Although we live in a world of constant motion, physicists have focused largely on systems in or near equilibrium. In the past few decades, interest in non-equilibrium systems has increased, spurred by developments that are taking quantum mechanics from fundamental science to practical technology. Physicists are therefore tasked with an important question: what organizing principles do non-equilibrium quantum systems obey? Writing in Nature, Prüfer et al.1, Eigen et al.2 and Erne et al.3 report experiments that provide a partial answer to this question. The studies show, for the first time, that ultracold atomic systems far from equilibrium exhibit universality, in which measurable experimental properties become independent of microscopic details.
The researchers use low-density gases of rubidium1,3 or potassium2 atoms that are cooled to temperatures close to absolute zero. At sufficiently low temperatures, these atoms begin to show quantum-mechanical behaviour, forming a macroscopic quantum state known as a Bose–Einstein condensate. Starting from either such a condensate1,2 or an uncondensed gas3, the researchers rapidly change experimental parameters — a process known as a quench. Rather like a cartoon character that looks down to discover they have accidentally run off a cliff, the quench initiates far-from-equilibrium dynamics.
Such quenches are relatively easy to realize, but what the researchers see next is surprising. Consider all the variables that can be associated with a given experiment: power fluctuations of lasers, variations in the lab’s temperature, microscopic details of atomic interactions, and so on. The researchers find that the dynamics of their experiments, despite involving strongly interacting atoms far from equilibrium, become independent of these variables.
Eigen et al. accomplish this universality by carefully eliminating all but two of the variables in their experiment: the density of the atomic gas and the scattering length. The latter describes how closely two atoms can pass without interacting. The authors then go one step further and eliminate the dependence of the scattering length on variables in a clever way.
First, to prepare the initial condensate, the authors set the scattering length to zero — they ‘turn off’ the interactions — using a magnetic field4. Second, they quench the scattering length to infinity, again using the magnetic field. If we consider increasing the density of the gas by, for example, a factor of eight, the spacing between the atoms decreases by a factor of two. Zooming in (rescaling) by this factor of two, the atomic system looks exactly the same as it did before the density was increased, because the scattering lengths of zero and infinity are unchanged.
Eigen and colleagues vary the density of the gas by a factor of about ten, and observe that the experimental dynamics are independent of the density after rescaling both space and time. They also adjust the temperature of the gas and show that universality holds when one more variable is considered — namely, the length scale on which the gas exhibits quantum-mechanical behaviour.
Prüfer et al. and Erne et al. uncover a different form of universality. On the face of it, the experiments of these two groups are wildly different. Erne and colleagues start with a three-dimensional gas, quench to one dimension, and observe the density of the gas as a function of position and time. Prüfer and colleagues work in one dimension throughout, explore the internal states (spins) of the atoms and carry out a quench that allows these spins to fluctuate. But, after a short time, both groups observe universality, which they argue results from a phenomenon called a non-thermal fixed point.
For systems in equilibrium, the concept of a fixed point comes from one of the great discoveries of twentieth-century physics, known as the renormalization group. This framework studies how a system evolves as we zoom out from the microscopic to the macroscopic scale, and successfully describes the emergence of key phases of matter such as magnetism. Fixed points are states of a system that remain unchanged on zooming out. Non-thermal fixed points occur when non-equilibrium systems approach such a state, with the role of zooming out played by the passage of time5.
A classic example of a non-thermal fixed point is wave turbulence, in which the energy of waves is transferred from large to small scales. Prüfer et al. and Erne et al. demonstrate the first examples of universality caused by non-thermal fixed points in systems dominated by quantum mechanics. Like Eigen and colleagues, the groups show that their results are robust by widely varying the initial conditions of their experiments and observing that the dynamics are effectively unchanged.
Although Prüfer et al. and Erne et al. use different quenches and measure different properties, their results are remarkably similar. This resemblance provides perhaps the best evidence for the existence of universality in these atomic systems. At a technical level, the experiments do differ in their critical exponents (numbers that describe the properties of fixed points), which indicates that the two fixed points are different.
Together, these three studies provide a substantial step forward in our understanding of quantum systems far from equilibrium. However, a complete picture of the underlying universality remains to be determined. A notable concern for all of the experiments is that the universality occurs over limited time and length scales. Longer times, in particular, would probably be required to realize non-equilibrium steady states that are useful for practical applications. By analogy with wave turbulence, one possibility for extending the reach of the universality could involve continuously pumping energy into the systems; it is well documented that universality is, at best, transient in the absence of an external drive.
From a fundamental perspective, these experiments pave the way for exploring a wide range of theoretical and experimental questions regarding non-equilibrium universality. For example, what are the possible classes of non-thermal fixed points? What happens at extremely high or low energy scales, at which the universality breaks down? And under what conditions does universality arise in generic quenched systems? These are challenging questions to answer, but I, for one, hope that these experiments open the door to placing non-equilibrium quantum systems alongside equilibrium ones in the lexicon of modern physics.
Nature 563, 191-192 (2018)