Journal of Experimental and Theoretical Physics Letters

Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian

Serge I. Doronin, Alexey N. Pyrkov, Edward B. Fel’dman

Published Jul 1, 2007• 42 citations

Abstract

Entanglement is studied in an open alternating chain of nuclear spins s = 1/2 with spin-spin couplings in an external magnetic field under the thermodynamic equilibrium conditions. A reduced density matrix has been calculated for an arbitrarily chosen spin pair. The entanglement of the spin pair has been estimated according to the Wootters criterion. The temperature at which an entangled state appears in a chosen pair has been determined. It has been shown that the numerical characteristics of the entanglement are oscillating functions of the position of the spin pair in the chain.

DOI: 10.1134/s0021364007100104

Related papers

Entanglement of spin pairs in alternating open spin-1/2 chains with the XY Hamiltonian

S. I. Doronin, A. N. Pyrkov, Edward B. Fel’dman

We investigate entanglement of spin pairs in alternating open spin chains ( s = 1/2) with spin-spin interactions (SSI) in the thermodynamic equilibrium state in an external magnetic field. The reduced density matrix of an arbitrarily chosen spin pair was calculated. The entanglement of a spin pair was evaluated with the Wootters criterion. The temperature at which the entangled state arises in the chosen pair was determined. Entanglement (concurrence) is shown to oscillate as a function of the position of a spin pair in the chain. The results demonstrate the dependence of the entanglement in arbitrarily chosen pairs of neighboring spins on the temperature, the position of the spin pair in the chain, chain length, and the ratio between the SSI constants. Qualitative explanation of these dependences is offered. The role of the terminal spins in the generation of entanglement is explained.

arXiv:quant-ph/0703010Journal of Experimental and Theoretical PhysicsNov 1, 20079 citations

Quantum entanglement in spin chains with the XY Hamiltonian at the quantum state transfer

E. I. Kuznetsova, I. D. Lazarev

In the present work the generation of entanglement between the receiver and sender is investigated in the process of the quantum state transfer in the homogeneous one-dimensional chain of spins 1/2 with the XY -Hamiltonian in the approximation of the nearest neighbour interactions. Fidelity is obtained for a quantum state transfer for various numbers of spins and temperatures and values of initial polarisation of the sender’s spin. The transmitted pure state is encoded in the state of first spin (sender) in the initial time moment. The other spins are in the thermodynamic equilibrium state. The reduced density matrix for the receiver and the sender is obtained for an investigation of entanglement in the “sender-receiver” system. The effect of temperature and polarization of the transmitted state on the generation of entanglement in the system is also investigated.

International Conference on Micro- and Nano-Electronics (ICMNE)Mar 15, 20190 citations

Entanglement Dynamics of End Spins in Heisenberg Chain with Alternating Magnetic Field

Liang Wu

The entanglement dynamics between two end spins in an anisotropic spin-1/2 Heisenberg chain is investigated when the external magnetic field and the nearest-neighbor coupling are periodically modulated.The entanglement resonance occurs at certain modulation frequency and magnitude of the external magnetic filed.The maximum entanglement appears only at some specific frequencies while it can keep the maximum for quite broad range of the magnitude.Thus,the entanglement can be controlled by the external magnetic field.

Acta Sinica Quantum OpticaJan 1, 20110 citations

Entanglement in an open Heisenberg spin chain

Subhendu Paul

We analyze the time evolution of a spin chain of three qubits with nearest-neighbour Heisenberg XX interaction, coupled to two thermal reservoirs. We use the ‘reduced density matrix approach’ to calculate the populations and correlations (concurrence) among the spins. The spin-reservoir interaction is of the energy conserving type. This allows us to analyze the evolution analytically without approximations – yielding explicit, yet complicated formulas for the spin dynamics. To analyze the latter and discuss it as a function of the various physical parameters and time (intial conditions, termperatures, coupling strenghts), we resort to numerical methods. Our main finding is that the external noise (coupling to reservoirs) causes the appearence of an asymptotic, stationary (time-periodic) regime for the dynamics of concurrence. We discuss the dependence of the relaxation time and the characteristics of the regime itself, on the various parameters.

Sep 1, 20180 citations

Entanglement of systems of dipolar coupled nuclear spins at the adiabatic demagnetization

Serge I. Doronin, Edward B. Fel’dman, M. M. Kucherov +1 more

We consider the adiabatic demagnetization in the rotating reference frame (ADRF) of a system of dipolar coupled nuclear spins s = 1/2 in an external magnetic field. The demagnetization starts with the offset of the external magnetic field (in frequency units) from the Larmor frequency being several times greater than the local dipolar field. For different subsystem sizes, we have found from numerical simulations the temperatures at which subsystems of a one-dimensional nine-spin chain and a plane nine-spin cluster become entangled. These temperatures are of the order of microkelvins and are almost independent of the subsystem size. There is a weak dependence of the temperature on the space dimension of the system.

arXiv:0812.2130Journal of Physics Condensed MatterDec 10, 20088 citations

General theory of entanglement enhancement by external fields in spin chains

Tomotaka Kuwahara

In the present thesis, we report several general properties of the enhancement of the entanglement by external fields. First, we investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which dose not depend on the temperature and that the corresponding optimized thermal entanglement decays as 1/(T log T ) at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the highand low-temperature phases. Second, we investigate the maximized entanglement of indirectly interacting two spins, that is, through other spins. We present a necessary condition for the indirect interaction to give a non-zero maximized entanglement between the focused spins. We also prove that if the focused spins are separated by two spins, there is a critical temperature above which the maximized entanglement between the focused spins vanishes. Then, we numerically calculate the maximized entanglement between the end spins of three-spin chains and four-spin chains. We discover that the maximizing local fields on the end spins have asymmetric forms. In the three-spin chains, we attribute the entanglement enhancement to the asymmetry of the local fields qualitatively and quantitatively in terms of the magnons. In XX and XY four-spin chains, we find that the critical temperature shows qualitatively different behavior depending on the conservation of the angular momentum in the z direction.

Jan 1, 20120 citations