Putting the Mechanics in Quantum Mechanics

I’m back from a long blogging hiatus during which I finished up my postdoc and moved across the country, and I’m hoping to post more frequently going forward. Today’s post was a guest contribution to the Junior Physics Society journal run by year 10 (ninth grade) students at St. Olave’s Grammar School in the UK. I chose to write about the basic principles of experimental quantum optomechanics, a field near and dear to my heart. You can check out the students’ essays on topics ranging from extraterrestrial civilizations to magnetic levitation here. For this blog post I’ve made some light edits and added footnotes.¹Who doesn’t love footnotes? Hope you enjoy!

Try to imagine a particle whose position is not just unknown but fundamentally undetermined: neither here nor there but instead suspended between two distinct points in space. This phenomenon, called superposition, is just one of the many strange behaviors allowed by the laws of quantum mechanics, which underlie nearly all of modern physics, from the dynamics of quarks and gluons to the organization of the periodic table to the origins of magnetism and superconductivity.²Superposition itself is not a uniquely quantum phenomenon nor especially mysterious. The math that describes quantum superposition is the same as the math describing how several musical notes played simultaneously combine to make a chord. But quantum mechanics allows the superposition of different kinds of physical quantities, the position of a particle being one of the most striking examples. See the middle section of this post for further discussion of how to think about superposition.

But ironically mechanics — the study of motion and forces acting on macroscopic bodies — is the domain in which quantum phenomena remain most elusive. This is not because the laws of quantum mechanics do not apply to large objects, but rather because quantum effects like superposition are extremely fragile. The systems that exhibit the most pristine quantum behavior — individual atoms levitated in vacuum chambers, electric currents in ultracold superconducting circuits, pulses of laser light bouncing back and forth between highly reflective mirrors — are exceptionally well isolated from environmental disturbances.

Physicists in the field of quantum optomechanics aim to bridge the gap between the quantum world and the world of our everyday experience by using lasers to measure and control mechanical resonators — physical systems that vibrate or swing back and forth at a very specific frequency.³I’ve written an explainer for Quanta magazine about the physics of resonance. In this short post I’ll explain the basics of how quantum optomechanics experiments work and show you how the tools of optomechanics could one day be used to put a macroscopic object into a quantum superposition.

An introduction to mechanical resonators

Let’s begin by exploring the behavior of some familiar mechanical resonators. Imagine you happen across a playground swing and give it a single sharp push: it will swing back and forth several times before coming to rest. Much the same thing happens when a diver vaults off the end of a long and springy diving board: the end of the board vibrates rapidly at a particular frequency for a few seconds and then settles down.

In both of these examples the behavior of the resonator can be described by two numbers: the frequency at which it vibrates or oscillates — also called its resonant frequency — and the time it takes for the motion to die down after external forces stop acting on the resonator. We can quantify this time using a number called the quality factor, which is usually represented by the symbol \(Q\). A resonator with quality factor \(Q\) will keep moving for about \(Q\) oscillation cycles before it comes to rest.

The motion inevitably decays because the resonator’s energy leaks into the surrounding environment, through friction in the hinges of the swing or air resistance, for example. But the exchange of energy between the resonator and its environment is a two-way street: precisely the same channels through which energy can escape the resonator also enable random forces from the environment to push the resonator around. Increasing the quality factor chokes off these channels, extending the lifespan of oscillations and simultaneously shielding the resonator from environmental disturbances. Quality factors \(Q < 10\) would be typical for the two examples above. The resonators used in quantum optomechanics experiments, by contrast, can have quality factors larger than 100,000, sometimes even as large as a billion!

From motion to light and back again

Now that we understand the basic physics of mechanical resonators, let’s consider a simple example of an optomechanics experiment. Imagine we suspend a heavy mirror from a very thin wire to make a pendulum that reflects incident light. We will put this reflective pendulum in a vacuum chamber so it isn’t buffeted about by passing air molecules. Even so, the mirror will not hang perfectly still, because the atoms that make up all solid materials are constantly vibrating with energy related to the ambient temperature. The vibrations of the pendulum’s support structure will be transmitted through the wire to the mirror, leading to random fluctuations in its position.⁴A macroscopic object like our mirror has lots of different ways it can vibrate — basically all the different combinations of motions of its constituent atoms. Here we’re only concerned with one specific kind of mirror motion: the center-of-mass motion in which the all the atoms in mirror move back and forth together.

