It was recently shown that entanglement in quantum systems being in a nonequilibrium state can appear at much higher temperatures than in an equilibrium state. However, any system is subject to the natural relaxation process establishing equilibrium. The work deals with the numerical study of entanglement dynamics in a dipolar coupled spin-1/2 system under the transition from a nonequilibrium state to an equilibrium state. The spin system is characterized by a two-temperature density matrix, and the process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator is used to describe the evolution of the system. The process of establishing an equilibrium state in the homonuclear spin systems at low temperature was first considered. It was shown that the time dependencies of the inverse temperatures of the spin subsystems are given by a solution of nonlinear equations in contrast to the linear equations in the well-known high-temperature approximation. We have first studied the entanglement dynamics during the equilibrium state establishment and have found that the concurrence changes nonmonotonically with time and temperatures while equilibrium is being established. Entanglement fades long before equilibrium is established in the system. It was shown that the entanglement dynamics depends strongly on the ratio of the Zeeman energy to the dipolar energy. At a high ratio, the concurrence in the system decreases quickly for a time of about 100 $\ensuremath{\mu}\text{s}$ whereas, at a low ratio, establishment of equilibrium and fading entanglement takes a prolonged time up to 1 $\text{ms}$ .It was recently shown that entanglement in quantum systems being in a nonequilibrium state can appear at much higher temperatures than in an equilibrium state. However, any system is subject to the natural relaxation process establishing equilibrium. The work deals with the numerical study of entanglement dynamics in a dipolar coupled spin-1/2 system under the transition from a nonequilibrium state to an equilibrium state. The spin system is characterized by a two-temperature density matrix, and the process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator is used to describe the evolution of the system. The process of establishing an equilibrium state in the homonuclear spin systems at low temperature was first considered. It was shown that the time dependencies of the inverse temperatures of the spin subsystems are given by a solution of nonlinear equations in contrast to the linear equations in the well-known high-temperature approximation. We have first studied the entanglement dynamics during the equilibrium state establishment and have found that the concurrence changes nonmonotonically with time and temperatures while equilibrium is being established. Entanglement fades long before equilibrium is established in the system. It was shown that the entanglement dynamics depends strongly on the ratio of the Zeeman energy to the dipolar energy. At a high ratio, the concurrence in the system decreases quickly for a time of about 100 $\ensuremath{\mu}\text{s}$ whereas, at a low ratio, establishment of equilibrium and fading entanglement takes a prolonged time up to 1 $\text{ms}$.

arXiv:1302.5231Physical Review ASep 26, 20126 citations

Entanglement in dipolar coupling spin system in equilibrium state

G. B. Furman, V. Meerovich, Vladimir Sokolovsky

Quantum Information ProcessingOct 29, 201133 citations

Electrodynamic Properties of a Gas of Spin-½ Particles in a Uniform Magnetic Field

V. Arunasalam

A rather complete discussion of the electrodynamic behavior of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is presented. The method presented here is based on the general principles of elementary nonrelativistic quantum theory and takes account of the Doppler-broadening effects arising from the random thermal motion of the particles and the Compton recoil effects arising from the emission (spontaneous plus the induced or the stimulated emission) and absorption of photons by the spin-\textonehalf{} particles. In the first half of the paper a method is presented for calculating the spin permeability tensor which determines the propagation of transverse electromagnetic radiation through a gas of spin-\textonehalf{} particles in a uniform external magnetic field. It is shown that the spin permeability tensor thus obtained yields the familiar results of solid-state physics, such as the nuclear and electronic-spin radiofrequency susceptibility and the spin paramagnetism. In the second half of this paper the subject of spin-radiative equilibrium of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is discussed in some detail. Simple closed-form expressions for the steady-state photon number density and the spin-radiative relaxation time of the system under study are thus derived. It is shown that the steady-state photon number density is the familiar distribution function corresponding to Bose---Einstein statistics for "complete thermodynamic equilibrium." The conditions under which the system of spin-\textonehalf{} particles in a uniform magnetic field can become unstable for transverse electromagnetic radiations are also discussed.A rather complete discussion of the electrodynamic behavior of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is presented. The method presented here is based on the general principles of elementary nonrelativistic quantum theory and takes account of the Doppler-broadening effects arising from the random thermal motion of the particles and the Compton recoil effects arising from the emission (spontaneous plus the induced or the stimulated emission) and absorption of photons by the spin-\textonehalf{} particles. In the first half of the paper a method is presented for calculating the spin permeability tensor which determines the propagation of transverse electromagnetic radiation through a gas of spin-\textonehalf{} particles in a uniform external magnetic field. It is shown that the spin permeability tensor thus obtained yields the familiar results of solid-state physics, such as the nuclear and electronic-spin radiofrequency susceptibility and the spin paramagnetism. In the second half of this paper the subject of spin-radiative equilibrium of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is discussed in some detail. Simple closed-form expressions for the steady-state photon number density and the spin-radiative relaxation time of the system under study are thus derived. It is shown that the steady-state photon number density is the familiar distribution function corresponding to Bose---Einstein statistics for "complete thermodynamic equilibrium." The conditions under which the system of spin-\textonehalf{} particles in a uniform magnetic field can become unstable for transverse electromagnetic radiations are also discussed.

Physical ReviewJun 10, 19674 citations

The resonance shifts of aligned atoms in intense oscillating radiofrequency fields

R I Jackson, S. Swain

For a spin-1 atomic system subjected to an oscillating radiofrequency field applied at right angles to a DC magnetic field, the Block-Siegert shift has been calculated to sixth order in V, the amplitude of the oscillating field, and the three-quantum resonance has been calculated to eight order. The results are obtained for the three different polarisations- pi , sigma and t (unpolarised)-and expressions for the maxima are also obtained. For simplicity the atomic levels were assumed to have zero natural lifetime. It is shown that the level-crossing criterion may be used to calculate the positions of the p-quantum resonance minimum to the order of 2(p-1) in the oscillating field amplitude. Expressions are given for this quantity to order V 6 , and the separation of the maxima is calculated to order V p . The author's analytic results are compared with the numerical and experimental work of Jacobson (1980) and reasonable agreement is found.For a spin-1 atomic system subjected to an oscillating radiofrequency field applied at right angles to a DC magnetic field, the Block-Siegert shift has been calculated to sixth order in V, the amplitude of the oscillating field, and the three-quantum resonance has been calculated to eight order. The results are obtained for the three different polarisations- pi , sigma and t (unpolarised)-and expressions for the maxima are also obtained. For simplicity the atomic levels were assumed to have zero natural lifetime. It is shown that the level-crossing criterion may be used to calculate the positions of the p-quantum resonance minimum to the order of 2(p-1) in the oscillating field amplitude. Expressions are given for this quantity to order V 6 , and the separation of the maxima is calculated to order V p . The author's analytic results are compared with the numerical and experimental work of Jacobson (1980) and reasonable agreement is found.

Journal of Physics B Atomic and Molecular PhysicsFeb 28, 19823 citations

Entanglement in quantum spin systems

Jeffrey Scott Pratt

Jan 1, 20050 citations

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