Collective spin modes in ultracold atoms

Physicists created a Bose-Einstein condensate of chromium atoms, ensured the atomic spins were each aligned 90º to the condensate’s plane, applied a magnetic field gradient and separated the atoms by a small but relatively significant distance, fired radio pulses at the condensate to get the atoms’ spins to rotate – and then measured the way the atoms were spinning. They found that instead of each atom having its own direction of spin, they all exhibited a collective spin that they tried to maintain!

This is fascinating because such behaviour has previously only been observed in solids in liquids, where atoms are more closely situated, and not in a Bose-Einstein condensate, which is more like a dilute gas. That it has been observed in the latter points to the presence of quantum mechanical phenomena that are reaching across atoms to influence them to behave collectively.

A Bose-Einstein condensate is a group of particles that has been cooled to such a low temperature that each particle behaves like just one kind of particle, the boson. In this state, all of the particles acquire the same quantum numbers and coexist to form a new phase of matter: the condensate.

There are four kinds of quantum numbers for every particle, and each particle can’t have the same set of four numbers as that of another particle in the same system. E.g. all the electrons in an atom have different values for each of these numbers. However, particles called bosons (such as the photon) flout this rule when cooled to a really low temperature, when they form a Bose-Einstein condensate: a system of particles that all have the same four quantum numbers, i.e. occupying the same lowest energy state.

In this state, all the particles in the condensate together behave like a liquid-like fluid while being more similar to a dilute gas. Physically this may sound boring but in quantum mechanics, a Bose-Einstein condensate is known to have unique properties that particles don’t otherwise exhibit.

In the experiment described above, physicists created a Bose-Einstein condensate by cooling approx. 40,000 chromium atoms to 400 nK and then confining them using an optical trap. While atoms aren’t exactly particles, and are instead imagined to be composed of them, the Stern-Gerlach experiment showed in 1922 that atomic-scale systems, including atoms, do exhibit quantum mechanical properties as a whole.

The chromium atoms’ spins – for simplicity’s sake imagined to be the atoms’ individual orientation – were aligned perpendicular to the axis of the rugby-ball-shaped Bose-Einstein condensate. Next, using a technique similar to the Stern-Gerlach experiment, the physicists applied a graded, i.e. uneven, magnetic field along the plane of the condensate. This caused each atom’s spin to become coupled with – or affected by – those of its neighbours such that all the atoms were encouraged to have the same alignment (keeping the condensate in its ground state). The graded magnetic field also caused the atoms to move apart slightly. Finally, radio pulses were fired at the atoms such that they produced a torque that caused the atoms to spin, i.e. change their orientation.

When the spins fall out of alignment, the spin coupling should also fall out of alignment, and the atoms would all become aligned differently. … at least this is what the physicists thought would happen. It didn’t. The atoms were found to be reorienting under the radio pulses’ assault in a spin wave. It was if each atom’s spin was holding the hands of the two spins on either side of it and refusing to let go, causing the atoms to move together.

In this video, looking upon the surface of the liquid is akin to looking upon a sea of atoms in the condensate. Imagine you were looking at the waterbody edge on. The ripples would be the atomic spins bobbing up and down because of the radio pulses, which would be the metaphorical stones thrown in the water. According to the physicists, when the magnetic field’s gradient is smaller, the shape of the bobbing motion – a.k.a. the spin wave – would more look like the graph below:

Graphical representation of a damped oscillation. Source: Quora

This is the first time such a phenomenon has been observed in a Bose-Einstein condensate and more so in a dilute gas. In their effort to understand what could be causing this so-called collective spin mode, the physicists also found some interesting connections. As they write in their preprint paper:

Although complex oscillatory behaviours are obtained when b [the magnetic field gradient] is large, at low gradients we observe a rather simple damped oscillatory behaviour for both the population dynamics and the separation [between atoms], … The amplitude of oscillation also depends on b, and vanishes for b → 0. … These observations indicate that the interaction with magnetic field gradients has excited a collective mode which couples the [condensate’s] spin degrees of freedom to [its] spatial degrees of freedom. (emphasis mine)

Even more interestingly, according to the physicists, the condensate under these specially engineered circumstances behaved like a ferrofluid, a type of fluid that, in the words of Physics World, “becomes strongly magnetised when placed in a magnetic field”. They realised this was the case because they found that they could predict the condensate’s behaviour using the rules of ferrofluid hydrodynamics.