The quantum mechanical and topological systems explored in the Simon Lab can be complex, but we feel strongly that an important part of science is communication. To this end, we have developed some animations, primarily for our talks, that aim to share the ideas underlying our science in the simplest, most accessible terms possible.
Have you ever wondered what a day in the life of a quantum manybody optometrist looks like? Watch this quick clip to find out!
As we twist a periscope, the image it produces rotates; this may be understood as a dove prism, but the important point is this: adding two more mirrors to close the path results in a round-trip image rotation, which turns the lab frame into a rotating frame.
One of the simplest tests of whether a surface has gaussian curvature is whether it can be created by rolling up a flat sheet. Here we demonstrate that a sheet corresponding to a third of the plane can be rolled up into a cone; a conical surface thus lacks gaussian curvature (it is FLAT) everywhere but at the cone-tip, which cannot be made out of a flat sheet.
A particle in a magnetic field undergoes cyclotron orbits; if the global topology of the surface is changed to that of a cone, very little happens for orbits away from the cone tip; this is because, as shown above, a conical surface is flat, in the sense that it lacks gaussian curvature. The cone _tip_, however, is a singularity of gaussian curvature, and perturbs the orbits strongly. This is the origin of the Wen-Zee action.
Tracing many orbits as a sheet is wrapped into a cone reveals that orbits away from the tip remain the same size, while the orbit that encircles the tip becomes smaller; this is a clear indication that the local density of states is higher at the cone tip, which is the principal manifestation of the Wen-Zee action. How much higher, and how this density is distributed, are properties of the particular topological state being explored, and are directly reflected in the mean orbital spin and central charge of this state.
When a four-mirror Fabry-Perot resonator is twisted out of the plane, the photons within it experience a round-trip image-rotation, turning the lab frame into a rotating frame. This physics may be understood as introducing coriolis and centrifugal forces on the photon, akin to Lorentz forces and harmonic anti-trapping of an electron in a magnetic field.
By twisting the resonator past the point where harmonic confinement precisely cancels centrifugal anti-confinement, we produce a resonator which exhibits three simultaneous cyclotron orbits, offset by 120 degrees from one another. This is precisely the physics of Landau levels on a cone: dynamics in flat space, with edges of the 1/3 of the plane identified with one another.
In a parallel effort, we are inducing photons to interact with one another using cavity-Rydberg-Electromagnetically-Induced-Transparency. In this effect, a single photon passing through a properly dressed atomic medium changes the index of refraction of that medium so strongly that any other photon passing through simultaneously is substantially lensed. This effect, in conjunction with the Landau-levels explored above, will allow us to create topological few-to-many body states composed of photons, rather than electrons.
Interactions between photons are mediated by an admixed collective Rydberg excitation whose spatial structure mirrors (no pun intended) that of the optical field. As the atoms move (due to their temperature) this spatial structure in the collective atomic excitation washes out, as shown here. This leads to cross-thermalization between atomic and optical degrees of freedom.
We have built a time-reversal broken topological photonic crystal, composed of an array of tunnel-coupled re-entrant resonators. This animation shows the evolution of a pulse injected on the edge of such a system, within an energetic band-gap; the observed chiral, back-reflection-free dynamics are a direct signature that the (LTI) system under examination exhibits Chern bands.
The geometry of a pair of the tunnel-coupled re-entrant microwave resonators employed for our Chern insulator work. These low-loss resonators do not require a lid, and can operate at extremely high-Q in the superconducting regime, making them excellent tools for integration with Josephson junctions for exploration of topological manybody physics.