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Spinor Bose–Einstein Condensates

Tim Byrnes, Ebubechukwu O. Ilo-Okeke

Published Jul 23, 2021• 0 citations

Abstract

This chapter discusses spinor Bose--Einstein condensates and the various common states that are encountered with such systems. Many analogous concepts to optical systems are discussed, such as spin coherent states, spin squeezed states, uncertainty relations, and quasiprobability distributions such as the Q- and Wigner functions. A gallery of different spin states is shown for both the Q- and Wigner functions is shown, including that for highly non-classical states such as the Schrodinger cat state. Due to the different operators involved for spin systems, we describe the similarities and differences to optical squeezing, and introduce the one-axis and two-axis countertwisting spin squeezed states. The notion of entanglement in such systems, along with and ways of detecting this is are discussed. Several mappings, such as the Holstein--Primakoff transformation between spins and bosonic operators, as well asand the equivalence between condensed and uncondensed systems, is are discussed. We also introduce some key mathematical results involving important states, such as formulas to perform basis transformations between Fock states.

DOI: 10.1017/9781108975353.007

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