Showing papers on "Scattering length published in 2010"
TL;DR: The observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry is reported on.
Abstract: We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.
202 citations
TL;DR: The demonstrated spatial modulation of the scattering length proves that high resolution control of atomic interactions is possible and submicron spatial control of interatomic interactions in a Bose-Einstein condensate of ytterbium is demonstrated.
Abstract: We demonstrate submicron spatial control of interatomic interactions in a Bose-Einstein condensate of ytterbium (Yb). A pulsed optical standing wave, tuned near an optical Feshbach resonance, varies the s-wave scattering length continuously across the standing wave pattern. The modulated mean-field energy with a spatial period every 278 nm is monitored by a diffraction pattern in a time-of-flight image. We observe a wide scattering length control of up to 250 nm. The demonstrated spatial modulation of the scattering length proves that high resolution control of atomic interactions is possible.
171 citations
TL;DR: In this article, the authors measured the local internal energy of a trapped gas as a function of the particle density and temperature in a unitary Fermi gas where the scattering length diverges, and derived universal functions such as the Helmholtz free energy, chemical potential, and entropy.
Abstract: Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.
150 citations
01 Mar 2010
TL;DR: The thermodynamic properties of matter generally depend on the details of interactions between its constituent parts, but in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature.
Abstract: Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.
132 citations
TL;DR: In this article, a theory for Fano interference in light scattering by individual obstacles based on a temporal coupled-mode formalism is presented. But this theory is applicable for obstacles that are much smaller than the incident wavelength, or for systems with two-dimensional cylindrical or three-dimensional spherical symmetry.
Abstract: We present a theory for Fano interference in light scattering by individual obstacle, based on a temporal coupled-mode formalism. This theory is applicable for obstacles that are much smaller than the incident wavelength, or for systems with two-dimensional cylindrical or three-dimensional spherical symmetry. We show that for each angle momentum channel, the Fano interference effect can be modeled by a simple temporal coupled-mode equation, which provides a line shape formula for scattering and absorption cross-section. We validate the analysis with numerical simulations. As an application of the theory, we design a structure that exhibits strong absorption and weak scattering properties at the same frequency.
126 citations
TL;DR: A tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons is presented, where the low-energy transition operator is written as a product of local spin operators and fundamental x-rays absorption spectral functions.
Abstract: I present a tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons. The low-energy transition operator is written as a product of local spin operators and fundamental x-ray absorption spectral functions. This leads to simple selection rules. The scattering cross section linear (quadratic) in spin operators is proportional to the fundamental magnetic circular (linear) dichroic spectral function. RIXS is a novel tool to measure magnetic quasiparticles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy losses, in small samples, thin films, and multilayers, complementary to neutron scattering.
125 citations
TL;DR: In this article, the effect of coordination on transport was investigated theoretically using random networks of springs as model systems, and an effective medium approximation was made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination z is varied.
Abstract: The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination z is varied. Critical behaviors are obtained as z→zc where these networks lose rigidity. A sharp crossover from a regime where modes are plane-wave–like toward a regime of extended but strongly scattered modes occurs at some frequency ω*~z-zc, which does not correspond to the Ioffe-Regel criterion. Above ω* both the density of states and the diffusivity are nearly constant. These results agree remarkably with recent numerical observations of repulsive particles near the jamming threshold (Xu N. et al., Phys. Rev. Lett., 102 (2009) 038001). The analysis further predicts that the length scale characterizing the correlation of displacements of the scattered modes decays as with frequency, whereas for ωω* Rayleigh scattering is found with a scattering length ls~(z-zc)3/ω4. It is argued that this description applies to silica glass where it compares well with thermal conductivity data, and to transverse ultrasound propagation in granular matter.
113 citations
TL;DR: In this paper, a variational wave function was constructed to study whether a fully polarized Fermi sea of ultracold atoms is energetically stable against a single spin flip.
Abstract: We construct a variational wave function to study whether a fully polarized Fermi sea of ultracold atoms is energetically stable against a single spin flip. Our variational wave function contains short-range correlations at least to the same level as Gutzwiller's projected wave function. For the Hubbard lattice model and the continuum model with pure repulsive interaction, we show that a fully polarized Fermi sea is generally unstable even for infinite repulsive strength. By contrast, for a resonance model, the ferromagnetic state is possible if the s-wave scattering length is positive and sufficiently large and the system is prepared to be orthogonal to the molecular bound state. However, we cannot rule out the possibility that more exotic correlations can destabilize the ferromagnetic state.
110 citations
TL;DR: In this paper, a binary mixture of ultracold atoms and a species-selective 1D optical lattice was used to confine only one atomic species in 2D.
