Quantum mechanics comes with something called the uncertainty principle. This states that there are pairs of properties that cannot be simultaneously known to arbitrary precision. This is not due to the way a measurement changes the properties of what it measures. Instead, it is due to how quantum mechanics forces us to make measurements.
The uncertainty principle was once something that was discussed as, well, something that would only cause problems in principle. But since the 1980s, physicists have been making measurements that bump up against the uncertainty principle. These were once time-consuming and difficult measurements that only a few labs could do. Two decades later, and we are contemplating mass production of sensors that are going to be limited by the uncertainty principle.
Avoiding the uncertainty principle is now a cottage industry in physics. The way to go about it is to more carefully examine the sort of measurement you want to make. For instance, the position and momentum of an oscillator are bound by the uncertainty principle. But the relative position and momentum of two oscillators is not. By ensuring that your measurement device depends on that relative measurement, you can gain a substantial advantage, according to a group of international researchers who recently published in Nature.
Uncertainty is a principle to live by
Think of the uncertainty principle like this: if I want to know the position of an electron, then I can shine a laser across the path of an electron and record the moment that I see light scattered by the electron. I know that at that particular time, the electron was within the laser beam. But I know nothing about the speed (momentum, really) of the electron.
To measure the momentum of the electron, I need to make a different measurement. Now, let’s be clever and use the direction of the light scattered by the electron to record the electron’s momentum. If the laser beam is a beautifully parallel beam with only a single color, then the photons in the beam all have the same momentum. I can record the angle of the scattered light and know the electron’s momentum very accurately, because I know the photon momentum very accurately. But, to increase the accuracy of the position measurement, I need a smaller diameter laser beam.
At some point, the only way to achieve that—and this applies to all measurement techniques—is to focus the laser beam. Once the laser beam is focused, the laser light is made up of photons with a range of momenta, and I don’t know which photon scattered off the electron. So, the accuracy of my momentum measurement is decreased as I increase the precision of the position measurement.
You can even ignore reality and focus the laser beam to a point: now you know the position of the electron to a precision beyond your wildest dreams, but you don’t have the slightest clue about its momentum. No matter what measurement scheme you devise, you run into the same problem.
Pulling certainty out of uncertainty
In many cases, it is enough to know the change in position and momentum of the thing we are measuring. Change with respect to what, though? If we measure the change of one oscillator (think swing) with respect to a different oscillator, then the uncertainty principle can be evaded. In other words, to avoid the uncertainty principle, we don’t measure the position and momentum of one oscillator—we measure the difference in position and momentum of two oscillators. That means having two oscillators and two measurement setups all carefully coupled.
Making measurements on two oscillators has its own drawbacks, though, the main one being something called back action (which we’ll get back to). The uncertainty principle is subtle, though. It turns out that a measurement that evades the uncertainty principle can also be performed in such a way that it avoids back action.
So what is “back action?”
Stop shoving me around
Quantum back action is an unavoidable consequence of making a measurement. To get an idea of what back action involves, imagine a playground swing. You get the swing moving and then want to measure the position of the swing. Unfortunately, the swing, once moving, is invisible. So, you stick your arm in the path of the swing and record the moment when you feel pain and, as quickly as possible, withdraw your bruised hand. The swing continues to move, but its motion has been slowed considerably.
Of course, you can imagine less intrusive measurements. But the point is that there are no measurements that do not slow the swing and change the results of future measurements. That’s the idea of back action.
To demonstrate the avoidance of back action and the defeat of the uncertainty principle, the researchers in Nature created a very tiny drum. They measure the oscillation of the drum skin by shining laser light on the drum—actually, they do this in a very clever way, but the principle is similar. The position of the drum skin is revealed by how far the photon has to travel before it is reflected.
Each time a photon is reflected, though, it gives the drum a tiny kick. The kick has two possible outcomes: imagine that the drum skin is moving away from the photon as the photon is reflected. The result is that the drum skin ends up moving away a little faster: the photon has increased the amplitude of motion. If the drum is moving toward the photon, then the photon’s kick slows the drum’s motion.
Measuring one oscillator instead of two would seem to make matters worse, since both measurements are subject to back action. If the measurements are performed in exactly the same way, on exactly the same oscillators, then the back action will be identical in both cases and add up to double the trouble.
However, what if the sign of the back action was reversed in one case? Then the back action of one measurement would exactly cancel the back action of the second measurement. Now you’d have a measurement that evaded the uncertainty principle and avoided back action.
Please, be negative
Reversing the sign of back action is not very easy. Imagine that I have two drum skins that are exactly the same and are set in motion in exactly the same way. Now, a photon that is approaching the drum skin for the first oscillator gives it a little shove, timed to excite the drum motion. The photon hitting the second drum is also timed to excite the drum motion as well (everything is identical, remember). But, its effect needs to be slowing the drum skin.
If one of the oscillators has a negative mass, then the back action will have the opposite effect. Unfortunately, mechanical oscillators, like drum skins, always have a positive mass.
Luckily, quantum mechanics doesn’t say anything about the physical construction of the oscillator. As long as they are mathematically identical, that is good enough. To obtain an oscillator with a negative mass, researchers turned to a gas of cesium. Cesium atoms, with the right preparation, will align their spin momentum to each other. Each atom spins like a top—the orientation of the spin axis rotates around some center orientation. The collective motion of the atoms’ spin orientation forms an oscillator. It turns out that if we apply a magnetic field that is aligned to the collective spin, then the oscillator behaves as if it has a positive mass. The mass is given by the strength of the magnetic field.
A negative mass is created by reversing the direction of the magnetic field. The spins oscillate as before, but now a measurement that would have excited the oscillator actually damps it.
Negative mass achieved.
Not to get technical, but…
In a nutshell, the researchers made a tiny drum skin that was protected from the environment. The position and momentum of the drum skin is probed by laser light. But, instead of measuring the light, the light is sent on to the cesium atoms. The equivalent of position and momentum of the spin oscillator is then subtracted from the laser light. As a result, the light only holds the difference in the position and momentum. That is then measured.
The cool thing about this way of performing the measurements is that the researchers can switch between oscillators that are negative and positive mass by switching the orientation of the magnetic field. The difference between the cases for when the back action adds to the noise and when it reduces the noise is remarkable and clear.
Even better, by tuning the strength of the magnetic field around the cesium atoms, the researchers can vary the effective mass of the oscillator. That is, they started with oscillators that are mathematically identical and then continuously increased the mass difference to see how effective the back action cancellation was. It turns out that the best case is for oscillators that are just a tiny bit different from each other, though the researchers don’t go into exactly why that is.
In terms of performance, the researchers measure with an accuracy that is about 30 percent better than the limit given by the uncertainty principle.
Yes, I do enjoy uncertainty. Why do you ask?
I’m pretty excited by this because it demonstrates the subtlety of quantum mechanics. We teach all of these ideas, like back action and the uncertainty principle, as absolutes. And they are. But, by taking them seriously rather than as mantras, you can figure out that they are very specific statements about the physical world. Once that idea is grasped, you can use uncertainty and back action to understand nature at a deeper level.
As for improving the sensitivity of measurements… That will take a while. To put it in perspective, the researchers needed to cool their drum to liquid helium temperatures, and the drum was on a special membrane that shielded it from outside vibrational noise—the membrane is worth an article all by itself. And you need a cesium gas that is well-shielded from outside magnetic fields. The simplest part of the system is probably the laser measurement system, which only requires a laser with very high polarization purity and five photodiodes, all mounted on a very, very stable table.
Or to put it another way, there is some work to be done to miniaturize this.