A combination of leading-edge techniques has enabled interaction-induced magnetic motion to be observed for pairs of ultracold atoms — a breakthrough in the development of models of complex quantum behaviour. See Letter p.519
Particle interactions have a defining role in many properties of materials, but are often difficult to incorporate into a theoretical framework. Although theories that omit these interactions can describe some behaviours, a full understanding of a material can come only from a complete account of the system, including its interactions. Interaction-based phenomena such as magnetism are poorly understood at the microscopic level, and so the ability to study them using the bottom-up approaches offered by ultracold quantum gas experiments holds considerable promise. On page 519, Tai et al.1 report such an experiment in which pairs of atoms exhibit chiral motion — movement that has a particular 'handedness' — only as a result of the system's interactions. The work is an early step towards the simulation of non-trivial many-body quantum systems, which will allow exotic condensed-matter phenomena to be studied.
Tai and colleagues combine, for the first time, two of the most valuable tools for studying ultracold quantum gases. One is the quantum gas microscope, which can be used to image the individual sites of an optical lattice (an array of interfering laser beams used to trap a quantum gas). The other is an artificial (effective) magnetic field, which causes the neutral atoms in such experiments to behave like charged particles in a real magnetic field.
The first quantum gas microscope capable of probing many-body physics was pioneered2 in the authors' lab in 2009. For solid-state, many-body quantum systems, experimentalists rely on either bulk measurements of ensembles of many particles, or atomic-scale imaging techniques such as scanning tunnelling microscopy or atomic force microscopy, which are limited to studying surfaces. But in quantum gas systems, the optical lattice keeps atoms a few hundred nanometres apart (the resolution limit for optical systems), meaning that direct interrogation of the constituent particles in a many-body ensemble is possible using optical methods. By carefully integrating high-quality optics with custom-designed apparatus, experimentalists can observe how atoms move about in such a system when they interact with each other and with applied fields, for a certain set of well-controlled conditions.
In the current work, Tai et al. engineer an effective magnetic field based on the Harper–Hofstadter model3,4, a quantum-mechanical description of the motion of particles in a magnetic field when they are confined to a lattice. The model emerged from the pioneering hypothesis5 of physicist Rudolf Peierls, who in 1933 suggested that the magnetic field induces a change in the phase of a particle — a property only indirectly detectable in quantum systems — as it travels through the lattice.
Some aspects of the current work have been explored in previous experiments, including the first atomic-gas simulations of the Harper–Hofstadter model6,7 and observations of the chiral motion of particles in effective magnetic fields using synthetic dimensions8,9,10,11. But Tai and colleagues' study deepens our understanding of the interplay between interaction effects and the effective magnetic fields. The key to observing these effects lies in the chiral circular motion that results from the field. Particles show chiral motion as they hop around the lattice, analogous to the way in which the movement of a charged particle is affected by a magnetic field.
The authors first verify that they have established the Harper–Hofstadter effective magnetic field by observing the chiral motion of single atoms of rubidium moving around a lattice system. The authors then extend their work to a two-particle system, in which two atoms have an innate repulsive interaction (Fig. 1). A naive interpretation of the Harper–Hofstadter model that is engineered into the system predicts that the chiral motions of the two atoms cancel each other out, so that no chiral motion is observed for the whole system.
However, for atoms that are located at adjacent sites, a small reduction in the energy of the system occurs because of an exchange interaction — a virtual process by which an atom hops to a neighbouring site that already contains an atom and back again, without ever occupying the second site. The symmetric two-particle configuration of the system therefore has a slightly lower total energy than other configurations and is the preferred state of the system. This configuration is also expected to exhibit overall chiral motion. Tai and colleagues observe such chirality in their experiments, indicating that their system finds this preferred state. This demonstrates that interactions can dictate the many-body configuration of quantum systems, albeit in a system of only two particles.
The authors' experiment is a milestone on the path towards full experimental quantum simulations of many-body systems; such simulations are expected to be able to make predictions that are beyond the capabilities of conventional computational simulations. However, the work is still at an early stage. For example, although Tai et al. compare their results to the theory of many particles, a maximum of two particles is used. Moreover, their system is not in equilibrium, which precludes the direct observation of a stable ground state. And despite their theory showing that there is no chiral motion in the absence of interactions, this could not be proved experimentally with the tools at hand.
Extensions of the work that address these issues and others will be eagerly anticipated. In particular, it will be fascinating to see what happens when there are many particles, when new geometries or the dimensionality of the particles' environment are engineered, or when different kinds of interactions between particles are applied.Footnote 1
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