In this paper, we study behavior of the correlations, both quantum and classical, under adiabatic demagnetization process in systems of nuclear spins with dipole–dipole interactions in an external magnetic field and in the temperature range including positive and negative temperatures. For a two-spin system, analytical expressions for the quantum and classical correlations are obtained. It is revealed that the field dependences of the quantum and classical correlations at positive and negative temperatures are substantially different. This difference most clearly appears in the case of zero magnetic field: at negative temperature, the measures of quantum correlations tend to the maximum values with a temperature increase. At positive temperature, these quantities tend to zero at a decrease of magnetic field. It is also found that, for the nearest-neighboring spins in the same field, the values of concurrence and discord are larger at negative temperatures than at positive ones.
Adiabatic demagnetization (AD) is an effective way to achieve low temperatures required for generating quantum correlations. The emergence and behavior of quantum and classical correlations in a one-dimensional dipolar-coupled nuclear spin-1/2 system cooled using the conventional AD technique are theoretically investigated. The case is considered where the Zeeman energy is of the order of or even less than the dipolar interaction one. It is shown that, the mutual information and classical correlations increase monotonically in the AD process and achieve their maximums at switching off the magnetic field. The quantum correlations achieve the maximum at the point where the Zeeman energy is the order of the dipolar energy and decrease to zero with decreasing the field. Discord and classical correlations are asymmetrical with respect to permutation of asymmetrically located spins.
We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of
1∕2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with nearest-neighbor dipole-dipole interactions and (2) a more realistic model with interactions between all spins. It is shown that the entangled states appear between remote particles which do not interact directly (model 1), while the interaction between all spins (model 2) not always results in entanglement between remote spins.
In this paper, we aim to provide a theoretical study of thermal entanglement of two qubits coupled to a spin chain with considering multiple-spin correlations which accompanies decay in multiple quantum nuclear magnetic resonance (MQ NMR) system. We show an explicit connection between the coherence factor and entanglement, and numerically and analytically study the dynamical process of entanglement in weak coupling cases for dipolar ordered initial states. We provide results that the entanglement evolution depends not only on the coupling constant between central two qubits and the system-environment couplings but also on temperature and the number of spins in chain.
We study the dynamics of entanglement for a one-dimensional spin system, where spins are coupled through nearest-neighbor exchange interaction and subject to different external magnetic fields. First we examine the system size effect on the entanglement with three different external magnetic fields changing with time
t: an exponential function ${e}^{[\ensuremath{-}Kt]}$ and two periodic
sin[Kt] and
cos[Kt] functions, where
K is a control parameter. We have found that the entanglement fluctuates shortly after a disturbance by an external magnetic field when the system size is small. For larger system size, the entanglement reaches a stable state for a long time before it fluctuates. However, this fluctuation of entanglement disappears when the system size goes to infinity. We also show that in a periodic external magnetic field, the nearest-neighbor entanglement displays a periodic structure with a period related to that of the magnetic field. Moreover, changing the direction of the magnetic field will destroy the concurrence in the system.
We study the dynamics of nearest-neighbor entanglement for a one-dimensional spin chain with a nearest-neighbor time-dependent Heisenberg coupling
J(t) between the spins in the presence of a time-dependent external magnetic field
h(t) at zero and finite temperatures. We consider different forms of time dependence for the coupling and magnetic field: exponential, hyperbolic, and periodic. Solving the system numerically, we examined the system-size effect on the entanglement asymptotic value. It was found that, for a small system size, the entanglement starts to fluctuate within a short period of time after applying the time-dependent coupling. The period of time increases as the system size increases and disappears completely as the size goes to infinity. Testing the effect of the transition constant for an exponential or hyperbolic coupling showed a direct impact on the asymptotic value of the entanglement; the larger the constant is, the lower the asymptotic value and the more rapid decay of entanglement are, which confirms the nonergodic character of the system. We also found that, when
J(t) is periodic, the entanglement shows a periodic behavior with the same period, which disappears upon applying periodic magnetic field with the same frequency. Solving the case $J(t)=\ensuremath{\lambda}h(t)$, for constant $\ensuremath{\lambda}$, exactly, we showed that the time evolution and asymptotic value of entanglement are dictated solely by the parameter $\ensuremath{\lambda}=J/h$ rather than the individual values of
J and
h, not only when they are time independent and at zero temperature, but also when they are time dependent but proportional at zero and finite temperatures for all degrees of anisotropy.