Mirrors confine light, and light exerts pressure on mirrors. The combination of these effects can be exploited to cool tiny, flexible mirrors to low temperatures purely through the influence of incident light.
Looking at how a poppy oscillates back and forth in a gentle breeze tells us something about the rigidity of the flower's stem and the strength of the prevailing wind. Observing the movement of a tiny mirror attached to a stem-like post in a 'photon breeze' might be similarly illuminating. Such displacements could reveal the spooky quantum-mechanical behaviour of the mirror itself and maybe even gravity's role in quantum mechanics1 — no mean feat. The problem is that under normal, room-temperature conditions such effects are masked: the mirror contains an exceedingly large number of thermally excited atoms, so it is in a state of permanent random agitation around its average position on its stalk. And cooling by traditional cryogenic means does not go far enough to remove these 'non-coherent' thermal effects.
In this issue, three papers2,3,4 show two ways of using the pressure of incident photons to damp down thermal agitations. Gigan et al. (page 67)2 and Arcizet et al. (page 71)3 both build on an earlier method5,6 for mirror cooling, and for the first time succeed in using radiation pressure to cool miniature mirrors down from room temperature to effective temperatures of just 10–20 kelvin. And Kleckner and Bouwmeester (page 75)4 reach a record low temperature of 0.135 K by using a variant of radiation-pressure cooling that uses two lasers in a method known as cold damping7. Although spotting intriguing quantum-mechanical effects is probably still some distance away, the research marks a promising step in that direction.
To understand how these experiments work, imagine a conical plunger that is rigidly attached to a mass on a spring (Fig. 1). If such a system is in thermal equilibrium with its environment, it will normally be animated by permanent random (brownian) vibrations around its average position. These vibrations peak at a frequency corresponding to the natural frequency of oscillation of the mass and spring, and can be used to regulate the leakage of light from a cavity that is continuously filled with photons from a separate light source.
The photons exert pressure not just on the walls of the cavity, but also on the plunger, acting to force it outwards. The strength of the pressure depends on the number of photons stored in the cavity at any one time. This is in turn determined by the leakage rate, and so by the position of the plunger. At each sudden random fluctuation of the plunger's position, the cavity fills or empties to a new photon density, and so a new radiation pressure. This readjustment cannot happen instantaneously, as light travels at a finite velocity. While it takes place, a temporary 'back-action' force results that is crucial to the optical cooling, or quiescence, scheme.
Assume, in the first instance, that the tip of the plunger cone is pointing into the cavity (Fig. 1a). With this geometry, if the initial fluctuation drives the plunger outwards, more photons leak out, and the pressure inside the cavity is reduced. The result is a suction force that acts to pull the plunger back in again. Conversely, when the initial fluctuation acts to drive the plunger inwards, an excess pressure is created in the cavity, resulting in a back-action that pushes the plunger out again. The net result is that the plunger and the attached mass experience a viscous drag that dampens the system's random fluctuations, whatever their initial direction. In other words, the system cools down.
A regular damping mechanism, such as a hydraulic shock absorber or immersing the oscillating body in oil, cannot bring about cooling in this way: the damping fluid would s imply heat under the effect of the thermal fluctuations and thus reheat the mass. The beauty of the optical scheme is that, despite the high energy density of photons in the cavity, the light acts as an 'ultracold' damping fluid that does not restore heat to the body. The excess energy gained from the damping will escape irreversibly into the surrounding vacuum, taking away some of the thermal energy that drives the random vibrational motion.
Incidentally, the converse heating effect can be obtained by using a plunger with its conical tip oriented outwards instead (Fig. 1b). In this case, an initial thermal fluctuation outwards will limit the number of photons escaping, increasing the pressure in the cavity, and a fluctuation inwards will lead to a greater leakage of photons, reducing the internal pressure. Thus, whichever way it goes, the thermal fluctuation is amplified.
The experimental challenge facing the authors of these papers2,3,4 is keeping the photons in the cavity over a timescale similar to the natural oscillation time of the mass–spring system. One can then ensure that the photons impinge on the mirror at just the right time in the system's cycle to achieve a maximum damping (or amplification) effect — rather as a hand on a child's swing at the right time in the cycle increases or decreases its amplitude of oscillation.
With tiny mirrors, this kind of control is far from trivial. Gigan et al.2and Arcizet et al.3 achieve it by constructing a mirror that forms one end of a very high-quality optical cavity and functions as plunger, mass and spring all in one. Kleckner and Bouwmeester4, by contrast, use the cavity only for 'reading out' the position of the fluctuating flexible mirror through precise measurements of the transmitted and reflected light-intensity profiles. The position parameter is then fed with a delay into an electronic feedback loop that controls the intensity of a second laser beam separate from the source of the cavity photons. This beam impinges directly on the mirror7. Such a configuration mimics the function of the plunger, but the precise timing of the second beam that thus becomes possible provides a tremendous amplification to the damping, and hence a record optical quiescence effect.
In all these experiments2,3,4, the degree of cooling achieved so far is limited by the heating that results from vibrations of the mirror's flexible attachments, and most probably from residual optical absorption by the mirror. To observe the promised quantum-mechanical effects, cooling to just a few millikelvin is needed. That could require the use of microfabrication techniques to produce mechanical oscillators of lower mass that are more easily damped, and cavities of increased optical quality.
Among the prizes for such endeavours could be the chance to study quantum superpositions of a photon and a macroscopic mechanical oscillator. That in turn might find practical use in ultra-precise methods for displacement sensing and for measuring the mass of single atoms and molecules. The road to that destination is a long one; but it is at least now well signposted.
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Frontiers of Physics in China (2008)