The idea of using ultracold atoms to simulate the behaviour of electrons in new kinds of quantum systems — from topological insulators to exotic superfluids and superconductors — is a step closer to becoming a reality. See Letter p.83
During the past decade or so, physicists have been trying to implement one of the last of Richard Feynman's ingenious ideas. This was to build a 'quantum scale model'1, using controllable quantum particles, to simulate the workings of otherwise intractable quantum systems and to investigate thorny problems in condensed-matter physics. On page 83 of this issue, Lin and colleagues2 inch closer to building a new kind of quantum simulator using cold gases of atoms.
At less than one-millionth of a degree above absolute zero, cold atomic gases are extremely versatile and can be controlled with great precision. They can be composed of bosons (particles with integer spin) or fermions (particles with half-integer spin). And, just like electron gases, they can be confined in a variety of environments, including crystalline lattices and disordered media. Furthermore, the mutual interactions between the atoms of a gas can be controlled, by modifying atomic collisions, to mimic real, solid-state systems. Using these tools, researchers have been able to reproduce the essential quantum physics of several canonical condensed-matter systems, including superfluids, in which particles (electrons or atoms) move without resistance, and insulators, in which particles are pinned to an underlying lattice structure.
However, exploring some of the remaining uncharted territory in condensed-matter physics using cold atomic gases will require additional tools. One of the things missing from the toolbox had been the ability to mimic the effects of magnetic fields on the electron's charge — a challenge because atoms are neutral. These effects are central to many exotic phenomena, including the quantum Hall effect and superconductivity. In an earlier study, Lin and colleagues demonstrated3,4 a solution: they generated a fictitious magnetic field in an atomic system, using tailored beams of light. Now, the same group2 adds a new tool to the toolbox by creating artificial 'spin–orbit coupling' in a neutral atomic system. But in order to understand the significance of this experimental achievement, let us take a step back and understand the concept of spin–orbit coupling.
In addition to their electronic charge, electrons (like all fundamental particles) have an intrinsic spin. Loosely, we can think of the electron as spinning about an axis through its centre, with the spinning giving it a magnetic character similar to that of a tiny bar magnet. Atoms, being composed of fundamental particles, also have an intrinsic spin. But how does the spin of particles interact with their orbital motion?
The interaction of an object's spin with its orbit (spin–orbit coupling) is ubiquitous in both the microscopic and macroscopic worlds. One example is the synchronization of the rotation (spinning) of the Moon and its orbit around Earth, which means that we can only see one face of the Moon. Another example is the motion of electrons orbiting an atom's nucleus: the motion is altered by the spin of the electrons owing to the electric field of the nucleus, and this gives rise to the atom's fine structure (small shifts in its energy levels). Similar effects occur in free electrons moving through electric fields in solids, for example the fields generated by the underlying crystalline lattice.
It is hoped that quantum simulators based on atomic gases will illuminate the physics of electron systems. But it is first necessary to devise a technique to make neutral atoms mimic the interaction of the spin of moving electrons with electric fields, and so engineer spin–orbit coupling (Fig. 1). Building on a recent theoretical suggestion5 of how this might be accomplished, Lin et al.2 were able to create experimentally an artificial coupling between the spin of rubidium (87Rb) gas atoms (bosons of spin 1) and their centre-of-mass motion. To achieve the coupling, the authors used a pair of lasers to transfer linear momentum to the atoms' centre-of-mass and create mixed atomic spin states, which are composed of two different spin orientations. The mixed-spin states couple directly with the momentum transferred to the atoms' centre-of-mass (orbital) motion, creating a 'dressed state', thus leading to an artificial spin–orbit coupling. (For a review of related ideas, see ref. 6.)
A great advantage of the authors' experiment2 lies in the possibility of controlling spin–orbit coupling — from no coupling at all to strong coupling — through optical means. If the lasers are turned off, spin–orbit coupling disappears: the spin and the centre-of-mass motion are independent. If the lasers are turned on, spin–orbit coupling occurs and scales with the lasers' intensity. This type of control is not typically available in condensed-matter systems such as in semiconductors or superconductors.
What's more, Lin and colleagues2 have shown that the artificial spin–orbit coupling can be used to change the interaction between atoms that are in different spin states. The ability to change the interactions between a pair of atoms allows the researchers to study transitions between a phase in which atoms with different spin states repel weakly, and are mixed in the same spatial region (lasers off), to a phase in which atoms with different spin states repel strongly and are spatially separated (above a threshold of laser intensity).
The authors' creation and control of artificial spin–orbit coupling in atoms has implications beyond atomic-gas physics, in particular because there is no fundamental reason why their experiments should not be performed with fermions. In condensed-matter systems, the spin–orbit coupling of the constituent electrons (fermions of spin ½) can have important consequences for semiconductors, superconductors and magnetic materials. In mercury telluride (HgTe) semiconductors, for example, strong spin–orbit coupling can produce topological insulators7. These unconventional semiconductors insulate electric current in their bulk but conduct electricity on their surface, a rather unusual and peculiar effect that may be useful for electronic applications. The creation of adjustable artificial spin–orbit coupling in atoms opens up exciting possibilities for realizing quantum simulators of topological insulators and exotic forms of superfluidity and superconductivity.
Feynman, R. P. Int. J. Theor. Phys. 21, 467–488 (1982).
Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Nature 471, 83–86 (2011).
Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Nature 462, 628–632 (2009).
Zwierlein, M. Nature 462, 584–585 (2009).
Liu, X.-J., Borunda, M. F., Liu, X. & Sinova, J. Phys. Rev. Lett. 102, 046402 (2009).
Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Preprint at http://arxiv.org/abs/1008.5378v1 (2010).
Qi, X. L. & Zhang, S. C. Physics Today 63(1), 33–38 (2010).
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Physical Review Letters (2020)
Color superfluidity of neutral ultracold fermions in the presence of color-flip and color-orbit fields
Physical Review A (2018)
Low Temperature Physics (2018)
Generalized Stoner criterion and versatile spin ordering in two-dimensional spin-orbit coupled electron systems
Physical Review B (2017)