Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED

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Superconducting qubits1,2 behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multiphoton excitations3,4,5,6,7 occupies an important role. Moreover, coupling superconducting qubits to onchip microwave resonators has given rise to the field of circuit quantum electrodynamics8,9,10,11,12,13,14,15 (QED). In contrast to quantum-optical cavity QED (refs 16, 17, 18, 19), circuit QED offers the tunability inherent to solid-state circuits. Here, we report on the observation of key signatures of a two-photon-driven Jaynes–Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit20 coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one- and two-photon-driven level anticrossings of the qubit–resonator system. This results from the controlled symmetry breaking of the system hamiltonian, causing parity to become a not-well-defined property21. Our study provides fundamental insight into the interplay of multiphoton processes and symmetries in a qubit–resonator system.

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Figure 1: Experimental architecture and theoretical model.
Figure 2: Qubit microwave spectroscopy: data and simulations.
Figure 3: Qubit microwave spectroscopy close to the qubit–resonator anticrossing under two-photon driving: data and simulations.
Figure 4: Two-photon spectroscopy simulations close to the optimal point using the time-trace-averaging method.


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We thank H. Christ for fruitful discussions. This work is supported by the Deutsche Forschungsgesellschaft through the Sonderforschungsbereich 631. Financial support by the Excellence Cluster ‘Nanosystems Initiative Munich (NIM)’, the EuroSQIP EU project, the Ikerbasque Foundation and UPV-EHU Grant GIU07/40 is gratefully acknowledged. This work is partially supported by CREST-JST, JSPS-KAKENHI(18201018) and MEXT-KAKENHI(18001002).

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Correspondence to Frank Deppe.

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Deppe, F., Mariantoni, M., Menzel, E. et al. Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED. Nature Phys 4, 686–691 (2008) doi:10.1038/nphys1016

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