We propose a device for the reversible and quiet conversion of microwave photons to optical sideband photons that can reach 100% quantum efficiency. The device is based on an erbium-doped crystal placed in both an optical and microwave resonator. We show that efficient conversion can be achieved so long as the product of the optical and microwave cooperativity factors can be made large. We argue that achieving this regime is feasible with current technology and we discuss a possible implementation.

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...

We examine the dynamics of a quasi-two-dimensional spin-1 condensate in which the quadratic Zeeman energy q is suddenly quenched to a value where the system has a ferromagnetic ground state. There are two distinct types of ferromagnetic phases, i.e. a range of q values where the magnetization prefers to be in the direction of the external field (easy-axis), and a range of q values where it prefers to be transverse to the field (easy-plane). We study the quench dynamics for a variety of q values and show that there is a single dynamic critical exponent to characterize the scale invariant domain growth for each ferromagnetic phase. For both quenches we give simple analytic models that capture the essential scale invariant dynamics, and correctly predict the exponents. Because the order parameter for each phase is different, the natures of the domains and the relevant topological defects in each type of coarsening is also different. To explore these differences we characterize the fractal dimension of the domain walls, and the relationship of polar-core spin vortices to the domains in the easy-plane phase. Finally, we consider how the energy liberated from the quench thermalizes in the easy-axis quench. We show that local equilibrium is established in the spin waves on moderate time scales, but continues to evolve as the domains anneal.