Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates

It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. An asymptotic expansion of this wave function at large interparticle distances is derived, from which is defined a quantity $D$ named three-body scattering hypervolume, which is an analog of the two-body scattering length. Given any finite-range interaction potentials, one can thus predict the effective three-body force from a numerical solution of the Schr\"{o}dinger equation. In this way the constant $D$ for hard-sphere bosons is computed, leading to the complete result for the ground state energy per particle of a dilute Bose-Einstein condensate (BEC) of hard spheres to order $\rho^2$, where $\rho$ is the number density. Effects of $D$ are also demonstrated in the three-body energy in a finite box of size $L$, which is expanded to the order $L^{-7}$, and in the three-body scattering amplitude in vacuum. Another key prediction is that there is a violation of the effective field theory (EFT) in the condensate fraction in dilute BECs, caused by short-range physics. EFT predictions for the ground state energy and few-body scattering amplitudes, however, are corroborated.Comment: 24 pages, no figur

The continuum description with pseudo-state wave functions

Benchmark calculations are performed aiming to test the use of two different pseudo-state bases on the the Multiple Scattering expansion of the total Transition amplitude (MST) scattering framework. Calculated differential cross sections for p-6He inelastic scattering at 717 MeV/u show a good agreement between the observables calculated in the two bases. This result gives extra confidence on the pseudo-state representation of continuum states to describe inelastic/breakup scattering.Comment: 4 pages, 2 figures. Published in Physical Review

Axions Scattering From a Quadrupole Magnetic Field

We study the 2D scattering of axions from an accelerator like quadrupole magnet using the eikonal approximation in order to learn whether or not such a setup could serve as a new possible method for detecting axions on terrestrial experiments. The eikonal approximation in 2D is introduced and explained. We also apply the eikonal approximation to two known cases in order to compare it with previous results, obtained using Born's approximation, and discuss its correctness

Quantitative rescattering theory for laser-induced high-energy plateau photoelectron spectra

A comprehensive quantitative rescattering (QRS) theory for describing the production of high-energy photoelectrons generated by intense laser pulses is presented. According to the QRS, the momentum distributions of these electrons can be expressed as the product of a returning electron wave packet with the elastic differential cross sections (DCS) between free electrons with the target ion. We show that the returning electron wave packets are determined mostly by the lasers only, and can be obtained from the strong field approximation. The validity of the QRS model is carefully examined by checking against accurate results from the solution of the time-dependent Schr\"odinger equation for atomic targets within the single active electron approximation. We further show that experimental photoelectron spectra for a wide range of laser intensity and wavelength can be explained by the QRS theory, and that the DCS between electrons and target ions can be extracted from experimental photoelectron spectra. By generalizing the QRS theory to molecular targets, we discuss how few-cycle infrared lasers offer a promising tool for dynamic chemical imaging with temporal resolution of a few femtoseconds.Comment: 19 pages, 19 figure

Electron release of rare gas atom clusters under an intense laser pulse

Calculating the energy absorption of atomic clusters as a function of the laser pulse length $T$ we find a maximum for a critical $T^*$. We show that $T^*$ can be linked to an optimal cluster radius $R^*$. The existence of this radius can be attributed to the enhanced ionization mechanism originally discovered for diatomic molecules. Our findings indicate that enhanced ionization should be operative for a wide class of rare gas clusters. From a simple Coulomb explosion ansatz, we derive an analytical expression relating the maximum energy release to a suitably scaled expansion time which can be expressed with the pulse length $T^*$.Comment: 4 pages, 5 figure

Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure

We have developed a theoretical method to study scattering processes of an incident electron through an N-electron quantum dot (QD) embedded in a two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger equations including the electron-electron exchange interaction in this system are solved for the continuum electron by using the method of continued fractions (MCF) combined with 2D partial-wave expansion technique. The method is applied to a one-electron QD case. Cross-sections are obtained for both the singlet and triplet couplings between the incident electron and the QD electron during the scattering. The total elastic cross-sections as well as the spin-flip scattering cross-sections resulting from the exchange potential are presented. Furthermore, inelastic scattering processes are also studied using a multichannel formalism of the MCF.Comment: 11 pages, 4 figure

Relativistic electronic dressing

We study the effects of the relativistic electronic dressing in laser-assisted electron-hydrogen atom elastic collisions. We begin by considering the case when no radiation is present. This is necessary in order to check the consistency of our calculations and we then carry out the calculations using the relativistic Dirac-Volkov states. It turns out that a simple formal analogy links the analytical expressions of the differential cross section without laser and the differential cross section in presence of a laser field.Comment: 11 pages, 18 figures, Late

Sympathetic cooling and collisional properties of a Rb-Cs mixture

We report on measurements of the collisional properties of a mixture of $^{133}$Cs and $^{87}$Rb atoms in a magnetic trap at $\mu\mathrm{K}$ temperatures. By selectively evaporating the Rb atoms using a radio-frequency field, we achieved sympathetic cooling of Cs down to a few $\mu\mathrm{K}$. The inter-species collisional cross-section was determined through rethermalization measurements, leading to an estimate of $a_s=595 a_0$ for the s-wave scattering length for Rb in the $|F=2, m_F=2>$ and Cs in the $|F=4, m_F=4>$ magnetic states. We briefly speculate on the prospects for reaching Bose-Einstein condensation of Cs inside a magnetic trap through sympathetic cooling

Four-photon scattering in birefringent fibers

Four-photon scattering in nonlinear waveguides is an important physical process that allows photon-pair generation in well defined guided modes, with high rate and reasonably low noise. Most of the experiments to date used the scalar four-photon scattering process in which the pump photons and the scattered photons have the same polarization. In birefringent waveguides, vectorial four-photon scattering is also allowed: these vectorial scattering processes involve photons with different polarizations. In this article, the theory of four-photon scattering in nonlinear, birefringent, and dispersive fibers is developed in the framework of the quantum theory of light. The work focusses on the spectral properties and quantum correlations (including entanglement) of photon-pairs generated in high-birefringence and low-birefringence fibers.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Variational approach to the scattering of charged particles by a many-electron system

We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering theory, which allows to obtain nonperturbative scattering cross-sections of moving projectiles from the knowledge of the linear and quadratic density-response functions of the target. Our theory is illustrated with a calculation of the energy loss per unit path length of slow antiprotons moving in a uniform electron gas, which shows good agreement with a fully nonlinear self-consistent Hartree calculation. Since available self-consistent calculations are restricted to low heavy-projectile velocities, we expect our theory to have novel applications to a variety of processes where nonlinear screening plays an important role.Comment: 10 pages, 2 figures; Accepted to Physical Review