Noise is usually viewed as the bane of measurements. But a neat experiment has confirmed a long-standing prediction for an exotic electronic state of matter through the increase of noise in charge transmission.
On page 585 of this issue, Bid et al.1 report the observation of neutral particles propagating upstream along the edge of certain fractional quantum Hall systems — exotic electronic phases of matter that belong to the larger family of topologically ordered systems. The result confirms a never-before-verified theoretical prediction and has possible implications for quantum computation.
In a topologically ordered system2, or topological phase of matter, the long-distance, low-frequency properties of the system are immune to local perturbations. A subset of these exotic systems, termed non-Abelian topological phases, are those in which a collection of the system's particle-like excitations, called quasiparticles, has many states with the same energy. (If there is a unique state, the topological order is said to be Abelian.) Braiding these quasiparticles — that is, winding their trajectories around one another to form a braid — causes these states to be rotated into each other in a way that depends only on the topological class of the braid and the particular form of topological order that is manifested in the phase. Thus, quantum information that is stored in these states is automatically protected from local perturbations. This property is the basis for proposed architectures for topological quantum computing3,4. But it also makes it very difficult to experimentally determine when a system is in a topological phase of matter and, if it is, which type of topological phase.
Fortunately, many topologically ordered systems have low-energy excited states that are confined to their boundaries5. These edge excitations can, in some topological phases, be particle-like in nature and are thus often called quasiparticles. They carry energy and may carry electrical charge. The topological properties of the bulk are imprinted on the dynamics of the edge excitations — an example of a 'holographic' correspondence. Thus, experiments that probe electrical charge transport along the edge can also shed some light on the braiding properties of quasiparticles in the bulk. However, the correspondence between bulk and edge is not one-to-one. The structure of the edge excitations depends not only on bulk properties but also on precisely how the edge of the system is engineered. As a general rule, the more sharply defined the edge of the system, the simpler the relationship to the bulk6. But even in the case of wider edges, experiments probing the edge can help identify a bulk topological phase.
Many topological phases have been found in the fractional quantum Hall regime, in which electrons are trapped at a planar interface or 'quantum well' in a semiconductor device and subjected to low temperatures and a strong magnetic field. They have been identified primarily by their Hall conductance, σ = ν e2/h, where e and h are the electrical charge of an electron and Planck's constant, respectively, and ν is a fraction (hence, the name fractional quantum Hall effect). The Hall conductance, a topological property of the bulk and also a dynamical property of the edge, is the ratio between the electric current and the voltage drop at right angles to the current; in a quantum Hall state in a large device there is no current parallel to the voltage drop, so the longitudinal conductance vanishes. When it has a constriction, or quantum point contact, the quantum Hall device is small at its narrowest point, and the electric current perpendicular to the voltage drop is suppressed from the quantized value that it assumes in a large device, whereas the current parallel to the voltage drop becomes non-zero. The dependence of the longitudinal electric current on the temperature and applied voltage is an important probe of the edge excitations of a quantum Hall state5.
Even at fixed temperature and applied voltage, the electric current through a point contact fluctuates in time because it is due to a series of discrete events at which electrical charge passes through the point contact. Remarkably, the fluctuations, or noise, in the current are another probe of the edge excitations of a quantum Hall state7. In some temperature and voltage regimes, the noise is proportional to the average current through the point contact, and the ratio between the two gives a measure of the electrical charge of the quasiparticles responsible for carrying current. The fractional charge of quasiparticles in the ν = 1/3 state was measured8,9 in this way.
There is broad agreement between experimental observations and the theoretically predicted properties of edge excitations, although a few puzzles and discrepancies remain. In my opinion, these are due to overly simplistic modelling of quantum point contacts and uncertainty about the sharpness of the edge, and they will disappear as we learn more about these devices. However, there is one crucial aspect of the theory of edge excitations that has not been experimentally confirmed. All fractional quantum Hall states must have at least one branch of edge excitations that propagate in the direction prescribed by the magnetic field — 'downstream'. But some states are also predicted to have one or more branches that propagate in the opposite direction — 'upstream'10. However, it has not, until now, been possible to directly observe the upstream excitations11.
In their study, Bid and colleagues1 have developed a novel method by which they could observe these upstream excitations through their effect on noise at a quantum point contact. The authors excite neutral quasiparticles downstream from the point contact by running current from an external source downstream from the point contact to an external drain even further downstream. Because none of the injected current makes it to the point contact, this cannot affect the total average current through it. However, the electric current creates neutral quasiparticles at the current source and along the edge. If the neutral quasiparticles are counter-propagating, they will then move upstream to the point contact, where they will increase the current noise. Bid et al. find such an effect at those fractional quantum Hall states at which theory predicts neutral quasiparticles with an upstream mode of propagation, namely ν = 2/3, 3/5 and 5/2. They do not see such an effect at those values of ν at which theory predicts that all modes propagate downstream, such as ν = 2/5.
The authors' observation of a counter-propagating neutral mode for the ν = 5/2 state is particularly intriguing. Theoretical work12,13,14 suggests that this state is non-Abelian in nature and, therefore, might provide a platform for topological quantum computation15. There is some indirect experimental evidence that the state is non-Abelian16. There is also one experiment17 that may, at ν = 5/2, have directly observed the effects of the peculiar statistics that non-Abelian quasiparticles obey, but more data are needed to unambiguously establish this result. There are two primary non-Abelian candidate theories: the Moore–Read (MR) Pfaffian state12 and the anti-Pfaffian state18,19. Although they are very similar, they differ in several ways, including the nature of their edge quasiparticles. The anti-Pfaffian state will always have upstream neutral edge quasiparticles. The MR Pfaffian state can have upstream neutral edge quasiparticles in a wide edge but not in a sharply defined one20; it is not known whether the edge in Bid and colleagues' experiments is wide enough to be in the former situation. The most plausible Abelian candidate state does not have upstream modes. Thus, the observation of upstream modes at ν = 5/2 is indirect evidence that this state is non-Abelian.
It would be premature to conclude at this stage that the ν = 5/2 state is the anti-Pfaffian state. But if the sharpness of the edge can be more fully understood, and if the increase in noise can be made more quantitative, then an experiment of this type could even distinguish between these two non-Abelian candidates. Even without making this finer distinction, however, Bid and colleagues' technique has already confirmed a key aspect of the theory of edge excitations of fractional quantum Hall states. It has also produced further independent evidence that the ν = 5/2 state is non-Abelian, which would make it a candidate platform for fault-tolerant quantum computation.