Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we more closely examine the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized. Performing full diagonalizations of an XXZ spin model with random longitudinal fields, we identify two factors contributing to the spreading rate: the localization length (ξ), which depends on the disorder strength, and the final value of entanglement per spin (s∞), which primarily depends on the initial state. We find that the entanglement entropy grows with time as ∼ ξ × s∞ log t, providing support for the phenomenology of many-body localized systems recently proposed by Huse and Oganesyan [arXiv:1305.4915v1].

The quantum O(N ) model in the infinite N limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of N in varying spatial dimensions (d > 1). Here we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late time state could be inferred from the finite temperature phase diagram. In the infinite N limit, we show that not only does the model not lead to equilibration on account of an infinite number of conserved quantities, it also does not relax to a generalized Gibbs ensemble (GGE) consistent with these conserved quantities. Instead, an infinite number of new conservation laws emerge at late times and the system relaxes to an emergent GGE consistent with these. Nevertheless, we still find that the late time states following quenches bear strong signatures of the equilibrium phase diagram. Notably, we find that the model exhibits coarsening to a non-equilibrium critical state only in dimensions d > 2, that is, if the equilibrium phase diagram contains an ordered phase at non-zero temperatures.

A common goal of quantum control is to maximize a physical observable through the application of a tailored field. The observable value as a function of the field constitutes a quantum control landscape. Previous works have shown, under specified conditions, that the quantum control landscape provide a basis for understanding the generally observed ease of optimizing a state-to-state transition probability.

We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state, and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubitbath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.

Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor XX-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapserevival behavior in the intermediate-time regime. Under an antiferromagnetic bath initial condition, the two methods give excellently consistent central spin decoherence dynamics for finite-size baths of N ≤ 14 bath spins. The decoherence factor is found to drop off abruptly on a short time scale and approach a finite plateau value which depends on the intrabath coupling strength non-monotonically. In the ultrastrong intrabath coupling regime, the plateau values show an oscillatory behavior depending on whether N/2 is even or odd. The observed results are interpreted qualitatively within the framework of the EOM and perturbation analysis. The effects of anisotropic spin-bath coupling and inhomogeneous intrabath bath couplings are briefly discussed. Possible experimental realization of the model in a modified quantum corral setup is suggested.