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Journal of Physics Communications

Generation of quantum correlations at adiabatic demagnetization

G. B. Furman, S. D. Goren, V. Meerovich, Vladimir Sokolovsky

Published Nov 13, 2017• 2 citations
Publisher

Abstract

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.

DOI
10.1088/2399-6528/aa91ff

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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.
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.
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.
The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization β I in addition to the electron polarization β S have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β S ≈ β I and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.
The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay (FID) and spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central spin model in the high-temperature approximation. The same formulas describe the quantum discord in both the FID and the spin echo although the forms of the dependences are different because of difference in the parameters entering into the formulas. Discord of the spin echo compared with the FID has a strong dependence on time at short times, and it tends to zero with decreasing of the magnetic field, whereas in the case of the FID it reaches a plateau.
We study the steady-state entanglement and correlations of an open system comprising two coupled fermions in the equilibrium or nonequilibrium environments and distill the nonequilibrium contribution to the quantum correlations. We show that in the equilibrium condition, the steady-state quantum correlations exhibit nonmonotonic behavior, while in the nonequilibrium case, the monotonicity is determined by many parameters. The entanglement vanishes abruptly upon the increase of the temperature (bias) and chemical potential bias, and it witnesses a critical chemical potential above which the concurrence always remains positive. In the fermionic reservoirs, quantum correlations reach the maximal values when one chemical potential of the reservoirs matches the system frequency. We separate the quantum correlation generation due to the averaged effect from the pure nonequilibrium effect. In contrast with previous results, when the averaged effect is separated out, the nonequilibrium generation of quantum correlation shows a distinctive monotonic behavior. The difference between the large-tunneling regime with decaying correlations and the small-tunneling with increasing correlations is discussed. Near the boundary of the two regimes, the entanglement behavior is a mixture of two extremes, and it resurrects with the increase of chemical potential bias after its previous drop to zero.
The Hamiltonian and the spin operators for a spin 3/2 are represented in the basis formed by the Kronecker productions of the [Formula: see text] Pauli matrices. This reformulation allows us to represent a spin 3/2 as a system of two coupled fictitious spins 1/2. Correlations between these fictitious spins are studied using well-developed methods. We investigate the temperature and field dependences of correlations, such as mutual information, classical correlations, entanglement, and geometric and quantum discords in the fictitious spin-1/2 system describing a nuclear spin 3/2 which is placed in magnetic and inhomogeneous electric fields. It is shown that the correlations between the fictitious spins demonstrate properties which differ from those of real two-spin systems. In contrast to real systems all the correlations between the fictitious spins do not vanish with increasing external magnetic field; at a high magnetic field the correlations tend to their limiting values. Classical correlations, quantum and geometric discords reveal a pronounced asymmetry relative to the measurements on subsystems (fictitious spins) even in a uniform magnetic field and at symmetrical EFG, [Formula: see text]. The correlations depend also on the distribution of external charges, on the parameter of symmetry [Formula: see text]. At [Formula: see text] quantum and geometric discords have finite values in a zero magnetic field. The proposed approach may be useful in analysis of properties of particles with larger angular momentum, can provide the way to discover new physical phenomenon of quantum correlations, and can be a useful tool for similar definitions of other physical quantities of complex systems.