Quantum Quenches in a Spinor Condensate

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals $XY$ ordering either at a specific wave vector, or the “light-cone” correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.

Figure 1

Zero temperature phase diagram of a spin-1 condensate in terms of the linear and quadratic Zeeman energies. The shaded area corresponds to the region of $XY$ ordering. The experiment of Ref. 5 involved a quench through the special point at $p=0$ (red dot) from the paramagnetic region.