Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

Abstract

We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σ z σ z interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.Quantum coherence is one of the central concepts in quantum physics, and hence its detection and quantification is a fundamental task. Traditionally, the distinction between quantum and classical coherence is made using phase space distributions 1,2 and higher order correlation functions 3 . While this gives some insight into the nature of coherence, these techniques do not quantify coherence in a rigorous sense. Recently a scheme for measuring coherence was developed by Baumgratz and co-workers in ref. 4 based on the framework of quantum information theory. Fundamental quantities such as incoherent states, maximally coherent states and incoherent operations which are needed for the development of the procedure were introduced and analyzed. Rapid developments have been made in understanding the theory of quantum coherence through numerous works 5-16 and in using it as a resource in quantum information theory [17][18][19][20][21][22][23] . Investigations on the role of quantum coherence in thermodynamic processes [24][25][26] , assisted subspace discrimination 27 , quantum state merging 28 and in the generation of gaussian entanglement 29 have been carried out. Currently there is a lot of interest in applying the procedure of quantifying coherence and relating them to experimental quantities in feasible systems like Bose-Einstein condensates 30,31 , cavity optomechanical system 32,33 and spin systems [34][35][36][37][38][39] .In ref. 4 the set of properties a functional should satisfy in order to be considered as a coherence measure were proposed. Based on these developments several functions were introduced to serve as measures of coherence 4,40-47 . All these measures of coherence can be broadly classified into either the entropic or the geometric class of measures. This depends on whether the measure is based on the entropy functional or has a metric nature which can give rise to a geometric structure. A mathematical functional is deemed to be a metric if it obeys the axioms of distance and satisfies the triangle inequality. In ref. 47 we introduced a new...

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Quantum Coherence of Atoms with Dipole–Dipole Interaction and Collective Damping in the Presence of an Optical Field

“…Coherence, along with many other quantum properties, is often studied without considering the influence of the environment on the quantum systems. Recently, many works have been focused on the dynamics of the quantum coherence under the effect of the external environment [36][37][38][39][40][41][42][43][44][45]. Based the above considerations, the purpose of this paper is to investigate the effect of atom distance and reservoir temperature on the evolution of quantum coherence and total correlation considering DDI and CDE.…”