We can measure this thermal motion by shining a laser at the mirror through a window in the vacuum chamber. It’s helpful to think of this laser beam as a steady stream of photons — discrete particles of light. We will simply count the photons that are reflected towards us: as the mirror swings closer to us, the photons traverse a shorter path and therefore return sooner, and when the mirror swings away, returning photons will be delayed. In this way, we can reconstruct the mirror’s trajectory from measurements of the reflected light.

But there’s another side to this story. Each incident photon imparts a tiny momentum kick to the mirror, like a ball bouncing off a fence: the resulting force on the mirror is called radiation pressure. If we continuously dial the laser intensity up and down at a regular frequency, the beam will push the mirror around at the frequency of the intensity variation. We can enhance the extremely weak radiation pressure force by varying the intensity at the resonant frequency of the pendulum, just as pushing a swing at its resonant frequency maximizes its motion.⁵All real experiments also further enhance the radiation pressure force using an optical cavity, which is itself a kind of resonator. We create an optical cavity by placing a fixed mirror that transmits a tiny fraction of incident light opposite the suspended mirror whose motion we’re trying to control. The photons that get into the cavity bounce back and forth many times before escaping, and the momentum kicks they deliver to the mirror on each bounce add up coherently.

Put simply, the incident light affects the motion of the mirror, which is in turn mapped onto the reflected light. By timing things right — increasing the laser intensity as the mirror moves towards us and reducing the intensity as it moves away — we can cancel out the mirror’s random thermal motion, effectively reducing its temperature. This technique, called feedback cooling, is one of the many tools that physicists working in quantum optomechanics use to manipulate the motion of an object with light.⁶Another widely used technique that doesn’t require active feedback to mirror motion is sideband cooling, which uses an optical cavity to enhance the rate at which photons bounce off the mirror and carry away energy relative to the rate of scattering processes that add energy. This is the method we used in the optomechanics lab I worked in as a postdoc.

Recall that a mechanical resonator’s quality factor \(Q\) is basically a measure of how well it’s isolated from the outside world. High \(Q\) makes it easier for the weak radiation pressure force on the mirror to compete with random thermal forces transmitted through the wire. If we can make \(Q\) large enough, we can feedback cool the mirror all the way down to its quantum ground state, in which the energy of the mirror’s oscillations is at the lowest level permitted by the laws of quantum mechanics.⁷At the fundamental level, temperature is a measure of energy fluctuations, and in this sense physical systems can have many different temperatures associated with different ways their energy can fluctuate. When we speak of optomechanically cooling the mirror, we really mean cooling its center-of-mass motion. Other kinds of mirror vibrations wouldn’t be “cold” in this sense, and if you were to touch the mirror (please don’t), it wouldn’t feel cold.

Beyond the quantum ground state

Cooling a mechanical resonator to its quantum ground state opens the door to even more extraordinary experiments. Today’s quantum technology makes it straightforward to generate a weak laser pulse in an equal superposition of one photon and zero photons: a quantum state in which the very presence of the photon is indeterminate. What happens if we send this quantum state of light towards our pendulum? In one half of the superposition state, the photon pushes the mirror, while in the other half, there’s no photon, so the mirror stays at rest. So we can use the tools of optomechanics to transfer a quantum superposition from light to the motion of a macroscopic object: this is quantum mechanics in the truest sense!⁸For a more general discussion of macroscopic superposition states, I recommend this article by science journalist Phillip Ball.

Real optomechanics experiments use a wide variety of different mechanical resonators, ranging from tiny levitated silicon spheres containing about 100 million atoms to heavy mirrors suspended from quartz fibers less than a millimeter in diameter, very like the pendulum in our thought experiment above. Scientists working with the LIGO gravitational wave observatory have observed the effects of radiation pressure on the 40-kilogram mirrors in their detector and used feedback cooling to bring a particular combination of the motions of these mirrors tantalizingly close to the ground state. Full quantum control of these very heavy resonators remains an outstanding challenge, but quite remarkable quantum behavior has been demonstrated in optomechanics experiments using much smaller resonators.

These experiments are very technically challenging: the radiation pressure force is extremely weak, and random fluctuations in laser intensity, absorption of photons, and thermal motion all conspire to wash out fragile quantum effects. But optomechanical systems have already begun to push the boundaries of macroscopic quantum mechanics.⁹I’ve written another blog post about a more dubious claim to have observed macroscopic quantum behavior. In the future, they may help us network quantum computers, detect new fundamental particles, and even explore the quantum nature of gravity. The era of quantum mechanical mechanics is only just beginning.