arXiv subjects

D. Blume

Publications and source records attributed to D. Blume.

At least 55 records · Page 3Linked to original sources

arXiv2016

Scattering framework for two particles with isotropic spin-orbit coupling applicable to all energies

Previous work developed a K-matrix formalism applicable to positive energies for the scattering between two $s$-wave interacting particles with two internal states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H. Duan, L. You and B. Gao, Phys. Rev A {\bf{87}}, 052708 (2013)]. This work extends the formalism to the entire energy regime. Explicit solutions are obtained for the total angular momentum $J=0$ and $1$ channels. The behavior of the partial cross sections in the negative energy regime is analyzed in detail. We find that the leading contributions to the partial cross sections at the negative energy thresholds are governed by the spin-orbit coupling strength $k_{\text{so}}$ and the mass ratio. The fact that these contributions are independent of the two-body scattering length $a_s$ is a direct consequence of the effective reduction of the dimensionality, and hence of the density of states, near the scattering thresholds due to the single-particle spin-orbit coupling terms. The results are analytically continued to the energy regime where bound states exist. It is shown that our results are consistent with results obtained by alternative approaches. Our formulation, which can be regarded as an extension of the standard textbook partial wave decomposition, can be generalized to two-body systems with other types of spin-orbit coupling, including cases where the center-of-mass momentum does not vanish.

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arXiv2016

Broken scale-invariance in time-dependent trapping potentials

The response of a cold atom gas with contact interactions to a smoothly varying external harmonic confinement in the non-adiabatic regime is studied. The time variation of the angular frequency is varied such that the system is, for vanishing or infinitely strong contact interactions, scale invariant. The time evolution of the system with broken scale invariance (i.e., the time evolution of the system with finite interaction strength), is contrasted with that for a scale invariant system, which exhibits Efimovian-like expansion dynamics that is characterized by log-periodic oscillations with unique period and amplitude. It is found that the breaking of the scale invariance by the finiteness of the interactions leads to a time dependence of the oscillation period and amplitude. It is argued, based on analytical considerations for atomic gases of arbitrary size and numerical results for two one-dimensional particles, that the oscillation pe riod approaches that of the scale-invariant system at large times. The role of the time-dependent contact in the expansion dynamics is analyzed.

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arXiv2016

Path integral Monte Carlo determination of the fourth-order virial coefficient for unitary two-component Fermi gas with zero-range interactions

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 $b_4$ of such a strongly-interacting Fermi gas using a customized \textit{ab initio} path integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of $b_4$, our $b_4$ 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.

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arXiv2015

Tunneling dynamics of two interacting one-dimensional particles

We present one-dimensional simulation results for the cold atom tunneling experiments by the Heidelberg group [G. Zürn {\em{et al.}}, Phys. Rev. Lett. {\bf{108}}, 075303 (2012) and G. Zürn {\em{et al.}}, Phys. Rev. Lett. {\bf{111}}, 175302 (2013)] on one or two $^6$Li atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic field gradient. At the non-interacting particle level, we find that the WKB (Wentzel-Kramers-Brillouin) approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data. We use our numerical calculations along with the experimental tunneling rates for the non-interacting system to reparameterize the trapping potential. The reparameterized trapping potentials serve as input for our simulations of two interacting particles. For two interacting (distinguishable) atoms on the upper branch, we reproduce the experimentally measured tunneling rates, which vary over several orders of magnitude, fairly well. For infinitely strong interaction strength, we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics. For two attractively-interacting atoms on the molecular branch, we find that single-particle tunneling dominates for weakly-attractive interactions while pair tunneling dominates for strongly-attractive interactions. Our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates. We obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement.

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arXiv2015

Spin structure of harmonically trapped one-dimensional atoms with spin-orbit coupling

We introduce a theoretical approach to determine the spin structure of harmonically trapped atoms with two-body zero-range interactions subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic hyperfine states. The spin structure of bosonic and fermionic two-particle systems with finite and infinite two-body interaction strength $g$ is calculated. Taking advantage of the fact that the $N$-boson and $N$-fermion systems with infinitely large coupling strength $g$ are analytically solvable for vanishing spin-orbit coupling strength $k_{so}$ and vanishing Raman coupling strength $Ω$, we develop an effective spin model that is accurate to second-order in $Ω$ for any $k_{so}$ and infinite $g$. The three- and four-particle systems are considered explicitly. It is shown that the effective spin Hamiltonian, which contains a Heisenberg exchange term and an anisotropic Dzyaloshinskii-Moriya exchange term, describes the transitions that these systems undergo with the change of $k_{so}$ as a competition between independent spin dynamics and nearest-neighbor spin interactions.

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arXiv2015

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

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 new 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.

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arXiv2015

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

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 {\em{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.

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arXiv2015

Efimov physics and the three-body parameter for shallow van der Waals potentials

Extremely weakly-bound three-boson systems are predicted to exhibit intriguing universal properties such as discrete scale invariance. Motivated by recent experimental studies of the ground and excited helium trimers, this work analyzes the three-body parameter and the structural properties of three helium atoms as the s-wave scattering length is tuned artificially. Connections with theoretical and experimental studies of the Efimov scenario as it pertains to cold atom systems are made.

