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Acta Physica Sinica

Tripartite entanglement of {Cu3} single molecular magnet with magnetic field in thermal equilibrium

Yidan Zheng, Bin Zhou

Published Jan 1, 2016• 1 citation
Publisher

Abstract

Quantum entanglement is one of the most fundamental properties of quantum mechanics. Because of the nonlocality, quantum entanglement is widely used in quantum computation and quantum information. Considering the fact that thermal fluctuation suppresses quantum effects, the concept of thermal entanglement is introduced to refer to the idea that the effect of temperature should be viewed as external control in the preparation of entangled state. It has been found that nanoscale single molecular magnet has a novel quantum effect at low temperature. Furthermore, single-molecular magnet is viewed as a promising candidate for realizing encoding and manipulation of quantum information. Na9[Cu3Na3(H2O)9(-AsW9O33)2]26H2O (denoted as {Cu3} for convenience) is one of the typical representatives of nanoscale single molecular magnets. In this paper, we will theoretically analyze the properties of tripartite entanglement in {Cu3} with an external magnetic field in thermal equilibrium. The tripartite negativity is used to characterize the tripartite entanglement. The tripartite negativity of {Cu3} single molecular magnet is calculated numerically by using the equivalent spin model and experimental fitting parameters. We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring, respectively, and the case with a tilted magnetic field is also discussed in this paper. It is shown that the magnitude and direction of magnetic field, and temperature have importance effects on the tripartite negativity of the system. It is found that the larger extra strong magnetic field will inhibit the generation of the quantum state of tripartite entanglement at higher temperature. In addition, compared with the magnetic field along the parallel direction of triangular spin ring and the tilted magnetic field, the magnetic field along the vertical direction of triangular spin ring obtains larger values of tripartite negativity under the same temperature and magnetic field. We also plot the variations of the critical temperature with the magnetic field along different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the range of parameters in which the tripartite entanglement of the system exists. We also find that entanglement revival behaviors may occur in the specific range of parameters. Therefore, the properties of the tripartite entanglement in the {Cu3} triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.

