Orientation-to-alignment conversion and spin squeezing

Abstract

The relationship between orientation-to-alignment conversion (a form of atomic polarization evolution induced by an electric field) and the phenomenon of spin squeezing is demonstrated. A "stretched" state of an atom or molecule with maximum angular-momentum projection along the quantization axis possesses orientation and is a quantum-mechanical minimum-uncertainty state, where the product of the equal uncertainties of the angular-momentum projections on two orthogonal directions transverse to the quantization axis is the minimum allowed by the uncertainty relation. Application of an electric field for a short time induces orientation-to-alignment conversion and produces a spin-squeezed state, in which the quantum state essentially remains a minimum-uncertainty state, but the uncertainties of the angular-momentum projections on the orthogonal directions are unequal. This property can be visualized using the angular-momentum probability surfaces, where the radius of the surface is given by the probability of measuring the maximum angular-momentum projection in that direction. Brief remarks are also given concerning collective-spin squeezing and quantum nondemolition measurements.

Efficient polarization of high-angular-momentum systems

“…A particular application of the stretched state is the generation of spin squeezing (a redistribution of uncertainties from one spin component to another) induced by a mechanism known as orientation-to-alignment-conversion (OAC) [9]. In this process, atoms in a stretched state interact with an electric field and the state evolves into one in which the spin-projection uncertainty in a certain direction is diminished at the expense of uncertainty in another direction.…”

Spin squeezing a cold molecule

“…(23) As pointed out earlier [18,65], the y quadrature is maximally squeezed for cos (2n opt + 2δ) = −1, i.e. along the axis…”

“…The theoretical analysis for spin squeezing using H KU was first provided by Kitagawa and Ueda [18], and more recently by Rochester et al [65]. Nonetheless, we restate the procedure here, in order to compare with fully numerical calculations to be presented later.…”

“…Interesting applications to the measurement of magnetic fields also seem possible [66][67][68][69][70], especially following recent discussions of magnetometry using single SiC spins with angular momentum 3/2 [71]; ground state ultracold OH also carries rotational angular momentum 3/2, and is sensitive to magnetic fields via the Zeeman shift. As well, spin squeezing is related to the alignment-to-orientation transition [65], and we expect this perspective will be of relevance to our work, given the recent interest in the stereochemical properties of the OH molecule [72]. We emphasize that compared to previous proposals for spin squeezing molecules [61], which employ spin 1/2 interacting molecules squeezed collectively, we consider a single noninteracting molecule with angular momentum 3/2.…”

“…Possibilities also exist for Dysprosium which offers states with spins from 8 upto 12.5. Theoretical calculations of single-spin squeezing have been presented as well [65]. The squeezing in this case is limited by the much smaller angular momentum available.…”