Abstract
We consider a quantum nonlinear Kerr-like oscillator externally pumped by a series of ultrashort coherent pulses to analyze the quantum time-correlations appearing while the system evolves. For that purpose, we examine the violation of the Leggett–Garg inequality. We show how the character of such correlations changes when the system’s dynamics correspond to the regular and chaotic regions of its classical counterpart.
Highlights
Quantum correlations, such as quantum entanglement [1,2,3,4,5], Einstein–Podolsky– Rosen steering [6,7,8,9,10], and Bell’s nonlocality [11,12,13,14] are one of the most intriguing phenomena of quantum physics.The analogs of the Bell’s inequalities in the temporal domain are so-called Leggett– Garg inequalities (LGI)
We propose the use of inequalities based on temporal correlations between the states of a system which is exposed to several projective measurements for distinguishing between the regular and chaotic evolution of a given quantum system
We focus on the temporal correlations between the outcomes of the measurements made on that quantum system
Summary
Quantum correlations, such as quantum entanglement [1,2,3,4,5], Einstein–Podolsky– Rosen steering [6,7,8,9,10], and Bell’s nonlocality [11,12,13,14] are one of the most intriguing phenomena of quantum physics. Inequalities, proposed for the first time by Leggett and Garg in 1985 [15], are based on the assumptions of macrorealism and noninvasive measurements and are used for witnessing non-classicality appearing in a macroscopic system. The existence of strong nonclassical time correlations of this type has led to the proposal of the concept of quantum entanglement in the time-domain [5], and the application of such type of correlations in the research related to quantum information theory and quantum computing [17] Up to this time, various successful experiments have proven the existence of a violation of LGI, proving the appearance of nonclassical correlations in the time domain in real systems.
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