1. cQED Susceptibility of Superconducting Transmons coupled to a Microstrip Resonator Cavity David Pappas, Martin Sandberg, Jiansong Gao, Michael Vissers NIST, Boulder, CO 80303 Anton Kockum, Goran Johansson Chalmers University of Technology, G ӧ teborg, Sweden

2. Outline What do you do when your qubit frequency is too close to your cavity? “Quantum art” Response of a coupled qubit-cavity system to a strong drive at finite temperature – Singly dressed - qubit + cavity – Doubly dressed system – qubit+cavity+ drive two photon processes – Triply dressed three photon processes

3. “2½D” - Transmon coupled to microstrip cavity Sandberg, et al., APL 102, 072601 (2013) Qubit

4. Cavity response to a probe tone VNA S 21 probe 1 2 Measure transmission, S 21 at T ∽ 100 mK Susceptibility of the system frequency & power dependence High power – bare cavity Low power – excitation spectrum of “singly dressed” qubit+cavity cavity Qubit-cavity excitations High power Low power

5. Model with Jaynes-Cummings Hamiltonian Excitation spectrum TransitionFrequency (GHz) 0 - 718.535 0 - 617.650 0 - 513.225 0 - 412.660 1 - 712.431 0 - 312.003 2 - 711.919 1 - 611.546 2 - 611.034 1 - 57.121 0 - 26.616 2 - 56.609 1 - 46.556 3 - 76.532 0 - 16.104 2 - 46.044 1 - 35.899 4 - 75.875 3 - 65.647 2 - 35.387 5 - 75.310 4 - 64.990 5 - 64.425 3 - 51.222 6 - 70.885 3 - 40.657 4 - 50.565 1 - 20.512

6. Line identification TransitionFrequency (GHz) 0 - 718.535 0 - 617.650 0 - 513.225 0 - 412.660 1 - 712.431 0 - 312.003 2 - 711.919 1 - 611.546 2 - 611.034 1 - 57.121 0 - 26.616 2 - 56.609 1 - 46.556 3 - 76.532 0 - 16.104 2 - 46.044 1 - 35.899 4 - 75.875 3 - 65.647 2 - 35.387 5 - 75.310 4 - 64.990 5 - 64.425 3 - 51.222 6 - 70.885 3 - 40.657 4 - 50.565 1 - 20.512 cavity 0-2 1-4 3-7 Use low power probe tone to measure the system Add high power drive (i.e. pump) for susceptibilty

7. Susceptibility measurement VNA S 21 probe 1 2 drive Drive tone, D (GHz)