Quantum rotor theory of spinor condensates in tight traps

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 [1] 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 Fz, 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.

Fluctuation-induced and symmetry-prohibited metastabilities in spinor Bose-Einstein condensates

“…whereâ † m is the creation operator of a particle with zero momentum and magnetic quantum number m F = m. Since these states are not the exact eigenstates of the many-body Hamiltonian (2), they will undergo quantum diffusions in spin space [44][45][46][47] and induce MQT. We now estimate the time scale of MQT by restricting the Hilbert space to the two states at local energy minima.…”

Spin fragmentation of Bose–Einstein condensates with antiferromagnetic interactions

“…Such super-Poissonian fluctuations ( N 2 0 ∝ N 0 2 ) deviate strongly from the value expected for a single condensate or any ensemble without correlations where N 2 0 ∝ N 0 . 3 It was pointed out by Ho and Yip [6] that such a state was probably not realized in typical experiments, due to its fragility toward any perturbation breaking spin rotational symmetry (see also [9][10][11][12][13][14]). In the thermodynamic limit N → ∞, an arbitrary small symmetrybreaking perturbation is enough to favor a regular condensed state, where almost all the atoms occupy the same (spinor) condensate wave function and N 0 N .…”

“…The dominant effect of an applied magnetic field is a second-order (or quadratic) Zeeman energy, of the form q(m 2 − 1) for a single atom in the Zeeman state with magnetic quantum number m. 4 The quadratic Zeeman (QZ) energy breaks the spin rotational symmetry, and favors a condensed state with m = 0 along the field direction. In [10][11][12][13], the evolution of the ground state with the QZ energy q was studied theoretically. Since experiments are likely to operate far from the ground state, it is important to understand quantitatively how the system behaves at finite temperatures.…”

Spin-1 microcondensate in a magnetic field

“…(15). On general grounds we expect this to be a good description when the number of particles N is large, in which case the operators A m , A † m can be treated as classical amplitudes A m , A * m of 'order √ N '.…”

“…Refs. [14,15] recently extended this description to the full spectrum in the single mode approximation. The rotor formulation is quite different from the approach pursued in this work, however.…”