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arXiv:1309.7767 · New Journal of Physics

Experimental quantification of entanglement through heat capacity

Harkirat Singh, Tanmoy Chakraborty, D Das, Hirale S. Jeevan, Y. Tokiwa, P. Gegenwart, Chiranjib Mitra

Published Nov 1, 2013• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/15/11/113001

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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 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
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.
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.
The thesis started with a short introduction about my research work and discussed about the systems I worked on. Later, it discussed about the experimental techniques that I have learned during the course of my work. This chapter includes the experimental approaches that I have used in sample preparation, characterization and measurements that I performed on my samples. In third chapter, I introduced about my first research work i.e. experimental quantification of entanglement in CN using magnetic susceptibility and heat capacity. In the fourth chapter, I briefly discussed about the magnetic field and temperature dependence of entanglement estimated using heat capacity. A good agreement with the theoretical predictions of our experimental results was also discussed. The fifth chapter consists of experimental study of quantum discord in CN quantified using magnetic susceptibility and heat capacity. In this chapter also I have discussed that our experimental results exhibits good correspondence with theoretical predictions and earlier reported results. In the sixth and last chapter of my thesis, I have discussed an experimental study we performed to investigate the magnetic properties of NiCr2O4 nanoparticles. Our experimental results have shown development of 2D spin-glass like phase in the nanoparticles of NiCr2O4. The parameter values we obtained by fitting the experimental data with the existing theoretical model for spin-glasses matches well with the reported values.
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.
We demonstrate that the presence of entanglement in macroscopic bodies (e.g., solids) in thermodynamical equilibrium could be revealed by measuring heat capacity. The idea is that if the system was in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimalization of the heat capacity over separable states and using its universal low-temperature behavior. Our results open up a possibility to use standard experimental techniques of solid-state physics---namely, heat-capacity measurements---to detect entanglement in macroscopic samples.