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A recent experiment [Cohen et al., Science 382, 542 (2023)] observed a quantized $e^2/2h$ conductance tunneling into a fractional quantum hall edge in the strong coupling limit, which is consistent with the prediction of a quantum Hall transformer. We model this quantum point contact (QPC) as a quantum wire with a spatially-varying Luttinger parameter and a back-scattering impurity and use a numerical solution to find the wavepacket scattering and microwave (i.e. finite frequency) has conductance at the interface. We then compare the microwave conductance to an analytic solution of a Luttinger liquid with an abruptly varying Luttinger parameter and a back-scattering impurity, which is obtained by mapping the problem to a boundary sine-Gordon (BSG) model. Finally, we show that the quantum Hall transformer can survive the inclusion of the domain wall which is expected to occur in a wide QPC, which is experimentally relevant, provided the momentum change in the QPC is generated by electrostatics. We find that back-scattering generated by the domain wall is of an order of magnitude consistent with the experiment., Comment: 5 pages, 3 figures

In ergodic quantum spin chains, locally conserved quantities such as energy or particle number generically evolve according to hydrodynamic equations as they relax to equilibrium. We investigate the complexity of simulating hydrodynamics at infinite temperature with multiple methods: time evolving block decimation (TEBD), TEBD with density matrix truncation (DMT), the recursion method with a universal operator growth hypothesis (R-UOG), and operator-size truncated (OST) dynamics. Density matrix truncation and the OST dynamics give consistent dynamical correlations to $t=60/J$ and diffusion coefficients agreeing within 1%. TEBD only converges for $t\lesssim 20$, but still produces diffusion coefficients accurate within 1%. The universal operator growth hypothesis fails to converge and only matches other methods on short times. We see no evidence of long-time tails in either DMT or OST calculations of the current-current correlator, although we cannot rule out that they appear at longer times. We do observe power-law corrections to the energy density correlator. At finite wavelength, we observe a crossover from purely diffusive, overdamped decay of the energy density, to underdamped oscillatory behavior similar to that of cold atom experiments. We dub this behavior "hot band second sound" and offer a microscopically-motivated toy model., Comment: 18 pages, 13 figures

Discrete time crystals, which are phases of matter that break the discrete time translational symmetry of a periodically driven system, have generated a wave of recent interest and activity. In this work, we propose a classical system of weakly nonlinear parametrically driven coupled oscillators as a testbed to understand these phases. Such a system of oscillators in the presence of dissipation has a period-doubling instability only at long wavelengths where a large number of oscillators are in phase. To show that this instability leads to a discrete time crystal when exposed to noise and non-linearity, we derive a general condition to predict when a Markov process will break time-translation symmetry. The first requirement of this condition is that the Markov chain over doubled time steps has a stationary probability distribution that spontaneously breaks a local symmetry. The second requirement is that the order parameter flips sign over a single time step. We show that our system of oscillators features period-doubling and yields a stationary probability distribution given by a spatially continuous Ginzburg-Landau Hamiltonian with spontaneous symmetry breaking. We then discuss applications of the general condition to existing time crystal platforms., Comment: 9 pages, 2 figures

We have developed a process to mass-produce quantum dot micropillar cavities using direct-write lithography. This technique allows us to achieve high volume patterning of high aspect ratio pillars with vertical, smooth sidewalls maintaining a high quality factor for diameters below 2.0 $\mu$m. Encapsulating the cavities in a thin layer of oxide (Ta$_2$O$_5$) prevents oxidation in the atmosphere, preserving the optical properties of the cavity over months of ambient exposure. We confirm that single dots in the cavities can be deterministically excited to create high purity indistinguishable single photons with interference visibility $(96.2\pm0.7)\%$.

Disorder in a proximitizing bulk superconductor can scatter quasiparticles in a putative topological superconductor and eventually destroy the topological superconducting state. We use a scattering approach and a random-matrix calculation to estimate the disorder scattering time in a topological Josephson junction. We find that the disorder scattering rate from the bulk of the superconductor, even in the strong coupling limit, is suppressed in the ratio of Fermi momenta between the semiconductor and superconductor. This suppression of disorder scattering is accompanied by near perfect Andreev reflection at such semiconductor/superconductor interfaces, which can be used as a signature of such clean proximity effect. We also find that these results can be understood by a semiclassical estimate of scattering. We discuss limits in other systems such as the semiconductor nanowire where disorder scattering is suppressed according to similar classical estimates., Comment: 13 pages, 2 figures

The $O(3)$ non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, and provides a simple system in which to study topological effects. In lattice QCD, the gradient flow has been demonstrated to remove ultraviolet singularities from the topological susceptibility. In contrast, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit, even in the presence of the gradient flow. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$., Comment: The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology