Quantum entanglement in nitrosyl iron complexes
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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS
Quantum Entanglement in Nitrosyl Iron Complexes S. M. Aldoshin, E. B. Feldman, and M. A. Yurishchev Institute for Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia e-mail: [email protected] Received April 28, 2008
Abstract—Recent magnetic susceptibility measurements for polycrystalline samples of binuclear nitrosyl iron complexes, [Fe2(C3H3N2S)2(NO)4] (I) and [Fe2(SC3H5N2)2(NO)4] (II), suggest that quantum-mechanical entanglement of the spin degrees of freedom exists in these compounds. Entanglement E exists below the temperature TE that we have estimated for complexes I and II to be 80–90 and 110–120 K, respectively. Using an expression of entanglement in terms of magnetic susceptibility for a Heisenberg dimer, we find the temperature dependence of the entanglement for complex II. Having arisen at the temperature TE, the entanglement increases monotonically with decreasing temperature and reaches 90–95% in this complex at T = 25 K, when the side effects are still small. PACS numbers: 03.67.Mn, 75.10.Jm, 75.50.Xx DOI: 10.1134/S1063776108110101
1. INTRODUCTION Entanglement is one of the most intriguing quantum-mechanical phenomena. A system of two spins in a state with the wave function |ψ〉 = ( |↑↓〉 + |↓↑〉 )/ 2 can serve as an example where this phenomenon manifests itself. This function, which describes a coherent superposition of qubits, cannot be represented as a product of the wave functions of the system’s individual constituents (the state is not separable). On the other hand, because of this property, the property of entanglement, measuring the state of one particle allows the state of the second particle to be instantly reduced no matter how far or close it is from the first one. At present, entanglement and related possibilities of quantum calculations, cryptography, teleportation, etc. are investigated not only theoretically but also experimentally. Moreover, there are real prerequisites for using these unique possibilities of quantum mechanics in practice already now. The literature on this subject matter is very extensive and diverse; to be specific, we will point out, for example, the reviews and books [1–5] as well as the sites www.qubit.org and xxx.arxiv.ru. Important relationships that allow predictions about the existence of entanglement in systems to be made using such experimentally measurable characteristics as the correlation functions, internal energy, and magnetic susceptibility have been established in recent years [6–9] (see also the review [10] and the dissertation [11]).
These theoretical results have opened a possibility of determining the temperature TE at which entanglement arises in actual materials. Brukner et al. [12] were the first to determine this temperature. They showed that TE ≈ 5 K in paramagnetic Cu(NO3)2 · 2.5H2O and Cu(NO3)2 · 2.5D2O crystals. In another quite recent paper, Souza et al. [13] presented evidence suggesting that quantum entanglement arises in Na2Cu5Si4O14
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