The superconducting transmon qubit as a microwave resonator
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it when discussing driven resonator equations and the circuit behind transmon qubits, citing specific minute marks for the diagrams and derivations.
Recommended by 1 people across 1 different months, 2022 to 2025.
What it is
Daniel Sank, a quantum hardware researcher, gives a 49-minute tutorial on how superconducting transmon qubits work as microwave resonant circuits, built from RLC-style circuit analysis and a driven resonator model. It was recorded for the European Microwave 2020 conference.
What people said
Recommends Allie · 2025-12 · Physics Stack Exchange · on “Obtaining the Differential Equation for a Driven Resonator”
Daniel Sank [LINK] provided this diagram and two-order differential equation for a driven RLC resonator circuit in this youtube video [this video] , around minute 16. I am having trouble following his math. [LINK] In particular, every time I solve this system using Krichhoff's laws, I end up with a third order differential equation for $\Phi$ . Any help in figuring out how he derived this equation would be much appreciated! My (Wrong) Solution First I define the current from the voltage source as $I$ , the current through the inductor is $I_L$ and the current through the capacitor ( $C$ ) is $I_C$ . Additionally call the voltage drop over the resistor $V_1$ , the voltage drop over the decoupling
Cites 19 99 · 2022-05 · Physics Stack Exchange · on “Quantum nonlinear resonator/ transmon qubit”
The transmon qubit -quantum non-linear resonator- has 4 elements in the electrical circuit. ( Here is the circuit [this video] ) starting at the 21:00 mark. We have R, L, C,Cd and Voltage. I already know which L,C,Cd and Voltage I need to use and how powerful they should be in order to work at the level of quantum computing. How much tolerance in ohm should the $R$ have in this case?
Cites DanielSank · 2025-07 · Physics Stack Exchange · on “Intuitive explanation for Rabi oscillations in a two-level system”
We can understand Rabi oscillations intuitively by considering a driven nonlinear classical oscillator. Start with a linear oscillator, which can be modeled as $$\dot \alpha(t) = i \Delta \alpha(t) + \epsilon(t) \, .$$ In this equation, the oscillator has some resonce frequency $\omega_0$ but we're working in a rotating frame at some frequency $\Omega = \omega_0 - \Delta$ and the position of the oscillator in the lab frame is $x(t) \propto \text{Re} \left[ \alpha(t) \exp(i \Omega t) \right]$ . In this representation, $\alpha$ is known as a "phasor", i.e. a complex number representing the real coordinate $x$ in a particular rotating frame where we've extracted a sinusoidal time dependence (se