Dynamics of Classical and Quantum Information on Spin-chains with Multiple Interactions

T. Boness

The Heisenberg spin-chain and the Quantum Kicked Rotor (QKR) are key models in condensed matter and quantum chaos respectively. The former, consisting of a line of qubits that interact with their neighbours through an exchange interaction, has recently received much attention in the context of quantum information and communication. In particular, it has been shown that a Heisenberg chain can be used as a channel for the transfer quantum states and the sharing of entanglement. The QKR, on the other hand, is a paradigm of quantum chaos. It is one of a valuable collection of quantum systems with a well de�ned classical limit that shows both regular and chaotic dynamics. This thesis investigates the dynamics of a Heisenberg chain subjected to periodic ±-kicks from a parabolic magnetic �eld. It will be shown that, when perturbed in this way, spin-chains can provide realizations of QKR systems. Using this connection, well-known features of the dynamics of kicked rotors can be used to manipulate the evolution of excitations and entanglement in the spin-chain. Conversely, results from the spin-chain analysis can inform our knowledge of the kicked rotor systems. The focus of the �rst part of this thesis is the dynamics of singly excited chains. In this case, the kicked Heisenberg chain is shown to be dynamically equivalent to a QKR. Similar correspondences can be found. Two examples, spin-chain realizations of the Double-Kicked Rotor and a double-well kicked rotor, are explored. Later sections are concerned with the dynamics of multiple excitations. These excitations interact - scattering or forming bound states of inverted spins. The kicked chain now corresponds to a system of coupled kicked rotors. It will be shown that by tuning the parameters it is possible to control the time-evolution of correlations in the chain.

Gerhard M�ller

Saikat Sur, V. Subrahmanyam

R. H. Crooks, Dmitri V. Khveshchenko

We study the dynamics of entanglement in an $XY$ spin chain subject to a staggered magnetic field and contrast it to the previously discussed uniform field case. We find that in the isotropic $(XX)$ limit a staggered field can provide almost equally favorable conditions for a high-fidelity transfer of entanglement, while even a modest amount of exchange anisotropy appears to have a strong detrimental effect. We also study interactions between different waves of entanglement and assess the possibility of simultaneous transmission of multiple bits of quantum information.

Joachim Stolze, Taras Verkholyak, Oleg Derzhko +1 more

E. I. Kuznetsova, Edward B. Fel’dman

A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains.