Liquid Droplets May Help Unravel the Secrets of Quantum Mechanics

Strange as it may sound, bouncing liquid droplets are changing our ideas of what happens at subatomic levels. By studying their movement across pools of liquid, Prof. John Bush from MIT is discovering how these droplets can help us understand the tiny particles that make up everything in our universe. But how can small droplets tell us about what’s going on at microscopic levels of matter? Don’t tiny, quantum particles act differently than anything in classical mechanics? Maybe not.

In 2005, Dr. Yves Couder discovered that droplets on the surface of a vibrating pool of silicone oil would appear to walk across the surface. These “walker” droplets create waves when they bounce, as if on a trampoline, and end up being pushed around by the waves of the previous bounce.

Image credit: Sáenz, et al. Spin lattices of walking droplets. APS Gallery of Fluid Motion

You’d hardly guess, but this experiment was groundbreaking: it hinted at connections to a little-known interpretation of quantum mechanics called Pilot Wave Theory.

Pilot Wave Theory says that subatomic particles and electromagnetic waves act similarly to how the walkers act in Couder’s experiment. The “pilot wave” pushes the particle around, rather than the electron existing as both a particle and a wave, as suggested in the current most widely adopted interpretation of quantum mechanics: the Copenhagen interpretation. The Copenhagen interpretation explains away the weirdness of quantum mechanics with the assertion that particles don’t have a definite position, existing as a semi-random “cloud” of probability until they’re measured or interact with something—an unsettling prospect. Pilot Wave Theory argues that particles do have definite positions at all times, even if we can’t observe them—meaning that the universe is deterministic. That’s part of why this experiment is so important: the core nature of reality depends on which of these interpretations you subscribe to.

Working with this experiment of moving droplets across a pool of liquid can stretch the analogy of Pilot Wave Theory to a larger scale, attempting to relate this interpretation of quantum mechanics to a more intuitive, classical system. With some of their latest work, showing how the walkers in Dr. Couder’s work interact with each other in very intricate ways, Prof. Bush and his collaborators are working to push this analogy to its limits.

Dr. Pedro Sáenz is an instructor at MIT working with Prof. Bush on analogs of quantum corrals and spin lattices. “This particular experiment was motivated by a recent work focusing on the statistical behavior of a walking droplet confined to an elliptical corral,” Sáenz explains. Not to get into too much detail, but at the microscopic level it’s been demonstrated that putting an atom at one focus of an ellipse made of magnetic atoms creates a sort of mirror image of that atom at the other end—an effect known as the “Quantum Mirage”. Sáenz and Bush recently showed that a similar effect emerges with walking droplets.

The purple peak on the right represents the effect of a magnetic atom on a surface’s conductance, while the purple spot to the left is the result of its “mirage” counterpart.
Image credit: IBM Almaden

To better study the droplet analogue of this behavior, the MIT group modified the shape of the liquid pool’s bottom: a deep “well” creates a sort of trap that gives the droplet a preference for one spot. Each walker emits waves when it bounces on the surface of the pool, and those waves are influenced by the well, giving rise to an attraction force, and by the corral walls, giving rise to a repulsive force.

Image credit: Sáenz, et al. Statistical projection effects in a hydrodynamic pilot-wave system. Nature Physics. 

Most recently, Sáenz and Bush have been examining how more of these droplets would work together in a lattice structure, or a pattern like a pentagon or triangular shape. Specifically, they created plates with wells in various patterns, and put droplets over the wells to test how the droplets interact with one another. Each walker acquires an angular momentum, walking clockwise or counterclockwise around the perimeter of its well. It’s not a perfect analogy, but it’s possible to think of these patterns of wells, and the droplets within them, as being like electron spin lattices. Because each walker’s motion is influenced by the waves of nearby walkers, the direction of one walker’s spin is also influenced by the spin of its neighbors—and it’s this relationship that Sáenz and Bush set out to study in this recent work.

Image credit: Sáenz, et al. Spin lattices of walking droplets. APS Gallery of Fluid Motion

This brings us to two terms: ferromagnetic and antiferromagnetic. In an atomic lattice, ferromagnetism arises when the magnetic fields of neighboring atoms are aligned—this is what gives bar magnets their pushing and pulling power. In the analogue atoms of Sáenz’s lattices, a ferromagnetic arrangement means that all walkers are spinning in the same direction, and antiferromagnetic means that walkers spin opposite their neighbors.

The blue dots are droplets spinning clockwise, and the red are spinning counterclockwise.
Image credit: Sáenz, et al. Spin lattices of walking droplets. APS Gallery of Fluid Motion

The group found that, if there are two walkers next to each other, they tend to spin in opposite directions, corresponding to antiferromagnetic order. This antiferromagnetic arrangement presumably is the lowest-energy state, so the system naturally evolves toward it like a ball rolling down a hill. But what if we looked at whole patterns of spinning droplets, like in a lattice? The more complicated the systems get, the more variance there will be among the many walkers.

“We have found the strongest antiferromagnetic correlations in 1D lattices,” says Sáenz; with the wells all in a line, each walker spins opposite its neighbors, so the first is clockwise, the second is counterclockwise, and so on. But when you get into 2D lattices with more complicated shapes, it’s impossible to reach this perfect antiferromagnetic state: in a triangular arrangement, two droplets will always be spinning the same direction. This leads to the important subject of frustrated spin systems.

Also under study is the phase of the walkers, i.e. where in its bounce cycle each droplet is at a given point in time. Two droplets hitting the surface at the same time are said to be “in phase”, but one going down when the other walker goes up would “out of phase”. That can impact the degree of antiferromagnetism. Bush and his collaborators found that “the strongest antiferromagnetic order occurs when the drops are in phase vertically,” or all of the drops go up and down at the same time. Now, they are looking at how to revert the system to a more ferromagnetic state, where all of the droplets are spinning in the same direction. The system naturally falls to an antiferromagnetic state, but the group has a few promising leads.

“The same way that an external magnetic field can be applied to an antiferromagnetic metal to realign the dipole moments…we are testing if system rotation may reproduce the same effect.” Developing an analogue for electron spin lattices in this kind of experiment is an exciting prospect: it might provide insights into the nature of condensed matter physics, the same way that Couder’s droplets have given countless people a more intuitive grasp of quantum mechanics.

Looking at the big picture, Prof. Bush’s research is working to expand and test the droplet analogy of Pilot Wave Theory. If this analogy actually reflects with a degree of accuracy what happens at subatomic levels of matter, how remarkable would it be that our universe operates in a manner closer to classical mechanics? Maybe particles and waves don’t have to operate under a different set of rules, and maybe the physics happening on a subatomic scale can be understood in terms of things we see every day. It’s an audacious idea, when the prevailing wisdom around quantum has long been “if you think you understand quantum mechanics, you don’t understand quantum mechanics,” but it might be a step toward the highest goal of physics: to know the nature of the universe.

—Phoebe Sharp

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