Thermalizing channel states for rapid qubit heating

Abstract

Although known for negatively impacting the operation of superconducting qubits, thermal baths are shown to exert qubit control in a positive way, provided they are properly engineered. We demonstrate an experimental method to engineer the transduction of microwave driving into heat flow through a leaky resonator. Given the precise conversion, a qubit receiving the heat flow obtains a quasi-thermal equilibrium with arbitrary target temperature in hundreds of nanoseconds. We show that the dynamics of the quantum transducing process is described by thermalizing channel states, generated from the double dressings of the resonator by the semi-classical driving and the qubit-resonator coupling. Their spectrum, coupling, and driving strength determine the channel rate of energy flow, along with the relaxation rates of photon leakage into the bath. The analytical prediction is shown to match well with the experimental measurements on an Xmon qubit circuit.

Figures (4)

• Figure 1: (a) Conceptual illustration of thermalizing channels of the QTM constructed from hybridizing a resonator mode with a continuous multimode bath. While being energy fed by an external pump, the leaky resonator has its states broadened by bath couplings so that multi-photon resonance with the bath are engaged before photons are absorbed by the two-level qubit. The bath resonance essentially converts single-mode photons (blue circles) into broad-spectrum thermal photons (red circles) such that energy carried by the driving photons are rendered into a heat flow. The LC circuit represents the low-Q coplanar stripped waveguide that provides the resonator modes for generating the thermalizing channels. (b) Equivalent circuit on the superconducting qubit chip, where the target Xmon qubit $Q_{T}$ while being driven from the left is monitored by a readout subcircuit (the shaded region) on the right. The readout is realized by a dispersively coupled qubit $Q_{RO}$, whose frequency shift is registered on another dedicated resonator.
• Figure 2: Measured excited state population or inversion $P_{e}$ (grey dots) of the Xmon qubit against time: (a) exhibiting Rabi oscillation (about the blue $P_{e}=1/2$ dash line) when the driving frequency $\omega_{d}/2\pi=5.46$ GHz is resonant with the qubit but far detuned from the leaky resonator frequency $\omega_{r}/2\pi=5.445$ GHz; (b) exhibiting rapid convergence to a saturated level when $\omega_{d}/2\pi=5.45$ GHz is simultaneously near resonant with both the qubit and the resonator, which is always under $P_{e}=1/2$. The orange solid curve are theoretical fit computed from numerical methods. The inset shows that even when the resonator is far-detuned from the driving, the bath mediation is effective as the discrepancy becomes apparent between the measured $P_{e}$ and the numerical prediction assuming only qubit-drive resonance, as time increases.
• Figure 3: Long-term population $P_{e}$ variation of the qubit excited state on a semi-log scale over time at driving strengthes $\Omega/2\pi=1.5$ MHz (blue), 2 MHz (orange), 3.5 MHz (green), and 5 MHz (purple). The circled dots are the experimental measurements. The solid curves are theoretical predictions from the analytical solutions to the master equation using the same experimental $\Omega$ values as parameters, showing a great fit to the measurements. The background is shaded in two colors to visually discern the separation of two dynamic stages: (i) the light-blue endothermic stage and (ii) the light-orange quasi-equilibrium stage.
• Figure 4: Qubit inversion $P_{e}$ plotted (a) as contour level against the driving frequency $\omega_{d}$ and driving strength $\Omega$; and (b) against $\omega_{d}$ only at the fixed strength $\Omega/2\pi=5.8$ MHz.