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Physica A Statistical Mechanics and its Applications

Genesis, selected applications, and future prospects of the mode coupling theory

Kyozi Kawasaki

Published Jun 1, 2000• 8 citations
Publisher
DOI
10.1016/s0378-4371(00)00027-3

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Mode-Coupling Theory for Dynamic Critical Phenomena

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Utilizing the general theory of open quantum systems to investigate the exact dynamical evolution of simple bilinear systems, we discover a mechanism of the dynamical genesis of quantum entanglement. We focus in detail on the exact quantum evolution dynamics of two photonic modes (or any two bosonic modes) coupled to each other through a linear interaction, as the simplest system of open quantum systems that we have investigated in the past two decades. Such a linear coupling alone fails to produce two-mode entanglement. We also start with an initially separable pure state of the two modes. By solving exactly the quantum equation of motion without relying on the probabilistic interpretation, we find that when the initial state of one mode is different from a coherent state (a minimum uncertainty wave packet with equal variance in the conjugate quadratures that corresponds to a well-defined classically "particle"), the causality in the time-evolution of each mode is internally violated. It also leads to the emergence of quantum entanglement between the two modes. The lack of causality is the nature of statistics. We discover that it is the internal violation of causality in the reduced (subsystem) dynamical evolution that results in the emergence of entanglement and statistic probability in quantum mechanics, even though the dynamical evolution of the whole system completely obeys the deterministic Schrödinger equation. This conclusion is valid for the quantum dynamics of more complicated composite systems. It may provide the fundamental mechanism of the dynamical genesis for both the entanglement and the statistical probability within the deterministic framework of quantum mechanics, which is the longest-standing problem that has not been fully understood since the birth of quantum mechanics.
Recent rapid advances in quantum nanoplasmonics offer the potential for accessing quantum phenomena at room temperature. Despite this, entangled states have not yet been realized, and remain an outstanding challenge. In this work, we demonstrate how entanglement emerges in plasmonic nanocavities, which are inherently multimode, and demonstrate the conditions necessary for entanglement to persist. We find that, in general, these conditions are broken due to coupling with multiple plasmonic modes of different parity. We address this challenge with a new nanocavity design that supports high selective coupling to a single mode, enabling the robust generation of persistent entanglement in nanoplasmonics. Our results open exciting prospects for leveraging simple plasmonic setups in ambient conditions for applications in quantum communication, sensing, and rapid quantum memories.