When it comes to quantum physics, light and matter are not so different. Under certain circumstances, negatively charged electrons can fall into a coordinated dance that allows them to carry a current through a material laced with imperfections. That motion, which can only occur if electrons are confined to a two-dimensional plane, arises due to a phenomenon known as the quantum Hall effect.
Researchers, led by Mohammad Hafezi, a JQI Fellow and assistant professor in the Department of Electrical and Computer Engineering at the University of Maryland, have made the first direct measurement that characterizes this exotic physics in a photonic platform. The research was published online Feb. 22 and featured on the cover of the March 2016 issue of Nature Photonics. These techniques may be extended to more complex systems, such as one in which strong interactions and long-range quantum correlations play a role.
Symmetry and Topology
Physicists use different approaches to classify matter; symmetry is one powerful method. For instance, the microscopic structure of a material like diamond looks the same even while shifting your gaze to a new spot in the crystal. These symmetries – the rotations and translations that leave the microscopic structure the same – predict many of the physical properties of crystals.
Symmetry can actually offer a kind of protection against disruptions. Here, the word protection means that the system (e.g. a quantum state) is robust against changes that do not break the symmetry. Recently, another classification scheme based on topology has gained significant attention. Topology is a property that depends on the global arrangement of particles that make up a system rather than their microscopic details. The excitement surrounding this mathematical concept has been driven by the idea that the topology of a system can offer a stability bubble around interesting and even exotic physics, beyond that of symmetry. Physicists are interested in harnessing states protected by both symmetry and topology because quantum devices must be robust against disturbances that can interfere with their functionality.
The quantum Hall effect is best understood by peering through the lens of topology. In the 1980s, physicists discovered that electrons in some materials behave strangely when subjected to large magnetic fields at extreme cryogenic temperatures. Remarkably, the electrons at the boundary of the material will flow along avenues of travel called ‘edge states’, protected against defects that are most certainly present in the material. Moreover, the conductance--a measure of the current--is quantized. This means that when the magnetic field is ramped up, then the conductance does not change smoothly. Instead it stays flat, like a plateau, and then suddenly jumps to a new value. The plateaus occur at precise values that are independent of many of the material’s properties. This hopping behavior is a form of precise quantization and is what gives the quantum Hall effect its great utility, allowing it to provide the modern standard for calibrating resistance in electronics, for instance.
Researchers have engineered quantum Hall behavior in other platforms besides the solid-state realm in which it was originally discovered. Signatures of such physics have been spotted in ultracold atomic gases and photonics, where light travels in fabricated chips. Hafezi and colleagues have led the charge in the photonics field.
The group uses a silicon-based chip that is filled with an array of ring-shaped structures called resonators. The resonators are connected to each other via waveguides (figure). The chip design strictly determines the conditions under which light can travel along the edges rather than through the inner regions. The researchers measure the transmission spectrum, which is the fraction of light that successfully passes through an edge pathway. To circulate unimpeded through the protected edge modes, the light must possess a certain energy. The transmission increases when the light energy matches this criteria. For other parameters, the light will permeate the chip interior or get lost, causing the transmission signal to decrease. The compiled transmission spectrum looks like a set of bright stripes separated by darker regions (see figure). Using such a chip, this group previously collected images of light traveling in edge states, definitively demonstrating the quantum Hall physics for photons.
In this new experiment Hafezi’s team modified their design to directly measure the value of the topology-related property that characterizes the photonic edge states. This measurement is analogous to characterizing the quantized conductance, which was critical to understanding the electron quantum Hall effect. In photonics, however, conductance is not relevant as it pertains to electron-like behavior. Here the significant feature is the winding number, which is related to how light circulates around the chip. Its value equals to the number of available edge states and should not change in the face of certain disruptions.
To extract the winding number, the team adds 100 nanometer titanium heaters on a layer above the waveguides. Heat changes the index of refraction, namely how the light bends as it passes through the waveguides. In this manner, researchers can controllably imprint a phase shift onto the light. Phase can be thought of in terms of a time delay. For instance, when comparing two light waves, the intensity can be the same, but one wave may be shifted in time compared to the other. The two waves overlap when one wave is delayed by a full oscillation cycle—this is called a 2π phase shift.
On the chip, enough heat is added to add a 2π phase shift to the light. The researchers observe an energy shift in the transmission stripes corresponding to light traveling along the edge. Notably, in this chip design, the light can circulate either clockwise (CW) or counterclockwise (CCW), and the two travel pathways do not behave the same (in contrast to an interferometer). When the phase shift is introduced, the CW traveling light hops one direction in the transmission spectrum, and the CCW goes the opposite way. The winding number is the amount that these edge-state spectral features move and is exactly equivalent to the quantized jumps in the electronic conductance.
Sunil Mittal, lead author and postdoctoral researcher explains one future direction, “So far, our research has been focused on transporting classical [non-quantum] properties of light--mainly the power transmission. It is intriguing to further investigate if this topological system can also achieve robust transport of quantum information, which will have potential applications for on-chip quantum information processing.”
This text was written by E. Edwards/JQI