Abstract: We experimentally investigate the mix-dimensional scattering occurring when the collisional partners live in different dimensions. We employ a binary mixture of ultracold atoms and exploit a species-selective 1D optical lattice to confine only one atomic species in 2D. By applying an external magnetic field in proximity of a Feshbach resonance, we adjust the free-space scattering length to observe a series of resonances in mixed dimensions. By monitoring 3-body inelastic losses, we measure the magnetic field values corresponding to the mix-dimensional scattering resonances and find a good agreement with the theoretical predictions based on simple energy considerations.
104 citations
TL;DR: In this article, the lowest-lying quadrupole mode of a Bose-Einstein condensate was excited by modulating the atomic scattering length via a Feshbach resonance.
Abstract: We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.
102 citations
TL;DR: In this article, a theory of density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length is presented.
Abstract: We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.
TL;DR: In this paper, the s-wave pion-pion scattering length in the isospin I = 2 channel in lattice QCD for pion masses ranging from 270 MeV to 485 MeV using two flavors of maximally twisted mass fermions at a lattice spacing of 0.086 fm.
TL;DR: In this paper, the authors analyzed energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive and showed that three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism.
Abstract: Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism. Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance. We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive. When the $s$-wave scattering length $a$ is sufficiently positive, three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the high-temperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion. The second and third virial coefficients are calculated. The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.
TL;DR: This work shows that universal relations that hold for any state can be derived and extended by using the short-time operator product expansion of quantum field theory, a general method for identifying aspects of many-body physics that are controlled by few- body physics.
Abstract: Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large-frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.
TL;DR: In this article, the authors used the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle and derived analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy.
Abstract: We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.
TL;DR: The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram.
Abstract: The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length a{sub s}, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.
TL;DR: In this paper, the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate were investigated by assuming that the interaction energy is much less than the kinetic energy in the transverse direction.
TL;DR: A frequency-domain finite element technique is presented that enables the complete characterization of a finite-sized scatterer using a minimum number of separate model executions and a relatively small spatial modeling domain.
Abstract: A frequency-domain finite element technique is presented that enables the complete characterization of a finite-sized scatterer using a minimum number of separate model executions and a relatively small spatial modeling domain. The technique is implemented using a commercial finite element package. A certain forcing profile is applied at a set of points surrounding the scatterer to cause a uni-modal plane wave to be incident on the scatterer from a specified direction. The scattered field is recorded and decomposed first into modes and then into far-field scattering coefficients in different directions. The data obtained from the model are represented in a scattering matrix that describes the far-field scattering response for all combinations of incident and scattering angles. The information in the scattering matrix can be efficiently represented in the Fourier domain by another matrix containing a finite number of Fourier coefficients. It is shown how the complete scattering behavior in both the near- and far-field can be extracted from the matrix of Fourier coefficients. Modeling accuracy is examined in various ways, including a comparison with the analytical solution for a circular cavity, and guidelines for the selection of modeling parameters are given.
TL;DR: It is shown that a suitably averaged value of the impedance can be computed from short ray trajectories in wave-chaotic systems open to outside scattering channels and that this can improve the ability to describe the statistical properties of the scattering systems.
Abstract: Predicting the statistics of realistic wave-chaotic scattering systems requires, in addition to random matrix theory, introduction of system-specific information. This paper investigates experimentally one aspect of system-specific behavior, namely, the effects of short ray trajectories in wave-chaotic systems open to outside scattering channels. In particular, we consider ray trajectories of limited length that enter a scattering region through a channel (port) and subsequently exit through a channel (port). We show that a suitably averaged value of the impedance can be computed from these trajectories and that this can improve the ability to describe the statistical properties of the scattering systems. We illustrate and test these points through experiments on a realistic two-port microwave scattering billiard.
TL;DR: In this paper, the modification of the Efimov trimers of three identical bosons in a finite cubic box and the dependence of their energies on the box size using effective field theory were computed.
Abstract: Three particles with large scattering length display a universal spectrum of three-body bound states called “Efimov trimers”. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite-volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. We investigate the effects of partial-wave mixing and study the behavior of shallow trimers near the dimer energy. Moreover, we provide numerical evidence for universal scaling of the finite-volume corrections.
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TL;DR: The strong interaction shift and broadening in pionic deuterium have been determined in a high statistics study of the 3p - 1s X-ray transition using a high-resolution crystal spectrometer.
