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Journal of Applied Physics

Experimental detection of thermal entanglement in a molecular chain

Tanmoy Chakraborty, Tamal K. Sen, Harkirat Singh, Diptaranjan Das, Swadhin K. Mandal, Chiranjib Mitra

Published Oct 10, 2013• 10 citations
Publisher

Abstract

Detection of entangled states from experimental magnetic susceptibility is reported for an organic radical. The present system exemplifies an ideal spin ½ chain with full isotropy. Experimental susceptibility data are modelled by the formulation described by Bonner and Fisher. An explicit correlation is established between the molecular structure and the spin chain interaction. Using experimental magnetic susceptibility as entanglement witness, entanglement is observed to exist up to 28 K in the present system. Evolution of entanglement with magnetic field is also studied and a surface plot is generated, which clearly exhibits the variation of entanglement with magnetic field and temperature.

DOI
10.1063/1.4824458

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Detection of entangled states from experimental magnetic susceptibility is reported for an organic radical. The present system exemplifies an ideal spin ½ chain with full isotropy. Experimental susceptibility data are modelled by the formulation described by Bonner and Fisher. An explicit correlation is established between the molecular structure and the spin chain interaction. Using experimental magnetic susceptibility as entanglement witness, entanglement is observed to exist up to 28 K in the present system. Evolution of entanglement with magnetic field is also studied and a surface plot is generated, which clearly exhibits the variation of entanglement with magnetic field and temperature.
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The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound Na2Cu5Si4O14. The presence of entanglement was investigated through two measured quantities, an entanglement witness and the entanglement of formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below 200 K. Tripartite entanglement was also observed below 240 K. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.
The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound Na2Cu5Si4O14{\mathrm{Na}}_{2}{\mathrm{Cu}}_{5}{\mathrm{Si}}_{4}{\mathrm{O}}_{14}Na2​Cu5​Si4​O14​. The presence of entanglement was investigated through two measured quantities, an entanglement witness and the entanglement of formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below $\ensuremath{\sim}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Tripartite entanglement was also observed below $\ensuremath{\sim}240\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.
We study the macroscopic entanglement properties of a low dimensional quantum spin system by investigating its magnetic properties at low temperatures and high magnetic fields. The tempera- ture and magnetic field dependence of entanglement from the susceptibility and magnetization data comparing the experimental extraction with theoretical estimates are given. Extraction of entan- glement has been made possible through the macroscopic witness operators magnetic susceptibility. The protocol followed in doing so has been outlined in some recent work. Various plots of entan- glement comparing the experimental extraction with theoretical estimates are given. Quantitative comparison between concurrence and entanglement witness is given for both the theoretical and experimental results. Theory and experiments match over a wide range of temperature and field. The spin system studied is a chain, which exhibits dimerisation and yields fascinating entanglement properties when the temperature and magnetic field is varied. These spin systems exhibit quantum phase transition (QPT) at low temperatures, when the magnetic field is swept through a critical value. We show explicitly for the first time, using tools used in quantum information processing (QIP), that quantum phase transition (QPT) can be captured experimentally using canonically conjugate observables. Macroscopically, quantum complementarity relation clearly delineates entangled states from separable states across the QPT. We have estimated the partial information sharing in this system from our magnetization and susceptibility data. The complementarity relation has been experimentally verified to hold in this system
The absolute temperature (T) and magnetic field (B) dependent magnetization(M) and study of entanglement out of the experimental data is reported for dichloro(thiazole)copper(II), a Heisenberg spin chain system. The magnetic susceptibility (χ) vs. T plot assures the behavior of infinite spin chain. The M vs. B data has been taken at different temperature as long as the antiferromagnetic(AFM) correlations persist significantly. M, B and T have been plotted in a 3D plot showing explicitly the dependence of the three parameters on one another. Since the concurrence is a measure of entanglement, the value of concurrence is extracted from the χ vs. T data and that's how the information about entanglement is extracted from the macroscopic magnetic susceptibility.
In the present work, we investigate the quantum thermal entanglement in molecular magnets composed of dimers of spin S , using an Entanglement Witness built from measurements of magnetic susceptibility. An entanglement temperature, T e , is then obtained for some values of spin S . From this, it is shown that T e is proportional to the intradimer exchange interaction J and that entanglement appears only for antiferromagnetic coupling. The results are compared to experiments carried on three isostructural materials: KNaMSi 4 O 10 (M=Mn, Fe or Cu).