DOI
10.7498/aps.65.120301

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Quantum entanglement is one of the most fundamental properties of quantum mechanics. Because of the nonlocality, quantum entanglement is widely used in quantum computation and quantum information. Considering the fact that thermal fluctuation suppresses quantum effects, the concept of thermal entanglement is introduced to refer to the idea that the effect of temperature should be viewed as external control in the preparation of entangled state. It has been found that nanoscale single molecular magnet has a novel quantum effect at low temperature. Furthermore, single-molecular magnet is viewed as a promising candidate for realizing encoding and manipulation of quantum information. Na9[Cu3Na3(H2O)9(-AsW9O33)2]26H2O (denoted as {Cu3} for convenience) is one of the typical representatives of nanoscale single molecular magnets. In this paper, we will theoretically analyze the properties of tripartite entanglement in {Cu3} with an external magnetic field in thermal equilibrium. The tripartite negativity is used to characterize the tripartite entanglement. The tripartite negativity of {Cu3} single molecular magnet is calculated numerically by using the equivalent spin model and experimental fitting parameters. We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring, respectively, and the case with a tilted magnetic field is also discussed in this paper. It is shown that the magnitude and direction of magnetic field, and temperature have importance effects on the tripartite negativity of the system. It is found that the larger extra strong magnetic field will inhibit the generation of the quantum state of tripartite entanglement at higher temperature. In addition, compared with the magnetic field along the parallel direction of triangular spin ring and the tilted magnetic field, the magnetic field along the vertical direction of triangular spin ring obtains larger values of tripartite negativity under the same temperature and magnetic field. We also plot the variations of the critical temperature with the magnetic field along different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the range of parameters in which the tripartite entanglement of the system exists. We also find that entanglement revival behaviors may occur in the specific range of parameters. Therefore, the properties of the tripartite entanglement in the {Cu3} triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.
We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.
We investigate global entanglement in the ground state of single-molecular magnet Na 9 [Cu 3 Na 3 (H 2 O) 9 (α-AsW 9 O 33 ) 2 ]·26H 2 O with an external magnetic field. The concurrence, tangle, and measure function Q , which characterize the pairwise entanglement, 3-party entanglement and total entanglement, respectively, are calculated numerically at zero temperature. The results show that the magnitude and direction of the applied magnetic field play a significant role in the properties of three kinds of entanglement measures. We give a physical interpretation of the variation of the global entanglement with the magnetic field. Finally, the phase diagram of the global entanglement characterized by the critical magnetic fields is presented.
The effect of uniaxial single-ion anisotropy on quantum entanglement is rigorously quantified using negativity in a mixed spin-(1,1/2,1) Heisenberg trimer, accounting for different exchange coupling constants between identical and distinct spins. Bipartite negativities between the single-spin entity and the remaining spin dimer are analyzed alongside the global tripartite negativity (gTN) of the whole trimer under the effect of an external magnetic field and both easy-axis and easy-plane types of single-ion anisotropy. Interestingly, the single-ion anisotropy significantly influences the degree of entanglement by altering the stability regions of energetically preferred ground states and it may also introduce additional phases in the overall ground-state phase diagram. Moreover, even an arbitrarily small single-ion anisotropy is sufficient to generate global tripartite entanglement in a state that remains biseparable in the isotropic limit. Finally, the thermal stability of entanglement is discussed in detail, including the emergence of a peculiar local minimum at finite temperatures. The obtained theoretical results may offer deeper insights into bipartite and tripartite entanglement in trimetallic Ni2+-Cu2+-Ni2+molecular compounds.
We investigate the quantum evolution of spin states of a single molecular magnet in a local electric field. The decoherence of a {Cu3}\texttt{\{}\emph{Cu}_3\texttt{\}}{Cu3​} single molecular magnet weakly coupled to a thermal bosonic environment can be analyzed by the spin-boson model. Using the finite-temperature time-convolutionless quantum master equation, we obtain the analytical expression of the reduced density matrix of the system in the secular approximation. The suppressed and revived dynamical behavior of the spin states are presented by the oscillation of the chirality spin polarization on the time scale of the correlation time of the environment. The quantum decoherence can be effectively restrained with the help of the manipulation of local electric field and the environment spectral density function. Under the influence of the dissipation, the pointer states measured by the von Neumann entropy are calculated to manifest the entanglement property of the system-environment model.
We investigate key quantum characteristics of the mixed spin-(1/2,1,1/2) Heisenberg trimer under the influence of an external magnetic field. Specifically, we analyze the distributions of bipartite and tripartite entanglement quantified through the respective negativities and the l1{l}_{1}l1​-norm of coherence with the help of rigorous analytical and numerical methods. Our findings suggest that the heterotrinuclear molecular nanomagnet $[{{{\text{Cu}}^{2+}\text{L}}}_{2}{\text{Ni}}^{2+}{({\text{H}}_{2}\text{O})}_{2}]{({\text{ClO}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}3{\text{H}}_{2}\text{O}$, which represents an experimental realization of the mixed spin-(1/2,1,1/2) Heisenberg trimer, exhibits a significant bipartite entanglement between Cu2+{\text{Cu}}^{2+}Cu2+ and Ni2+{\text{Ni}}^{2+}Ni2+ magnetic ions along with robust tripartite entanglement among all three constituent Cu2+Ni2+Cu2+{\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}Cu2+Ni2+Cu2+ magnetic ions. The significant bipartite and tripartite entanglement persists even at relatively high temperatures up to 37K37\phantom{\rule{0.16em}{0ex}}\text{K}37K and magnetic fields up to 46T46\phantom{\rule{0.16em}{0ex}}\text{T}46T, whereby the coherence is maintained even at elevated temperatures. It is evidenced that the aforementioned molecular complex with the magnetic core Cu2+Ni2+Cu2+{\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}Cu2+Ni2+Cu2+ provides an intriguing quantum resource, which exhibits a star-shaped state within the singlet eigenstate at low magnetic fields and W-like state within the triplet eigenstate at moderate magnetic fields.
Low dimensional spin systems are a class of interacting many body systems which often can suitably be described by physical models with possible experimental realizations. A series of inorganic, organometallic and organic systems representing different spin ½ models have been synthesized and their thermodynamics have been investigated. In most of the cases, antiferromagnetic coupling is favored and the system can be well described by Heisenberg model where the unpaired spins interact isotropically to the nearest neighbor with an intrachain coupling constant (J). Isothermal heat capacity plots as a function of field at low temperature captures the Quantum Critical Point (QCP) experimentally, owing to change in symmetry of the ground state. This change of phase is associated with the occurrence of first order quantum phase transition in NH4CuPO4·H2O which has been established by studying field dependent behavior of magnetization and entanglement. On one hand entanglement being a nonlocal property of the spins takes its maximum value when the applied magnetic field is zero. On the other hand magnetization describing the local properties of the individual spins takes its maximum value upon reaching the saturation magnetic field at the expense of entanglement. It signifies a physical picture of quantum information sharing and gives an to opportunity capture the critical magnetic field. We have investigated this scenario in NH4CuPO4·H2O and determined the critical field which shows an excellent match with the value obtained from the field dependent specific heat data.