.

2019

1. PRL

   Emergent Periodic and Quasiperiodic Lattices on Surfaces of Synthetic Hall Tori and Synthetic Hall Cylinders

   Yangqian Yan, Shao-Liang Zhang, Sayan Choudhury, and Qi Zhou

   Phys. Rev. Lett. 123, 260405 (2019)

   Abs PDF Supp Slides DOI

   Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface—an impossible mission in the real space. Such a synthetic Hall torus gives rise to a periodic lattice in real dimensions, in which the periodicity of the density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic-symmetry-protected band crossings in each cluster, leading to swaps of wave packets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.

2018

1. PRL

   Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

   Yangqian Yan, and Qi Zhou

   Phys. Rev. Lett. 120, 235302 (2018)

   Abs PDF Supp Slides DOI

   The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

2. PRL

   Observation of Quantum Interference and Coherent Control in a Photochemical Reaction

   David B. Blasing, Jesús Pérez-Ríos, Yangqian Yan, Sourav Dutta, Chuan-Hsun Li, Qi Zhou, and Yong P. Chen

   Phys. Rev. Lett. 121, 073202 (2018)

   Abs PDF Supp DOI

   Coherent control of reactants remains a long-standing challenge in quantum chemistry. In particular, we have studied laser-induced molecular formation (photoassociation) in a Raman-dressed spin-orbit-coupled 87Rb Bose-Einstein condensate, whose spin quantum state is a superposition of multiple bare spin components. In contrast to the notably different photoassociation-induced fractional atom losses observed for the bare spin components of a statistical mixture, a superposition state with a comparable spin composition displays the same fractional loss on every spin component. We interpret this as the superposition state itself undergoing photoassociation. For superposition states induced by a large Raman coupling and zero Raman detuning, we observe a nearly complete suppression of the photoassociation rate. This suppression is consistent with a model based upon quantum destructive interference between two photoassociation pathways for colliding atoms with different spin combinations. This model also explains the measured dependence of the photoassociation rate on the Raman detuning at a moderate Raman coupling. Our work thus suggests that preparing atoms in quantum superpositions may represent a powerful new technique to coherently control photochemical reactions.

2017

1. JPB

   Path integral Monte Carlo ground state approach: formalism, implementation, and applications

   Yangqian Yan, and D Blume

   J. Phys. B: At. Mol. Opt. Phys. 50, 223001 (2017)

   Abs PDF DOI

   Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.

2016

1. THESIS

   Path integral Monte Carlo studies of ultracold few-atom systems

   Yangqian Yan

   Ph.D. Thesis, Washington State University (2016)

   Abs PDF

   Motivated by the fact that ultracold atomic systems can nowadays be realized experimentally with varying number of particles, this thesis explores the transition from few- to many-body physics in ultracold matter via the path-integral Monte Carlo (PIMC) technique. The PIMC approach, which accounts for the particle statistics and yields thermodynamic observables, can be applied to both small and large systems. We determine the energy, Tan’s contact, various structural properties, the super- fluid fraction and density, and the condensate fraction of small harmonically trapped bosonic and fermionic systems as functions of the temperature and s-wave scattering length. We find that the superfluid fraction of fermions is negative for certain parameter combinations and develop a microscopic understanding of this, at first sight, surprising behavior. We further illustrate that the superfluid fraction and condensate fraction are distinct quantities by performing finite temperature two-body calculations. A simple model that can be used to extract the ground state energy of N-boson droplets from finite temperature calculations is proposed. This approach, combined with a novel two-body zero-range propagator, is used to explore the generalized Efimov scenario at unitarity. For three bosons, Efimov predicted the existence of an infinite series of geometrically spaced bound states. Whether the N-boson energy is fully determined by three-body physics or dependent on higher-body properties has long been debated in the literature. We find that the N-body ground state energies display a notable model-dependence, suggesting that corrections to Efimov universality become increasingly more important with increasing N. For van der Waals systems, a weaker universality is found. The equation of state (EOS) of spin-balanced equal-mass two-component Fermi gases at unitarity has been determined in cold atom experiments. At high temperature or low density, the virial expansion provides a good description of the EOS. While the second- and third-order virial coefficients have been calculated theoretically and verified experimentally, theory and experiment do not yet agree on the fourth-order virial coefficient. Our ab initio determination of the fourth-order virial coefficient agrees with experiments, thereby settling an ongoing debate in the literature.

2. PRL

   Path-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range Interactions

   Yangqian Yan, and D. Blume

   Phys. Rev. Lett. 116, 230401 (2016)

   Abs PDF Supp DOI

   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 astrophysics. 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 antisymmetrization 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.

3. PRA

   Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields

   X. Y. Yin, Yangqian Yan, and D. Hudson Smith

   Phys. Rev. A 94, 043639 (2016)

   Abs PDF DOI

   Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.

2015

1. PRA

   Energy 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

   Yangqian Yan, and D. Blume

   Phys. Rev. A 92, 033626 (2015)

   Abs PDF DOI

   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., dependencies 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 those in the literature.

2. PRA

   Incorporating exact two-body propagators for zero-range interactions into N -body Monte Carlo simulations

   Yangqian Yan, and D. Blume

   Phys. Rev. A 91, 043607 (2015)

   Abs PDF DOI

   Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that N-body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite-temperature and ground-state path-integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. Harmonically trapped one- and three-dimensional systems are considered. A propagator for the harmonically trapped two-body system with infinitely strong zero-range interaction, which may also have applications in real time evolution schemes, is presented.

3. PRA

   One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch

   Seyed Ebrahim Gharashi, X. Y. Yin, Yangqian Yan, and D. Blume

   Phys. Rev. A 91, 013620 (2015)

   Abs PDF DOI

   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.

2014

1. PRL

   Abnormal Superfluid Fraction of Harmonically Trapped Few-Fermion Systems

   Yangqian Yan, and D. Blume

   Phys. Rev. Lett. 112, 235301 (2014)

   Abs PDF DOI

   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 Letter 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 I_q. Analogous abnormal behavior of I_q has been observed in even-odd nuclei at low temperature. Our predictions can be tested in modern cold atom experiments.

2. PRL

   Generalized Efimov Scenario for Heavy-Light Mixtures

   D. Blume, and Yangqian Yan

   Phys. Rev. Lett. 113, 213201 (2014)

   Abs PDF Supp DOI

   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_4^(n,1) and E_4^(n,2), which are universally linked to the energy E_3^(n) of the nth Efimov trimer. For infinitely large ^133Cs-^6Li and vanishing ^133Cs-^133Cs scattering lengths, we find (E_4^(1,1)/E_3^(1))^1/2 ≈1.51 and (E_4^(1,2)/E_3^(1))^1/2 ≈1.01. The ^133Cs-^6Li 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.

3. PRA

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

   Yangqian Yan, and D. Blume

   Phys. Rev. A 90, 013620 (2014)

   Abs PDF Slides DOI

   While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path-integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wavelength is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal-to-noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a noninteracting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase-transition-like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.

2013

1. PRA

   Harmonically trapped Fermi gas: Temperature dependence of the Tan contact

   Yangqian Yan, and D. Blume

   Phys. Rev. A 88, 023616 (2013)

   Abs PDF Slides DOI

   Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the N-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.