Abstract: The strong interaction shift $\epsilon$ and broadening {\Gamma} in pionic deuterium have been determined in a high statistics study of the {\pi}D(3p - 1s) X-ray transition using a high-resolution crystal spectrometer The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen The hadronic broadening is related to pion absorption and production at threshold The results are \epsilon = (-2356 {\pm} 31)meV (repulsive) and {\Gamma}1s = (1171+23/-49) meV yielding for the complex {\pi}D scattering length a = [-(2499 {\pm} 033) + i (622+012/-026)]x10-3/m{\pi} From the imaginary part, the threshold parameter for pion production is obtained to be {\alpha} = (251 +5/-11) {\mu}b This allows, in addition, and by using results from pion absorption in 3He at threshold, the determination of the effective couplings g0 and g1 for s-wave pion absorption on isoscalar and isovector NN pairs
TL;DR: An analytical scattering model is derived that accounts for the self-correlation of a spherical core and surface adsorbed particles as well as the particle-particle and core-particles correlation terms characteristic of Pickering emulsions and raspberry particles.
TL;DR: In this article, a Bose-Einstein condensate of atoms confined in a toroidal trap with a variable strength of $s$-wave contact interactions is analyzed.
Abstract: We study a Bose-Einstein condensate of $^{52}\mathrm{Cr}$ atoms confined in a toroidal trap with a variable strength of $s$-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system from a pancake-shaped condensate when it is large to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity fields, finding that these also show a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the $z$ direction provides a qualitative measure of the difference between the velocity in the different density peaks.
TL;DR: It is shown that the pair-structure factor of scattering potential of the collection of particles can be determined from the cross-spectral density function of the scattered field.
Abstract: The method of determination of the pair-structure factor of a collection of particles has been discussed. It is shown that the pair-structure factor of scattering potential of the collection of particles can be determined from the cross-spectral density function of the scattered field.
TL;DR: In this paper, the phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms are discussed within a functional renormalization group approach.
Abstract: The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.
TL;DR: In this article, the authors study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap and present results at unitarity for three and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods.
Abstract: We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body interactions, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the no-core shell model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods (in the four-body case). We also present results for finite scattering lengths and nonzero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.
TL;DR: In this article, the decay energy spectrum was reconstructed from coincidence measurements between the emitted neutron and the 17 B fragment using the MoNA/sweeper setup, resulting in an upper limit for the scattering length of − 50 fm which corresponds to a decay energy s -wave decay of 18 B.
TL;DR: In this article, the energy spectrum of the equal-mass spin-balanced four-fermion system was derived as a function of the wave scattering length of the atom-atom pair.
Abstract: Trapped two-component Fermi gases allow the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave scattering length ${a}^{(\mathit{aa})}$ from attractive to repulsive, including vanishing and infinitely large values. Here, we numerically determine the energy spectrum of the equal-mass spin-balanced four-fermion system---the smallest few-particle system that exhibits BCS-BEC crossoverlike behavior---as a function of ${a}^{(\mathit{aa})}$ using the stochastic variational approach. For comparative purposes, we also treat the two- and three-particle systems. States with vanishing and finite total angular momenta as well as with natural and unnatural parities are considered. In addition, the energy spectrum of weakly attractive and weakly repulsive gases is characterized by employing a perturbative framework that utilizes hyperspherical coordinates. The hyperspherical coordinate approach allows the straightforward assignment of quantum numbers and furthermore provides great insight into the strongly interacting unitary regime.
TL;DR: In this paper, the authors studied the renormalization group of bosonic atoms with a wide Feshbach resonance at zero temperature in terms of renormalisation group and showed that this system will always collapse in the dilute limit and that the thermodynamics of this system in the unitary limit are identical to the one for an ideal Fermi gas.
Abstract: We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero-density fixed point. Moreover, we find that the $T=0$ thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.
TL;DR: In this paper, a comparative study of the three-nucleon force models is performed and the authors analyze their capability to describe the aforementioned binding energies as well as the doublet scattering length.
Abstract: Using modern nucleon-nucleon interactions in the description of $A=3,4$ nuclei, it is not possible to reproduce both the three- and the four-nucleon binding energies simultaneously. This is one manifestation of the necessity of including a three-nucleon force in the nuclear Hamiltonian. In this paper we perform a comparative study of some widely used three-nucleon force models. We analyze their capability to describe the aforementioned binding energies as well as the $n$-$d$ doublet scattering length. The correct description of these quantities can be considered a stringent requirement for a nuclear Hamiltonian containing two- and three-nucleon interaction terms. As we show, this requirement is not fulfilled by several of the models available in the literature. To satisfy it, we propose modifications in the parametrization of the three-nucleon forces and we study their effects on a few selected $N$-$d$ low-energy scattering observables.