Recently we have proposed a method to create thin matter-wave bubbles from coherent atoms trapped in a magnetic potential. In this article we discuss in detail some properties of these states. In particular, we numerically and analytically investigate the Wigner function to demonstrate their non-classical nature. Furthermore, we study the energy and lifetime of the bubbles, which are long-lived resonances in a radio frequency-induced adiabatic potential, and illustrate how they can be transformed into excited eigenstates of the original harmonic trapping potential.
Theoretical analyses have been made of polarization-and angular momentum-dependences of backward four-wave mixing in atomic lines. These results were also applied to the problem of "vectorial" phase-conjugation in atomic vapours. Experimental demonstration of the vectorial phase-conjugation was carried out in D2 resonance line of sodium. Concerning the phase-conjugation spectroscopy in condensed matter, it has been proposed to detect X(3)1221 component to eliminate thermal grating effect.