Four-Wave Mixing In BEC Systems With Multiple Spin States

TL;DR

This paper investigates four-wave mixing in multi-spin Bose-Einstein condensates, revealing how spin composition affects FWM strength and the formation of polarization gratings, with calculations for rubidium and sodium systems.

Contribution

It provides a detailed analysis of four-wave mixing involving multiple spin states in BECs, highlighting the differences in FWM efficiency and mechanisms based on spin composition.

Findings

FWM is stronger with fewer spin states involved.

Polarization gratings form in multi-spin FWM, affecting diffraction.

Calculations are provided for $^{87}$Rb and $^{23}$Na condensates.

Abstract

We calculate the four-wave mixing (FWM) in a Bose-Einstein condensate system having multiple spin wave packets that are initially overlapping in physical space, but have nonvanishing relative momentum that cause them to recede from one another. Three receding condensate atom wave packets can result in production of a fourth wave packet by the process of FWM due to atom-atom interactions. We consider cases where the four final wave packets are composed of 1, 2, 3 and 4 different internal spin components. FWM with 1- or 2-spin state wave packets is much stronger than 3- or 4-spin state FWM, wherein two of the coherent moving BEC wave packets form a polarization-grating that rotates the spin projection of the third wave into that of fourth diffracted wave (as opposed to the 1- or 2-spin state case where a regular density-grating is responsible for the diffraction). Calculations of FWM for $^{87}$Rb and $^{23}$Na condensate systems are presented.