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arXiv:quant-ph/0702215 · Physical Review A

Experimental demonstration of macroscopic quantum coherence in Gaussian states

Christoph Marquardt, Ulrik L. Andersen, Gerd Leuchs, Yuishi Takeno, Mitsuyoshi Yukawa, Hidehiro Yonezawa, Akira Furusawa

Published Sep 18, 2007• 16 citations
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Abstract

We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion [E. G. Cavalcanti and M. D. Reid, Phys. Rev. Lett. 97 170405 (2006)]. The macroscopic coherence stems from interference between macroscopically distinct states in phase space, and we prove experimentally that a coherent state contains these features with a distance in phase space of $0.51\ifmmode\pm\else\textpm\fi{}0.02$ shot noise units. This is surprising because coherent states are generally considered being at the border between classical and quantum states, not yet displaying any nonclassical effect. For squeezed and entangled states the effect may be larger but depends critically on the state purity.

DOI
10.1103/physreva.76.030101

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We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion [E. G. Cavalcanti and M. D. Reid, Phys. Rev. Lett. 97 170405 (2006)]. The macroscopic coherence stems from interference between macroscopically distinct states in phase space, and we prove experimentally that a coherent state contains these features with a distance in phase space of 0.51\ifmmode±\else\textpm\fi0.020.51\ifmmode\pm\else\textpm\fi{}0.020.51\ifmmode±\else\textpm\fi0.02 shot noise units. This is surprising because coherent states are generally considered being at the border between classical and quantum states, not yet displaying any nonclassical effect. For squeezed and entangled states the effect may be larger but depends critically on the state purity.
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As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an important quantum resource in the quantum information processing. The one-mode squeezed state and the two-mode squeezed state (Einstein-Podolsky-Rosen (EPR) entangled states) as the most representative examples of nonclassical states both have quantum coherence. The squeezing property of the squeezed state is described by the variance of quadrature components, and the positive partial transposition (PPT) criterion is used to describe the entanglement of the EPR entangled states. The research of the quantum coherence of Gaussian states is also a bridge between the properties of squeezing and entanglement. It has been shown that the quantum coherence with infinite-dimensional systems can be quantified by relative entropy. One of the widely used effective methods to obtain the value of quantum coherence experimentally is the quantum tomography. The covariance matrices of the quantum states are reconstructed via balanced homodyne detection and then taken into quantum coherence expression to calculate the corresponding value. The main factors affecting quantum coherence are the classical and uncorrelated noise in the actual experimental generation processing and the decoherence effect caused by the coupling between quantum resources and the surrounding environment. And the quantum coherence evolution in the generation and transmission process of the quantum resources is essential for the practical applications. Therefore, we analyze in detail the influences of the impurity of quantum resource on squeezing, entanglement and quantum coherence. The evolutions of quantum coherence of these Gaussian states in the lossy channels are demonstrated experimentally. The quantum coherence is shown to be robust against the loss in the lossy channels, which is similar to the case of squeezing and entanglement. The quantum coherences of the squeezed states and the EPR entangled states are robust against the thermal photons in the actual experimental generation processing, although the squeezing and entanglement of Gaussian states disappear at a certain number of thermal photons. Our research results provide a reference for the practical applications of quantum coherence of the squeezed state and entangled states in the lossy environment.
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Quantum entanglement and coherence, traditionally studied in microscopic systems, have recently been observed and manipulated in macroscopic platforms. These phenomena play a critical role in understanding the boundary between classical and quantum physics and in developing quantum technologies such as superconducting qubits, optomechanical resonators, and atomic ensembles. This article reviews theoretical models, numerical simulations, and experimental techniques used to probe entanglement and coherence in large-scale systems. Five thematic outlines are presented, with one outline including two graphs illustrating (i) time evolution of entanglement in a macroscopic oscillator system, and (ii) coherence decay under environmental coupling. Applications, limitations, and future directions are discussed to provide a comprehensive perspective.