Universal Coarsening Dynamics of a Quenched Ferromagnetic Spin-1 Condensate

Abstract

We demonstrate that a quasi-two-dimensional spin-1 condensate quenched to a ferromagnetic phase undergoes universal coarsening in its late time dynamics. The quench can be implemented by a sudden change in the applied magnetic field and, depending on the final value, the ferromagnetic phase has easy-axis (Ising) or easy-plane (XY) symmetry, with different dynamical critical exponents. Our results for the easy-plane phase reveal a fractal domain structure and the crucial role of polar-core spin vortices in the coarsening dynamics.Ultra-cold atomic systems are well isolated from the environment and present a pristine system for exploring nondissipative manybody dynamics. An emerging area of exploration with these systems involves the dynamics induced by a quench across a phase transition to a symmetry-broken phase. Following the quench domains form, with each of these domains having made an independent choice for the symmetrybreaking order parameter. An aspect that has seen experimental investigation [1][2][3][4] involves quantifying the production of topological defects that emerge between domains immediately after the quench [5,6]. Another aspect involves how these domains coarsen over time as the different brokensymmetry phases compete to select the equilibrium state. Often at late times, when the domains are large compared to microscopic length scales, the coarsening dynamics is universal: correlation functions of the order parameter collapse to a universal scaling function when the spatial coordinates are scaled by a characteristic length L(t), where t is the time after the quench [7]. The time dependence of this length scale L(t) ∼ t 1/z yields the dynamical critical exponent z. Most work in the classical theories of phase ordering kinetics has focussed on dissipative models relevant to temperature quenches. The late-time dynamics for systems undergoing conservative Hamiltonian evolution has developed as a new area of interest, particularly due to developments with ultracold atomic gases [8][9][10][11][12][13].Spinor Bose-Einstein condensates exhibit both superfluid and magnetic order [14,15] and present a rich phase diagram [16][17][18] for considering transitions between phases with different symmetry properties. The simplest non-trivial case is a spin-1 condensate, which has been realised using 87 Rb and 23 Na atoms with ferromagnetic and anti-ferromagnetic interactions, respectively. In general, an external magnetic field breaks the full spin symmetry of the Hamiltonian, reducing it to axial symmetry transverse to the field. The external field also leads to a quadratic Zeeman shift of the spin states that competes with the spin-dependent interaction to determine the equilibrium phase [16]. This system is ideally suited to studying phase transition dynamics because the Zeeman energy can be dynamically varied in experiments, allowing quenches between phases [19,20] (also see [21]), and because the subsequent magnetisation dynamics can be revealed with in situ imaging [22]. While the short-time dynamics fol...

Phase ordering kinetics of a nonequilibrium exciton-polariton condensate

“…2(a). The dynamical exponent attains the value z ≈ 1, in agreement with previous studies of conservative superfluids [6,12]. two-dimensional systems with a vector order parameter,…”

“…In Fig. 3(a) We note that in contrast to the case of scalar fields, where the correlation function often exhibits an oscillatory tail, in the present case there are no oscillations, which is generally the case if sharp domains walls are absent [12,45,46]. We obtain a perfect collapse for the scaled correlation function f (d/L(t)), which confirms that the scaling hypothesis is valid in this case; see Fig.…”

“…In the second case, the dynamical scaling of L(t) is found to be the same as determined previously for conservative superfluids [6,12], with z ≈ 1. This shows that polariton systems can display various types of universal dynamics, which can be achieved by modifying the material parameters of the sample.…”

Domain Size Distribution in Segregating Binary Superfluids

“…Our discussion demonstrated here will be essentially applicable similarly to the phase separation dynamics in the spinor condensates, discussed in Refs. 6,7 .…”

Domain percolation in a quenched ferromagnetic spinor condensate

“…see [13][14][15][16][17][18][19]), and on the universal growth laws describing how the domains anneal long after the system has passed through the phase transition (e.g. see [20][21][22][23][24]).…”