Coherent spin mixing dynamics in a spin-1 atomic condensate

Abstract

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate. Bose-Einstein condensation (BEC) has been one of the most active topics in physics for over a decade, and yet interest in this field remains impressively high. Recent experiments showcase the rich versatility of control over the atomic superfluid, e.g. the BEC-BCS crossover [1,2], quantized vortices [3,4,5], condensates in optical lattices [6], and low dimensional quantum gases [7,8]. While most of these efforts involve condensates of atoms in a single Zeeman state, activities in spinor condensates [9,10] have recently received significant boost with the addition of three new spin-1 experiments [11,12,13,14].In a spinor condensate, atomic hyperfine spin degree of freedom becomes accessible with the use of a far-off resonant optical trap instead of a magnetic trap. For atoms in the F = 1 ground state manifold, the presence of Zeeman degeneracy and spin dependent atom-atom interactions [9,10,11,15,16,17,18,19] leads to interesting condensate spin dynamics. In this article, we study spin mixing inside a spin-1 condensate [17,19,20], focusing on the interaction-driven coherent oscillations within a mean field description. Unlike the pioneering studies on this subject as in Refs. [17,19], we will highlight the important role of an external magnetic field, which is present in all experiments to date.Recently, a beautiful experiment has finally observed the long predicted Josephson type coherent nonlinear oscillations with a scalar condensate in a spatial double well potential [21].Although spin mixing driven by the internal spindependent interaction (not of the nature of a Rabi oscillation as driven by an external field [22,23]), has been observed in both F = 1 and F = 2 condensates [9,12,14,24], the coherence of this process has not yet been investigated. Over-damped single oscillations in spin populations have been observed in earlier experiments [24] although their interpretation has been limited because evolution from the initial (meta-stable) states was noise-driven. The main experimental obstacles to observe more oscillations are the dissipative atomic collisions among the condensed atoms and the decoherence collisions with noncondensed atoms [12,24]. A promising future direction relies on increased atomic detection sensitivity, thus the use of smaller condensates as in the experiment of Ref. [21], with lower number densities and at lower temperatures, two favorable conditions for the single spatial mode approximation (SMA) [17,19].The initial atomic population distribution in Fig. 1 corresponds to the (equi...

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

“…, and for the m ¼ 0 case that is relevant for these experiments, the spin dynamics are determined by the mean field equivalent to equation 1 21 .…”

“…As evolution proceeds, the phase, y s , converges towards the separatrix separating the librational and rotational trajectories, and the population starts to evolve along it. The separatrix has a divergent period 21 , and so the states disperse significantly due to the different evolution rates of nearby energy contours. It is this dispersion, together with the shape of the orbit, that gives rise to the highly non-Gaussian probability distributions.…”

“…In this case, the non-trivial dynamical evolution of the system occurs only in the internal spin variables, and the mean-field dynamics of the system can be described by a non-rigid pendulum similar to the two-site Bose-Hubbard model 20,21 . The system is fully integrable in both the quantum 22 and classical 21,23 limits, and provides the opportunity to explore non-equilibrium quantum dynamics that are not captured by mean-field approaches, and can be solved exactly with Schrödinger's equation. The condensate is prepared in a state corresponding to a hyperbolic fixed point in the spin-nematic phase space.…”

Spin-1 microcondensate in a magnetic field

“…T may be expressed as an elliptic integral [18]. Note that forq > 0 the separatrix divides the phase space into two disjoint regions (see Fig.…”

Magnetic-field-induced dynamical instabilities in an antiferromagnetic spin-1 Bose-Einstein condensate

“…F γ=x,y,z are spin-1 matrices. E i denotes the Zeeman shift of an alkali atom in the state |i (the Breit-Rabi formula) [38,39],…”