Fri. Feb 3rd, 2023
Negative mass swing defeats the uncertainty principle

Quantum mechanics comes up with something called the uncertainty principle. This states that there are pairs of properties that cannot be known with arbitrary precision at the same time. This is not because of how a measure changes the properties of what it measures. Instead, it’s due to how quantum mechanics forces us to make measurements.

The Uncertainty Principle was once something that was debated as, well, something that would, in principle, only cause problems. But since the 1980s, physicists have been making measurements that conflict with the uncertainty principle. These were once time-consuming and difficult measurements that only a few labs could do. Two decades later, we are considering mass production of sensors constrained by the uncertainty principle.

Avoiding the uncertainty principle is now homework in physics. The way to do this is to research more closely what kind of measurement you want to make. For example, 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 making your measurement device depend on that relative measurement, you can gain a significant advantage, according to a group of international researchers who recently published in Nature.

Insecurity is a principle to live by

Think of the uncertainty principle like this: if I want to know the position of an electron, I can shine a laser across an electron’s trajectory and record the moment when I see light scattered by the electron. I know that at that moment the electron was in the laser beam. But I don’t know anything about the speed (momentum actually) of the electron.

To measure the electron’s momentum, I need to make another measurement. Now let’s be smart and use the direction of the light scattered by the electron to capture the momentum of the electron. If the laser beam is a nice parallel beam with only one color, then the photons in the beam all have the same momentum. I can record the angle of the scattered light and know the momentum of the electron very accurately because I know the momentum of the photon 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 that applies to all measuring techniques – is to focus the laser beam. Once the laser beam is focused, the laser light consists of photons with a range of momenta, and I don’t know which photon was scattered from the electron. So the accuracy of my momentum measurement decreases as I increase the precision of the position measurement.

You can even ignore reality and aim the laser beam at a point: now you know the position of the electron with a precision beyond your wildest dreams, but you have no idea of ​​its momentum. Whatever measurement scheme you come up with, you will run into the same problem.

Extract certainty from uncertainty

In many cases it is enough to know the change in position and momentum of the thing we are measuring. Change regarding what though? If we measure the change of one oscillator (think swing) with respect to another oscillator, then the uncertainty principle can be circumvented. 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 two oscillators and two measurement setups, all carefully coupled.

However, making measurements on two oscillators has its own drawbacks, the most important of which is something called back-action (which we’ll come back to). However, the uncertainty principle is subtle. It turns out that a measurement that circumvents the uncertainty principle can also be performed in such a way that feedback is avoided.

So what is “back action?”

Stop pushing me around

Quantum feedback is an inevitable consequence of making a measurement. Imagine a playground swing to get an idea of ​​what a back swing entails. You get the swing moving and then want to measure the position of the swing. Unfortunately, once in motion, the swing is invisible. So, you put your arm in the path of the swing and record the moment you feel pain and withdraw your bruised hand as quickly as possible. The swing continues to move, but the movement has slowed down considerably.

Of course, you can imagine less drastic measurements. But the point is that there are no measurements that will not slow down the swing and change the results of future measurements. That’s the idea of ​​action behind it.

To demonstrate avoidance of retroactive effect and defeat of the uncertainty principle, the researchers in Nature created a very small drum. They measure the oscillation of the drum head 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 eardrum is revealed by how far the photon has to travel before it is reflected.

However, every time a photon is reflected, it gives the drum a little kick. The kick has two possible outcomes: Imagine the eardrum moving away from the photon as the photon is reflected. The result is that the eardrum moves away slightly faster: the photon has increased the amplitude of movement. As the drum moves toward the photon, the photon’s kick slows the drum’s motion.

Measuring one oscillator instead of two only seems to make matters worse, as both measurements are subject to feedback. If the measurements are performed in precisely in the same way, op precisely the same oscillators, then the back action will be identical in both cases and add up to double the problems.

But what if the sign of the back action was reversed in one case? Then the back action of one measure would exactly cancel the back action of the second measure. Now you would have a measurement that circumvents the uncertainty principle and backward action avoided.

Please be negative

Reversing the sign of back action is not very easy. Imagine I have two drumheads that are exactly the same and set in motion in exactly the same way. Now a photon approaching the drum head before the first oscillator gives it a small nudge, 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 the effect must be to slow down the eardrum.

If one of the oscillators has negative ground, the back action will have the opposite effect. Unfortunately, mechanical oscillators, such as drumheads, always have positive ground.

Fortunately, quantum mechanics says nothing about the physical construction of the oscillator. As long as they are mathematically identical, that’s good enough. To obtain a negative-mass oscillator, researchers turned to a gas of cesium. Cesium atoms, with proper preparation, will match their spin momentum. Each atom spins like a top – the spin axis orientation rotates around a central orientation. The collective motion of the spin orientation of the atoms forms an oscillator. It turns out that if we apply a magnetic field aligned with the collective spin, the oscillator behaves as if it had 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 dampens it.

Negative mass reached.

Not to get technical, but…

In a nutshell, the researchers made a small eardrum that was protected from the environment. The position and momentum of the eardrum is probed by laser light. But instead of measuring the light, the light is redirected to the cesium atoms. The equivalent position and momentum of the spin oscillator is then subtracted from the laser light. As a result, the light only holds the difference in position and momentum. That is then measured.

The nice thing about this way of measuring is that the researchers can switch between negative and positive mass oscillators by changing the orientation of the magnetic field. The difference between when the backing action adds to the noise and when it reduces the noise is remarkable and obvious.

In fact, 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 oscillators that differ only slightly from each other are best, although 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 of the uncertainty principle.

Yes, I like uncertainty. Why do you want to know that?

I’m pretty excited about this because it shows the subtleties of quantum mechanics. We teach all these ideas, such as back action and the uncertainty principle, as absolute values. And they are. But by taking them seriously rather than as mantras, you can find out that they are very specific statements about the physical world. Once that idea is understood, you can use uncertainty and retroactivity to understand nature on a deeper level.

As for improving the sensitivity of measurements… That will take some time. To put it into perspective, the researchers had to cool their drum to liquid helium temperatures, and the drum sat on a special membrane that protected it from outside vibration noise — the membrane is worth an article in its own right. 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 put another way, there is some work to be done to miniaturize this.

Nature2017, DOI: 10.1038/nature22980 (About DOIs).

By akfire1

Leave a Reply

Your email address will not be published.