We propose and analyze a scheme for conditional state transfer in a Heisenberg $XXZ$ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also present a possible realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions.
Understanding the dynamics of strongly interacting disordered quantum systems is one of the most challenging problems in modern science, due to features such as the breakdown of thermalization and the emergence of glassy phases of matter. We report on the observation of anomalous relaxation dynamics in an isolated XXZ quantum spin system realized by an ultracold gas of atoms initially prepared in a superposition of two-different Rydberg states. The total magnetization is found to exhibit sub-exponential relaxation analogous to classical glassy dynamics, but in the quantum case this relaxation originates from the build-up of non-classical correlations. In both experiment and semi-classical simulations, we find the evolution towards a randomized state is independent of the strength of disorder up to a critical value. This hints towards a unifying description of relaxation dynamics in disordered isolated quantum systems, analogous to the generalization of statistical mechanics to out-of-equilibrium scenarios in classical spin glasses.
We analyze a tripod atom light coupling scheme characterized by two dark states playing the role of quasi-spin states. It is demonstrated that by properly configuring the coupling laser fields, one can create a lattice with spin-dependent sub-wavelength barriers. This allows to flexibly alter the atomic motion ranging from atomic dynamics in the effective brick-wall type lattice to free motion of atoms in one dark state and a tight binding lattice with a twice smaller periodicity for atoms in the other dark state. Between the two regimes, the spectrum undergoes significant changes controlled by the laser fields. The tripod lattice can be produced using current experimental techniques.
The quantum entanglement measure is determined, for the first time, for antiferromagnetic trimer spin-1/2 Heisenberg chains. The physical quantity proposed to measure the entanglement is the distance between states by adopting the Hilbert-Schmidt norm. The method is applied to the new magnetic Cu(II) trimer system, 2b.3CuCl_2.2H_2O, and to the trinuclear Cu(II) halide salt, (3MAP)_2Cu_2Cl_8. The decoherence temperature, above which the entanglement is suppressed, is determined for the both systems. A correlation among their decoherence temperatures and their respective exchange coupling constants is established.
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of the phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.
We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies itself a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a system of trapped ions, and find that the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster than the regimes currently explored in experiments. We propose a scheme to test the bounds by measuring retarded correlation functions via the crystal fluorescence.