7,455 research outputs found
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 and the
free-space -wave scattering length between the identical
fermions and the distinguishable third particle in a cylindrically symmetric
waveguide whose symmetry axis is chosen to be along the -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 ), we determine the
binding energies for states with odd parity in . These full
three-dimensional energies deviate significantly from those obtained within a
strictly one-dimensional framework when the -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 and
positive parity in . These bound states arise on the positive -wave
scattering length side if the mass ratio is sufficiently large.
Implications of our results for ongoing cold atom experiments are discussed.Comment: 9 figure
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.Comment: 10 pages, 5 figures in Few-Body Systems (2015
Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum
Within the hyperspherical framework, the solution of the time-independent
Schroedinger equation for a n-particle system is divided into two steps, the
solution of a Schroedinger like equation in the hyperangular degrees of freedom
and the solution of a set of coupled Schroedinger like hyperradial equations.
The solutions to the former provide effective potentials and coupling matrix
elements that enter into the latter set of equations. This paper develops a
theoretical framework to determine the effective potentials, as well as the
associated coupling matrix elements, for few-body systems with finite angular
momentum L=1 and negative and positive parity. The hyperangular channel
functions are expanded in terms of explicitly correlated Gaussian basis
functions and relatively compact expressions for the matrix elements are
derived. The developed formalism is applicable to any n; however, for n greater
or equal to 6, the computational demands are likely beyond present-day
computational capabilities. A number of calculations relevant to cold atom
physics are presented, demonstrating that the developed approach provides a
computationally efficient means to solving four-body bound and scattering
problems with finite angular momentum on powerful desktop computers. Details
regarding the implementation are discussed
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 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 , our 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.Comment: 5 pages (2 figures) + 5 pages (1 figure). Added a table, included
more discussion about the fitted function, corrected a few typos, and updated
Fig.
Incorporating exact two-body propagators for zero-range interactions into -body Monte Carlo simulations
Ultracold atomic gases are, to a very good approximation, described by
pairwise zero-range interactions. This paper demonstrates that -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.Comment: 11 pages, 6 figure
Microscopic Superfluidity in Bose Gases: From 3D to 1D
The superfluid fraction of ideal and interacting inhomogeneous Bose gases
with varying asymmetry is investigated at finite temperature using well-known
properties of the harmonic oscillator as well as the essentially exact
microscopic path integral Monte Carlo method. We find that the superfluid
fraction (i) is essentially independent of the interaction strength for all
temperatures considered, (ii) changes profoundly as the effective
dimensionality is varied from three- to one-dimensional, (iii) is approximately
equal to the condensate fraction N0/N for spherical Bose gases, and (iv)
deviates dramatically from N0/N for highly-elongated Bose gases.Comment: 4 pages, 3 fig
Abnormal Superfluid Fraction of Harmonically Trapped Few-Fermion Systems
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 \textit{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 . Analogous abnormal behavior of
has been observed in even-odd nuclei at low temperature. Our
predictions can be tested in modern cold atom experiments.Comment: 5 pages, 4 figure
Harmonically trapped Fermi gas: Temperature dependence of the Tan contact
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.Comment: 5 figures (several subfigures
Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
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 Schroedinger equation.
Specifically, the PIGS approach allows for the determination of expectation
values with respect to eigen states of the few- or many-body Schroedinger
equation provided the system Hamiltonian is known. The theoretical framework
behind the PIGS algorithm, implementation details, and sample applications for
sermonic systems are presented.Comment: 56-page tutorial to be published in JPB; a related PIMC code,
authored by Yangqian Yan, can be found at
https://github.com/yangqian/PIMCcod
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 is calculated. Taking advantage of the fact that the -boson and
-fermion systems with infinitely large coupling strength are
analytically solvable for vanishing spin-orbit coupling strength and
vanishing Raman coupling strength , we develop an effective spin model
that is accurate to second-order in for any and infinite .
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 as a
competition between independent spin dynamics and nearest-neighbor spin
interactions.Comment: 23 pages, 10 figure
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