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Science

Nanomechanical Quantum Limits

M. P. Blencowe

Published Apr 1, 2004• 32 citations
Publisher

Abstract

Quantum effects usually manifest themselves only in the microscopic world of atoms, whereas macroscopic objects of the everyday world follow the classical laws of Newtonian mechanics. But can large objects also behave quantum mechanically? In his Perspective, Blencowe discusses work reported in the same issue by LaHaye et al. on attempts to observe the phenomenon of Heisenberg9s uncertainty principle in a relatively large vibrating beam. Although still small by everyday standards, the microfabricated beam consists of about 10atoms. The measurements indicate that the apparatus is within striking distance of direct observation of quantum fluctuations.

DOI
10.1126/science.1095768

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Quantum effects usually manifest themselves only in the microscopic world of atoms, whereas macroscopic objects of the everyday world follow the classical laws of Newtonian mechanics. But can large objects also behave quantum mechanically? In his Perspective,
Blencowe
discusses work reported in the same issue by
LaHaye
et al. on attempts to observe the phenomenon of Heisenberg9s uncertainty principle in a relatively large vibrating beam. Although still small by everyday standards, the microfabricated beam consists of about 10atoms. The measurements indicate that the apparatus is within striking distance of direct observation of quantum fluctuations.
A chip-scale optomechanical system with extremely low dissipation might enable the observation of quantum behavior in tangible objects visible to the naked eye. At the beginning of the last century Heisenberg formulated the theory of quantum mechanics. It dictates that mechanical motion—from that of electrons around nuclei to the macroscopic behavior of everyday objects—is quantized. It was only in 1986, more than 60 years after Heisenberg’s initial work, that scientists could directly observe quantum jumps of individual electrons.1 Ten years later, advances in laser techniques and optics enabled the observation of nonclassical motional states of trapped ions,2 which can be 100,000 times heavier than electrons. Yet a fun-damental question has remained: Why do larger objects behave classically, rather than following the rules that govern the small-est particles?
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in which quantum mechanics fails and classical mechanics takes over, although there has never been experimental evidence for such a failure. Even those who insisted that Newtonian mechanics would somehow emerge from the underlying quantum mechanics as the system became increasingly macroscopic were hindered by the lack of adequate experimental and theoretical tools. In the last decade, however, this quantum-to-classical transition has become accessible to experimental study and quantitative description, and the resulting insights are the subject of this article.
The motion of macroscopic objects such as soccer balls, vehicles and planets can be well described using classical mechanics. However, classical mechanics is inadequate to describe the movements or the structure of microscopic objects such as atoms, molecules or nuclei. To properly describe the properties of microscopic objects, the theory of quantum mechanics was developed. While quantum mechanics can be applied to macroscopic objects, it turns out that for objects of large dimensions the quantum mechanical laws evolve naturally into classical mechanics. In general, solving a problem in quantum mechanics is far more difficult than solving it in classical mechanics. Therefore, the laws of classical mechanics are employed when they can be applied safely.
Everyday macroscopic objects follow the laws of classical mechanics. For microscopic objects, such as atoms or nuclei, the wave character of their dynamics has to be taken into account within the framework of quantum mechanics. While wave-like behaviour can show up in various ways, one of the most striking is the tunnelling effect: some events that are classically forbidden for energetic reasons happen because the quantum particles can tunnel under a potential barrier. Similarly, events that are prohibited due to some other dynamical constraints can occur via a process known as dynamical tunnelling. Indeed, tunnelling plays a major role in a variety of physical phenomena, ranging from α-particle radioactivity to the current–voltage characteristics of transistors.
Conceptually different from the decoherence program, we present a novel theoretical approach to macroscopic realism and classical physics within quantum theory. It focuses on the limits of observability of quantum effects of macroscopic objects, i.e., on the required precision of our measurement apparatuses such that quantum phenomena can still be observed. First, we demonstrate that for unrestricted measurement accuracy, no classical description is possible for arbitrarily large systems. Then we show for a certain time evolution that under coarse-grained measurements, not only macrorealism but even classical Newtonian laws emerge out of the Schrödinger equation and the projection postulate.