We investigate the entanglement properties of finite spin rings, with noncollinear Ising interaction between nearest neighbors. The orientations of the Ising axes are determined either by the spin position within the ring (model
A) or by the direction of the bond (model
B). In both cases, the considered spin Hamiltonians have a point-group symmetry instead of the translation invariance that characterizes spin rings with collinear Ising interaction. The ground state of these models exhibit remarkable entanglement properties, resembling Greenberger-Horne-Zeilinger (GHZ)-like states in the absence of an applied magnetic field (model
B). Besides, the application of a homogeneous magnetic field allows to modify qualitatively the character of the ground-state entanglement, switching from multipartite to pairwise quantum correlations (both models
A and
B).
A variety of solitary waves, such as solitons, vortex rings, solitonic vortices, and more complex entities, have recently been predicted to exist. They can move in superfluid ultracold gases along elongated traps. The theoretical description of this motion requires knowledge of the inertial soliton mass and the effective number of particles in it as functions of the soliton energy. While these functions can be calculated by a microscopic theory, it is also possible to express them directly in terms of observable quantities, such as the order parameter phase jump and the particle number depletion in the soliton. In this article, the corresponding equations are derived in a simple and physically clear way and applied to the recently predicted `magnetic soliton' in mixtures of Bose gases in various spin states.
We study the real-time evolution of solitary excitations in one-dimensional quantum spin chains using exact diagonalization and the density-matrix renormalization group. The underlying question of this work is the correspondence between classical solitons and solitons in quantum mechanics. While classical solitons as eigensolutions of nonlinear wave equations are localized and have a sharp momentum, this is not possible in the corresponding quantum case due to the linearity of the Schr\"odinger equation or, seen in a more pictorial way, because of the uncertainty relation. For the case of the XXZ model it is shown that the real-time evolution of quantum wave packets accompanied by spreading is in qualitative accordance with that predicted by classical solitons.
We study finite spin-
21 rings with nearest-neighbor Heisenberg exchange, Dzyaloshinsky--Moriya interaction, and an external magnetic field. We introduce an interpolation parameter between the fully quantum Hamiltonian and a state-dependent mean-field description. Using dissipative Gisin--Schrödinger dynamics, we analyze the resulting quantum--classical crossover through local magnetization, connected spin correlations, single-site entropy, and the saturation field of the fully polarized state.
Motivated by a compelling need for time-efficient and robust schemes for quantum-state engineering in systems of neutral atoms in optical tweezers, we consider a ring-shaped array of qubits with nearest-neighbor Ising-type (
zz) coupling and transverse (
x and
y) global control fields. This system to a large extent mimics -- outside of the Rydberg-blockade regime -- a circular array of neutral atoms interacting through van-der-Waals type interaction. We investigate the preparation of
W and Dicke states in this system starting from the default initial state
∣00…0⟩ using two different optimal-control approaches: (i) NMR-like pulse sequence, which consists of instantaneous (delta-shaped) control- and Ising-interaction pulses, and (ii) time-dependent control scheme, which entails shaped control pulses in the presence of always-on Ising interaction between adjacent qubits. By making use of the underlying dihedral symmetry of this system -- which allows one to use a symmetry-adapted computational basis with
O(2N/N) states in an
N-qubit system -- and utilizing advanced global-optimization methods, we find optimal sequences of pulses for realizing
W and Dicke states within both approaches. In addition, we demonstrate robustness of these sequences against unavoidable control errors. Finally, using typical values of parameters in realistic Rydberg-atom systems, we show that our control schemes enable the preparation of the desired multiqubit states on time scales much shorter than the relevant coherence times of those systems.