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Optics Express

Unusual entanglement transformation properties of the quantum radiation through one-dimensional random system containing left-handed-materials

Yunxia Dong, Xiangdong Zhang

Published Oct 9, 2008• 7 citations
Publisher

Abstract

The quantum radiation through the multilayer structures containing the left-handed materials is investigated based on the Green-function approach to the quantization of the phenomenological Maxwell theory. Emphasis is placed on the effect of randomness on the generation and transmission of entangled-states. It is shown that some unusual properties appear for the present systems in comparison with those of the conventional dielectric structures. The quantum relative entropy is always enhanced with the increase of random degree due to the existence of nonlocalized mode in the present systems, while the maximal entanglement can be observed only at some certain randomness for the conventional dielectric structures. In contrast to exponential decrease in the conventional systems, the entanglement degrades slowly with the increase of disorder and thickness of the sample near the nonlocalized mode after transmission through the present systems. This will benefit the quantum communication for long distances.

DOI
10.1364/oe.16.016950

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The quantum radiation through the multilayer structures containing the left-handed materials is investigated based on the Green-function approach to the quantization of the phenomenological Maxwell theory. Emphasis is placed on the effect of randomness on the generation and transmission of entangled-states. It is shown that some unusual properties appear for the present systems in comparison with those of the conventional dielectric structures. The quantum relative entropy is always enhanced with the increase of random degree due to the existence of nonlocalized mode in the present systems, while the maximal entanglement can be observed only at some certain randomness for the conventional dielectric structures. In contrast to exponential decrease in the conventional systems, the entanglement degrades slowly with the increase of disorder and thickness of the sample near the nonlocalized mode after transmission through the present systems. This will benefit the quantum communication for long distances.
The quantum radiation through the multilayer structures containing the left-handed materials is investigated based on the Green-function approach to the quantization of the phenomenological Maxwell theory. Emphasis is placed on the effect of randomness on the generation and transmission of entangled-states. It is shown that some unusual properties appear for the present systems in comparison with those of the conventional dielectric structures. The quantum relative entropy is always enhanced with the increase of random degree due to the existence of nonlocalized mode in the present systems, while the maximal entanglement can be observed only at some certain randomness for the conventional dielectric structures. In contrast to exponential decrease in the conventional systems, the entanglement degrades slowly with the increase of disorder and thickness of the sample near the nonlocalized mode after transmission through the present systems. This will benefit the quantum communication for long distance.
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure.
Quantum communication schemes widely use dielectric four-port devices as basic elements for constructing optical quantum channels. Dielectrics with complex permittivity are typical examples of noisy quantum channels in which quantum coherence will not be preserved. Basing on quantization of phenomenological electrodynamics, we construct the transformation relating the output quantum state to the input quantum state without placing frequency restrictions. Knowledge of the full transformed quantum state enables us to compute the entanglement contained in the output state.
We propose a reinterpretation and reformulation of the single-particle Green's function in nonrelativistic quantum many-body theory with an emphasis on normalization. By downfolding a correlation function covering all of Fock space into the observable portion, we derive a nonlocal Dyson equation which depends on an unknown downfolding frequency. The downfolding frequency is determined by solving the inverse problem so that the spectral function of the single-particle propagator is a Dirac-δδδ function. Upon measurement, the system collapses stochastically onto one of these normalized solutions. This collapse has a nonlocal effect on the path the particle takes, in agreement with quantum entanglement. We postulate that the multiplicity of each quantized solution is directly related to the ensemble averaged spectrum and the entropy created by measurement of the particle. In the final part, we outline a new picture of dynamics in quantum many-body systems. As a function of the coupling strength, the multiplicity for collapse has a complicated form due to the shape of the quantization condition. This structure creates an entropic force from counting quantized solutions which is predominantly attractive but likely also has a narrow repulsive regime at weak coupling. Upon collapse, an internal spacetime forms between the two points in order to carry the information gained from the reduction of the probabilistic many-body state. The repeated creation of these spacetime bridges defines an internal spacetime with a complicated shape and history. We treat the quantum system as a finite informational resource that holds information about possible normalized outcomes, collapses the wave function to reset after encountering a conflict, and creates an internal spacetime to carry the information gained with every collapse.
A quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures. Starting from the phenomenological Maxwell equations, where the properties of the dielectric are described by a permittivity consistent with the Kramers-Kronig relations, an expansion of the field operators is performed that is based on the Green function of the classical Maxwell equations and preserves the equal-time canonical field commutation relations. In particular, in frequency intervals with approximately vanishing absorption the concept of quantization through mode expansion for dispersive dielectrics is recognized. The theory further reveals that weak absorption gives rise to space-dependent mode operators that spatially evolve according to quantum Langevin equations in the space domain. To illustrate the applicability of the theory to inhomogeneous structures, the quantization of the radiation field in a dispersive and absorptive one-interface dielectric is performed. \textcopyright{} 1996 The American Physical Society.
In this Letter we study the entanglement of a quantum radiation field interacting with a dielectric medium. In particular, we describe the quantum mixed state of a field interacting with a dielectric through plasma and Drude models and show that these generate very different entanglement behavior, as manifested in the entanglement entropy of the field. We also present a formula for a "Casimir" entanglement entropy, i.e., the distance dependence of the field entropy. Finally, we study a toy model of the interaction between two plates. In this model, the field entanglement entropy is divergent; however, as in the Casimir effect, its distance-dependent part is finite, and the field matter entanglement is reduced when the objects are far.