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arXiv:1109.1640

Experimental detection of quantum information sharing and their quantification in quantum spin systems

Diptaranjan Das, Tanmoy Chakraborty, Harkirat Singh, Chiranjib Mitra

Published Sep 8, 2011• 0 citations
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Abstract

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

DOI
10.48550/arxiv.1109.1640

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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 spin system chosen for this is copper nitrate (Cu(NO 3 ) 2 × 2.5H 2 O), which is a spin chain that exhibits dimerization. The temperature and magnetic field dependence of entanglement from the susceptibility and magnetization data are given, by comparing the experimental results with the theoretical estimates. Extraction of entanglement has been made possible through the macroscopic witness operator, magnetic susceptibility. An explicit comparison of the experimental extraction of entanglement with theoretical estimates is provided. It was found that theory and experiments match over a wide range of temperatures and fields. The spin system studied exhibits 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, that QPT can be captured experimentally using quantum complementary observables, which clearly delineate entangled states from separable ones across the QPT. We have also 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.
Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.
A new experimental realization of heat capacity as an entanglement witness is reported. Entanglement properties of a low–dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400 mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin half antiferromagnetic system that shows a clear signature of quantum phase transition at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.
We report macroscopic magnetic measurements carried out in order to detect and characterize field-induced quantum entanglement in low-dimensional spin systems. We analyze the pyroborate MgMnB2O5\mathrm{Mg}\mathrm{Mn}{\mathrm{B}}_{2}{\mathrm{O}}_{5}MgMnB2​O5​ and the warwickite MgTiOBO3\mathrm{Mg}\mathrm{Ti}\mathrm{O}\mathrm{B}{\mathrm{O}}_{3}MgTiOBO3​, systems with spin 5∕25∕25∕2 and 1∕21∕21∕2, respectively. By using the magnetic susceptibility as an entanglement witness we are able to quantify entanglement as a function of temperature and magnetic field. In addition, we experimentally distinguish a system exhibiting a random singlet-phase state from one with the Griffiths phase. This analysis opens the possibility of a more detailed characterization of low-dimensional materials.
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.
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.