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arXiv2015

Trapped unitary two-component Fermi gases with up to ten particles

The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground state energy for systems with up to ten particles interacting through finite-range two-body potentials for both even and odd number of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.

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arXiv2015

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

The transition from "few to many" has recently been probed experimentally in an ultra cold 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 {\em{et al.}}, Science {\bf{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.

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arXiv2014

Generalized Efimov scenario for heavy-light mixtures

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 $n$th Efimov trimer. For infinitely large $^{133}$Cs-$^6$Li and vanishing $^{133}$Cs-$^{133}$Cs scattering lengths, we find $(E_4^{(1,1)}/E_3^{(1)})^{1/2} \approx 1.51$ and $(E_4^{(1,2)}/E_3^{(1)})^{1/2} \approx 1.01$. The $^{133}$Cs-$^6$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.

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arXiv2014

Universal and non-universal effective $N$-body interactions for ultracold harmonically-trapped few-atom systems

We derive the ground-state energy for a small number of ultracold atoms in an isotropic harmonic trap using effective quantum field theory (EFT). Atoms are assumed to interact through pairwise energy-independent and energy-dependent delta-function potentials with strengths proportional to the scattering length $a$ and effective range volume $V$, respectively. The calculations are performed systematically up to order $l^{-4}$, where $l$ denotes the harmonic oscillator length. The effective three-body interaction contains a logarithmic divergence in the cutoff energy, giving rise to a non-universal three-body interaction in the EFT. Our EFT results are confirmed by nonperturbative numerical calculations for a Hamiltonian with finite-range two-body Gaussian interactions. For this model Hamiltonian, we explicitly calculate the non-universal effective three-body contribution to the energy.

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arXiv2014

Energy spectrum of a harmonically trapped two-atom system with spin-orbit coupling

Ultracold atomic gases provide a novel platform with which to study spin-orbit coupling, a mechanism that plays a central role in the nuclear shell model, atomic fine structure and two-dimensional electron gases. This paper introduces a theoretical framework that allows for the efficient determination of the eigenenergies and eigenstates of a harmonically trapped two-atom system with short-range interaction subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic hyperfine states. Energy spectra for experimentally relevant parameter combinations are presented and future extensions of the approach are discussed.

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arXiv2014

Three-body bound states in a harmonic waveguide with cylindrical symmetry

Highly-elongated quasi-one-dimensional cold atom samples have been studied extensively over the past years experimentally and theoretically. This work determines the energy spectrum of two identical fermions and a third distinguishable particle as functions of the mass ratio $κ$ and the free-space $s$-wave scattering length $a_{3\text{D}}$ between the identical fermions and the distinguishable third particle in a cylindrically symmetric waveguide whose symmetry axis is chosen to be along the $z$-axis. We focus on the regime where the mass of the identical fermions is equal to or larger than that of the third distinguishable particle. Our theoretical framework accounts explicitly for the motion along the transverse confinement direction. In the regime where excitations in the transverse direction are absent (i.e., for states with projection quantum number $M_{\text{rel}}=0$), we determine the binding energies for states with odd parity in $z$. These full three-dimensional energies deviate significantly from those obtained within a strictly one-dimensional framework when the $s$-wave scattering length is of the order of or smaller than the oscillator length in the confinement direction. If transverse excitations are present, we predict the existence of a new class of universal three-body bound states with $|M_{\text{rel}}|=1$ and positive parity in $z$. These bound states arise on the positive $s$-wave scattering length side if the mass ratio $κ$ is sufficiently large. Implications of our results for ongoing cold atom experiments are discussed.

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arXiv2014

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

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 wave length 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 non-interacting 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.

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arXiv2014

Harmonically trapped two-atom systems: Interplay of short-range s-wave interaction and spin-orbit coupling

The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" $k_{\text{so}}$. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body $s$-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small $s$-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

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arXiv2014

Molecular branch of a small highly-elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

We consider an impurity immersed in a small Fermi gas under highly-elongated harmonic confinement. The impurity interacts with the atoms of the Fermi gas through an isotropic short-range potential with three-dimensional free-space s-wave scattering length $a_{3\text{d}}$. We investigate the energies of the molecular branch, i.e., the energies of the state that corresponds to a gas consisting of a weakly-bound diatomic molecule and "unpaired" atoms, as a function of the s-wave scattering length $a_{3\text{d}}$ and the ratio $η$ between the angular trapping frequencies in the tight and weak confinement directions. The energies obtained from our three-dimensional description that accounts for the dynamics in the weak and tight confinement directions are compared with those obtained within an effective one-dimensional framework, which accounts for the dynamics in the tight confinement direction via a renormalized one-dimensional coupling constant. Our theoretical results are related to recent experimental measurements.

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arXiv2013

Tunable high-temperature thermodynamics of weakly-interacting dipolar gases

We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperature, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the $s$-wave scattering length for the bosonic system is tunable and its absolute value is made small, then the $s$-wave interactions dominate and the dipolar as behaves like a weakly-interacting Bose gas with isotropic $s$-wave interactions. If the generalized scattering lengths for the fermionic system are tunable, then the dipole length can enter linearly in the virial equation of state, enhancing the dipole-dipole effects in the thermodynamic observables.

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