Experiments reveal that the laws governing the immediate aftermath of the Big Bang also apply to the behaviour of coupled lasers. The findings could be used to solve complex computational problems.
Many thousands of papers have been published involving lasers, yet it is amazing how many surprises these devices can still deliver. Pal et al.1 report a particularly intriguing example in Physical Review Letters: when several lasers are coupled together, they can give rise to physics that might have had a role in the earliest stages of our Universe's development.
Right after the Big Bang, our Universe was incredibly dense and hot. It then gradually expanded and cooled to something much more dilute and ordered. In 1976, the physicist Tom Kibble suggested2 that the Universe did not 'freeze' out uniformly, but rather in a pattern of spatially separated domains, in each of which a different type of order was randomly generated. During the cooling process, these domains would grow until they touched each other, forming long-lived domain boundaries where they met. These boundaries can be thought of as defects in the overall structure of the Universe, and Kibble's theory predicts how likely it is for them to emerge during the cooling process — in particular, how theirformation depends on the cooling time.
The observation of such cosmological phenomena remains out of reach, but in 1985 another physicist, Wojciech Żurek, pointed out3 that the same kind of physics as predicted by Kibble should also govern the freezing behaviour of systems that are accessible in the laboratory. His prediction has been confirmed in various systems, including 'superfluid' helium4, liquid crystals5 and optical fields6.
The typical scenario in these experiments is to heat up a system, and then to cool (quench) it below the critical temperature at which ordering sets in. In a slow cooling process, the system continuously equilibrates and thus reaches an ordered state that has few, if any, boundary defects. However, a sudden quench does not leave enough time for equilibration; as a result, many defects survive the quench. For example, when hot, liquid iron is cooled sufficiently slowly, electron spins in the metal align in a well-defined direction, thereby forming a ferromagnet that produces a strong magnetic field. Sudden quenches instead lead to randomly oriented spins and to magnetic domains that have zero net magnetization.
Pal et al. realized that they could implement and study the physics of the Kibble–Żurek mechanism even without the expense of heating or cooling a system. Their ingenious idea is to arrange 10–30 identical lasers in a ring-like setting, so that each laser couples only to its two nearest neighbours through a spatial overlap of their beams. Because fabricating many identical lasers would be difficult, the researchers instead devised a system that uses a single laser cavity, in which light is bounced back and forth between two mirrors. Within the cavity, the authors placed not only the gain medium necessary for light amplification, but also a mask with holes punched in the form of a ring (Fig. 1). Each light beam that passes through one of these holes forms an individual laser.
The coupling between lasers was achieved by moving one mirror a short distance away from the mask; this creates an overlap between neighbouring beams such that light approaching the mirror through one hole gets reflected back through a neighbouring hole. Such coupling also causes some of the light to be lost, and so the entire system of coupled lasers naturally self-adjusts to find the optimal state that allows it to lase most efficiently. This lasing state radiates out through the second, slightly transparent mirror, producing a laser beam that has a specific spatial profile, which Pal et al. observed and analysed in their experiment.
The authors' system resembles an arrangement of guests at a round dinner-table. If the table is set such that each wine glass is placed halfway between the neighbouring dishes, then the first guest who picks up a glass from either the right or the left side of her dish determines which glass the neighbour on her right or left has to pick up. The first choice thus propagates from one guest to the next, until every guest has a glass within reach to drink from. In the context of the Kibble–Żurek formalism, one would say that the first guest's choice induces a 'spontaneous symmetry-breaking transition', because the overall symmetry of the table setting is broken by the assignment of each wine glass to a specific guest.
Cases in which some guests take the left wine glass and the others take the right are forbidden, because this would leave at least one guest without a glass. Similarly, the coupling between neighbouring lasers forces them to have a well-defined phase relationship (which defines where the peaks and troughs of one laser's light waves are with respect to those of another). It turns out that only the solution in which all the lasers have exactly the same phase is truly stable.
Nevertheless, the coupled lasers can still get stuck in less-stable arrangements — in perfect analogy to the boundary defects in the Kibble–Żurek formalism. To test the probability of getting such a defect solution, Pal and colleagues increased the number of lasers in the cavity, and the degree of light amplification in the gain medium, both of which increase the likelihood of a defect solution occurring. In this way, interesting analogies can be drawn between the relevant laser parameters and the cooling rate in a thermodynamic quench.
Because the number of coupled lasers is much smaller than the number of atoms in a macroscopic system, Pal and colleagues' experiment has the remarkable feature of allowing the Kibble–Żurek mechanism to be probed at the microscopic level, as a system involving several coupled elements (rather than as a continuous system). The ring arrangement provides only a one-dimensional model of the mechanism, however, and thus restricts the comparisons that can be drawn with the situation encountered in cosmology. An extension of the experiment to a 2D laser array would thus be the natural next step.
One of the most promising aspects of Pal and colleagues' work is that it will build a bridge between research communities that typically interact little with each other — such as optical scientists and cosmologists. Another is that the experimental set-up might serve as an analog computer that can solve challenging optimization problems efficiently7. The system could also be an ideal testing ground for studying hot areas in laser theory, such as the occurrence and topological aspects of 'exceptional points'8.