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Fortschritte der Physik

Bringing quantum strangeness to the macroscopic world

Stefano Mancini, David Vitali, P. Tombesi, Vittorio Giovannetti

Published Apr 24, 2003• 0 citations
Publisher

Abstract

Abstract We show that bouncing laser beams can entangle massive oscillators like movable mirrors. Such entanglement results robust against thermal noise and detectable with common optomechanical apparatus. Thus, a quantum strangeness (entanglement) can be brought to the macroscopic, everyday, world.
DOI
10.1002/prop.200310068

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In the classic Chinese novel Journey to the West, the Monkey King has a special power that enables him to be in two or more places simultaneously. Normally, an amazing thing such as this could never happen in real life. However, in the quantum world, where the motions of objects obey the rules of quantum mechanics, this could happen. These weird quantum rules usually only apply in the microscopic world to atoms and molecules, because quantum properties are generally very fragile in the macroscopic world. However, scientists have recently been making efforts to push macroscopic and mesoscopic mechanical systems into the quantum world, i.e. they are putting conventional mechanical systems into the quantum mechanical regime. Spring oscillators, swings, and pendulum clocks are typical mechanical systems that we often see in daily lives, and they can be described by a basic physical model: the harmonic oscillator. In the quantum regime, harmonic oscillators have some quantum properties, including discrete energy spectra and zero-point motion. To observe these quantum properties, the environmental thermal noise must be suppressed so that the energy of the quantum motion dominates over the energy of the thermal motion. To this end, a generic model of a cavity optomechanical system is used, as shown in Fig. 1. The system consists of an optical cavity with a fixed mirror and a movable mirror, where the latter is attached to a spring and undergoes harmonic oscillation. A laser beam is launched into the cavity and is reflected multiple times between the two mirrors, and the cavity field thus builds up, resulting in a greatly enhanced optical field, which then exerts a considerable force on the movable mirror. The interaction between the optical field and the mechanical motion can reduce the thermal motion noise to enable the fragile quantum properties to be observed. The study of such systems has produced an emerging field called cavity optomechanics [1–3]. The pioneering work was conducted by Braginsky and co-workers in the 1960s [4]. In recent years, various experimental systems have been proposed and investigated, including Fabry–Pérot cavities [by groups including MIT/Caltech LIGO Laboratory, the Mavalvala group at MIT, the Aspelmeyer group at the University of Vienna, the Heidmann group at the University of Pierre and Marie Curie, and the Bouwmeester group at the University of California, Santa Barbara (UCSB)], whispering-gallery cavities (by groups including the Vahala group at Caltech, the Kippenberg group at École Polytechnique Fédérale de Lausanne, the Wang group at the University of Oregon, the Lipson group at Cornell University, the Carmon group at the University of Michigan, the Bowen group at the University of Queensland, and the Xiao group at Peking University), photonic crystal cavities (by groups including the Painter group at Caltech, the Wong group at Columbia University, and the Tang group at Yale University), separated mechanical oscillators inside or near a cavity (by groups including the Harris group at Yale University, the Regal group at Joint Institute for Laboratory Astrophysics (JILA), the Favero group at Paris Diderot University, and the Weig group at the University of Munich), superconducting circuits (by groups including the Schwab group at Caltech, the Lehnert group at JILA, the Cleland group at UCSB, and the Teufel group at National Institute of Science and Technology, Boulder), and cold atoms (by groups including the Kimble group at Caltech, the Stamper-Kurn group at the University of California, Berkeley, and the Treutlein group at the University of Basel). Illustration of a generic cavity optomechanical system. The left mirror is fixed and the right mirror is attached to a spring. Cavity optomechanics has been featured as the most recent milestone in photon history in Nature. The research in cavity optomechanics is important to both fundamental physics studies and the applied sciences. First, cavity optomechanics provides a unique platform for the study of fundamental quantum physics, including macroscopic quantum phenomena, decoherence, and quantum–classical transitions. The field offers the best test bed to study effects like gravity-induced decoherence, which is important to the understanding of macroscopic quantum phenomena. Second, cavity optomechanics is promising for high-precision measurements of small forces, masses, displacements, and accelerations, and is considered to be capable of surpassing the standard quantum limit. Third, cavity optomechanics provides resources for both classical and quantum information processing. For instance, optomechanical devices can serve as information storage devices and act as interfaces between light beams with different wavelengths or even microwaves. In the last few years, researchers have made considerable efforts to put mechanical systems into their quantum ground states [5]. Recent efforts have demonstrated optomechanically induced transparency [6], normal-mode splitting [7], quantum-coherent coupling [8], wavelength conversion [9], and measurements performed below the standard quantum limit [10]. Future developments will aim to integrate different quantum systems to form hybrid quantum devices, e.g. hybrid optomechanical and electromechanical systems. In this way, we can enable phonons, photons, and electrons to work together in the quantum world. Recent years have seen rapidly growing interest in the field of cavity optomechanics. As shown in Fig. 2, the publications and citations in this field have grown exponentially. The now booming development in this field will turn the dream of manipulating macroscopic mechanical systems in a quantum manner into reality. Numbers of publications (a) and citations (b) per year in the period from 2005 to 2013 with the keyword ‘cavity optomechanics’, retrieved from the Web of Science.
We consider a generic optomechanical system and investigate quantum entanglement between the outgoing light fields and the mechanical motion of the mirror. In contract to traditional approach, we do not consider quantum correlations between the intracavity optical mode and the mechanical motion of a mirror, rather the correlations between the continuum of optical fields in the outgoing light wave and the mechanical degree of freedom. This entanglement is shown to be robust to thermal decoherence and depend on the ratio of measurement strength (light power) and decoherence rate ∝ T/Qm. Furthermore, we describe a feasible way to demonstrate quantum state steering, usinging time-variable homodyne detection scheme that allows to evade back-action. An intimate connection between optomechanical steerability and quantum state tomography [Phys. Rev. A 81, 012114 (2010)] is demonstrated.