RESUMEN
We develop the contact theory for spin-orbit-coupled Fermi gases. By using a perturbation method, we derive analytically the universal two-body behavior at short distance, which does not depend on the short-range details of interatomic potentials. We find that two new scattering parameters need to be introduced because of spin-orbit coupling, besides the traditional s- and p-wave scattering length (volume) and effective ranges. This is a general and unique feature for spin-orbit-coupled systems. Consequently, two new adiabatic energy relations with respect to the new scattering parameters are obtained, in which a new contact is involved because of spin-orbit coupling. In addition, we derive the asymptotic behavior of the large-momentum distribution, and find that the subleading tail is corrected by the new contact. This work paves the way for exploring the profound properties of spin-orbit-coupled many-body systems, according to two-body solutions.
RESUMEN
It is well known that the magnetic Feshbach resonances of cold atoms are sensitive to the magnitude of the external magnetic field. Much less attention has been paid to the direction of such a field. In this work we calculate the scattering properties of spin polarized fermionic atoms in reduced dimensions, near a p-wave Feshbach resonance. Because of the spatial anisotropy of the p-wave interaction, the scattering has a nontrivial dependence on both the magnitude and the direction of the magnetic field. In addition, we identify an inelastic scattering process which is impossible in the isotropic-interaction model; the rate of this process depends considerably on the direction of the magnetic field. Significantly, an Einstein-Podolsky-Rosen entangled pair of identical fermions may be produced during this inelastic collision. This work opens a new method to manipulate resonant cold atomic interactions.
RESUMEN
Some novel two-body effects analogous to the well-known three-body Efimov effect are predicted. In the systems considered, particle A is constrained on a truncated or bent one-dimensional line or two-dimensional plane, or on one side of a flat mirror in three dimensions (3D). The constraining potential is fine-tuned such that particle A's ground state wave function is a constant in the region in which it is constrained. Particle B moves in 3D and interacts with particle A, resonantly. An infinite sequence of giant two-body bound states are found in each case.
RESUMEN
Alhassid conjectured that the total energy of a harmonically trapped two-component Fermi gas with a short range interaction is a linear functional of the occupation probabilities of single-particle energy eigenstates. We confirm his conjecture and derive the functional explicitly. We show that the functional applies to all smooth (namely, differentiable) potentials having a minimum, not just harmonic traps. We also calculate the occupation probabilities of high energy states.
RESUMEN
We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations.
RESUMEN
We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351
RESUMEN
We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62