Quantum rotor theory of spinor condensates in tight traps

TL;DR

This paper develops an exact quantum rotor model for spinor Bose-Einstein condensates, revealing new insights into their eigenstates, regimes, and semiclassical behavior, and extends the approach to higher-spin systems.

Contribution

It introduces a precise rotor mapping for spinor condensates, analyzes physical regimes, and connects quantum and semiclassical descriptions, including higher-spin extensions.

Findings

Rotor eigenstates with lowest energy correspond to physical states within each F_z subset.

Identified three regimes: Rabi, Josephson, and Fock, with the latter indicating a fragmented condensate.

Extended the rotor model to spin-two condensates and provided theoretical details of the mapping.

Abstract

In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin F_z, the physical rotor eigenstates are always those with lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.