cQED Susceptibility of Superconducting Transmons coupled to a Microstrip Resonator Cavity

David Pappas, Martin Sandberg, Jiansong Gao, Michael VissersNIST, Boulder, CO 80303

Anton Kockum, Goran JohanssonChalmers University of Technology, Gӧteborg, Sweden

OutlineWhat 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

“2½D” - Transmon coupled to microstrip cavity• Standard large-pad transmon,

GHz• Measured with microstrip cavity

– Measured at 20 mK– Radiation decay suppressed due to

proximity of ground plane• T1 2 - 10 s

– Coupling strength MHz– = 6.525 Ghz

• – Lifetime strongly Purcell limited– In resonant regime (not dispersive)

Sandberg, et al., APL 102, 072601 (2013)

Qubit

Cavity response to a probe toneVNA S21

probe

1 2

• Measure transmission, S21 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

Model with Jaynes-Cummings Hamiltonian• Include 4 lowest qubit states, ,,, 3 lowest photon numbers in cavity, ,,

Excitation spectrum Transition Frequency (GHz)

0 - 7 18.5350 - 6 17.6500 - 5 13.2250 - 4 12.6601 - 7 12.4310 - 3 12.0032 - 7 11.9191 - 6 11.5462 - 6 11.0341 - 5 7.1210 - 2 6.6162 - 5 6.6091 - 4 6.5563 - 7 6.5320 - 1 6.1042 - 4 6.0441 - 3 5.8994 - 7 5.8753 - 6 5.6472 - 3 5.3875 - 7 5.3104 - 6 4.9905 - 6 4.4253 - 5 1.2226 - 7 0.8853 - 4 0.6574 - 5 0.5651 - 2 0.512

Line identificationTransition Frequency (GHz)

0 - 7 18.5350 - 6 17.6500 - 5 13.2250 - 4 12.6601 - 7 12.4310 - 3 12.0032 - 7 11.9191 - 6 11.5462 - 6 11.0341 - 5 7.1210 - 2 6.6162 - 5 6.6091 - 4 6.5563 - 7 6.5320 - 1 6.1042 - 4 6.0441 - 3 5.8994 - 7 5.8753 - 6 5.6472 - 3 5.3875 - 7 5.3104 - 6 4.9905 - 6 4.4253 - 5 1.2226 - 7 0.8853 - 4 0.6574 - 5 0.5651 - 2 0.512

cavitycavity

0-21-43-7

• Use low power probe tone to measure the system

• Add high power drive (i.e. pump) for susceptibilty

Susceptibility measurementVNA S21

probe

1 2

drive

Drive tone, D (GHz)