Orientation-to-alignment conversion and spin squeezing

• Published in: Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2012-02, Vol.85 (2), Article 022125
• Main Authors: Rochester, S. M., Ledbetter, M. P., Zigdon, T., Wilson-Gordon, A. D., Budker, D.
• Format: Article
• Language: English
• Subjects: Compressing; Conversion; Electric fields; Evolution; Projection; Quantization; Quantum nondemolition; Uncertainty
• ISSN: 1050-2947; 1094-1622
• DOI: 10.1103/PhysRevA.85.022125

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.