Topological Photonics on Superconducting Quantum Circuits with Parametric Couplings

Abstract

Topological phases of matter are an exotic phenomenon in modern condensed matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing research field. Due to the flexibility and diversity of superconducting quantum circuits system, it is a promising platform to realize exotic topological phases of matter and to probe and explore topologically‐protected effects in new ways. Here, theoretical and experimental advances of topological photonics on superconducting quantum circuits—via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and their coupled system—are reviewed. On superconducting circuits, the flexible interactions and intrinsic nonlinearity make topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less‐explored fundamental physics.

Quantum transport in nonlinear Rudner-Levitov models

“…These phenomena can be understood on the basis of the dynamic behavior of the effective time and position dependent hopping terms containing contributions of both the linear and nonlinear couplings. Our findings are relevant to experimental platforms, such as arrays of coupled optical waveguides and cavities, but may also be adapted to acoustic or electric circuit resonators as well as superconducting quantum circuits [25][26][27].…”

Difference‐Frequency Generation with and without Quantum Interference in Superconducting Circuits

“…Inspired by atomic cavity QED, coherent couplings of superconducting quantum qubits [25] to microwave fields have led to a lot of quantum optical phenomena, which opens up the fascinating realm of circuit QED. [26][27][28][29][30] Different from naturally occurring atoms, superconducting circuits can be designed and controlled artificially by tuning external parameters. Hence, by a controllable manner, circuit QED has been used to achieve many previously unproved or novel phenomena, including ultrastrong coupling regime, [31] dynamical Casimir effect, [32] and collapse and revival of coherent state.…”

Non-reciprocal population dynamics in a quantum trimer

“…In a pioneering experiment for chiral quantum optics, the team observed chiral ground-state currents and probed the unusual quantum phases of strongly interacting photons (for a review of strongly interacting photons, see [24]). The required synthetic magnetic fields were realized by sinusoidally modulating their qubit-qubit couplings, which led to the necessary complex phases attached to the coherent coupling constants [25]. Such complex phases can appear in various ways; for example: in a real magnetic field through the Peierls substitution [26,27], via a Peierls tunnelling phase even in the absence of an external magnetic field [28], using a time-dependent coupling Hamiltonian [29,30], constructing synthetic gauge fields using synthetic lattices [31], using light-induced gauge potentials [32][33][34], designing inductor-capacitor circuits [35], by considering circularly polarized dipoles [36] or by careful pumping, which gives rise to complex potentials [37].…”