Independent Control of Scattering Lengths in Multicomponent Quantum Gases

Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_\perp$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_\perp/a\approx 1.46$, and a dimer state for arbitrary $a_\perp/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_\perp/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_\perp/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. Th…

Recombination Amplitude Calculations of Noble Gases, in Length and Acceleration Forms, beyond Strong Field Approximation

Transition of an electron from a free to a bound state is critical in determining the qualitative shape of the spectrum in high-order harmonic generation (HHG), and in tomographic imaging of orbitals. We calculate and compare the recombination amplitude, from a continuum state described by a plane wave and an outgoing scattering eigenstate, to the bound state for the noble gases that are commonly used in HHG. These calculations are based on the single active electron model and the Hartree-Fock-Slater method, using both the length form and the acceleration form of the dipole matrix element. We …

Renormalized contact interaction in degenerate unitary Bose gases

We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this renormalized interaction to a degenerate unitary Bose gas to study its stationary properties and elementary excitations using the mean-field theory and the hyperspherical method. Since the scattering length is no longer a relevant length scale at unitarity, universal properties are obtained that depend only on the average particle density. Our treatment shows t…

Collision cross sections for the thermalization of cold gases

The collision cross section that controls thermalization of gas mixtures is the transport cross section $σ_η^{(1)}$ and not the elastic cross section $σ_{\rm el}$. The two are the same for pure s-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above 100 $μ$K for LiYb and 3 $μ$K for RbYb and RbCs. For simple systems both $σ_η^{(1)}$ and $σ_{\rm el}$ follow universal energy dependence that depends only on the s-wave scattering length when expressed in red…

Dilute resonating gases and the third virial coefficient

We study dilute gases with short range interactions and large two-body scattering lengths. At temperatures between the condensation temperature and the scale set by therange of the potential there is a high degree of universality. The first two terms in the expansion of thermodynamic functions in powers of the fugacity $z$, which measures the diluteness of the system, are determined by the scattering length only. The term proportional to $z^3$ depends only on one new parameter describing the three-body physics. We compute the third term of the expansion and show that, for many values of this n…

Efficient generation of high-order harmonics in gases

High-order harmonic generation (HHG) in gases leads to short-pulse extreme ultraviolet (XUV) radiation useful in a number of applications, for example, attosecond science and nanoscale imaging. However, this process depends on many parameters and there is still no consensus on how to choose the target geometry to optimize the source efficiency. Here, we review the physics of HHG with emphasis on the macroscopic aspects of the nonlinear interaction. We analyze the influence of medium length, pressure, position of the medium and intensity of the driving laser on the HHG conversion efficiency (CE…

Anisotropic pseudo-potential for polarized dilute quantum gases

Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of dilute quantum gases, such as molecules polarized by electric field or metastable $^3P_2$ atoms polarized by magnetic field. The pseudopotential is expressed in terms of reactance (K--) matrix and derivatives of Dirac delta-function. In most applications it may be represented as a sum of traditional spherically-symmetric contact term and anisotropic part. Th…

Rydberg optical Feshbach resonances in cold gases

We propose a novel scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering-state to an excited Rydberg-molecular state using laser light. For the s-wave scattering of two colliding ${^{87}}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimised. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homo-nuclear …

激光场下原子气体中的同时多光子-多原子过程

Simultaneous Multiphoton-Multiatom Processes in Atomic Gases under Laser Fields

本文研究激光场下原子气体中多原子同时吸收光子激发的集体QED过程，揭示其独立于原子间相互作用的特征长度尺度，并提出实验方案加以验证。