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arXiv:1308.0520 · Physical Review B

Autler-Townes splitting in a three-dimensional transmon superconducting qubit

S P Novikov, J. E. Robinson, Z.K. Keane, Baladitya Suri, F. C. Wellstood, B. S. Palmer

Published Aug 2, 2013• 61 citations
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Abstract

We have observed the Autler-Townes doublet in a superconducting Al/AlO${}_{X}$/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time ($\ensuremath{\sim}$$40\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{s}$) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be $99.6%--99.9%$.

DOI
10.1103/physrevb.88.060503

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We observe the Autler—Townes splitting effect in a Δ-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.
We experimentally study a vacuum-induced Autler-Townes doublet in a superconducting three-level artificial atom strongly coupled to a coplanar waveguide resonator and simultaneously to a transmission line. The Autler-Townes splitting is observed in the reflection spectrum from the three-level atom in a transition between the ground state and the second excited state when the transition between the two excited states is resonant with a resonator. By applying a driving field to the resonator, we observe a change in the regime of the Autler-Townes splitting from quantum (vacuum-induced) to classical (with many resonator photons). Furthermore, we show that the reflection of propagating microwaves in a transmission line could be controlled by different frequency microwave fields at the single-photon level in a resonator.
We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The inverse Fourier transform of cavity spectrum indicates that there is a quantum coherence Rabi oscillation of the populations between cavity and qubit.
When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.
We report on the spectrum of a superconducting transmon device coupled to a planar superconducting resonator in the strong dispersive limit where discrete peaks, each corresponding to a different number of photons, are resolved. A thermal population of 5.474 GHz photons at an effective resonator temperature of T = 120 mK results in a weak n = 1 photon peak along with the n = 0 photon peak in the qubit spectrum in the absence of a coherent drive on the resonator. Two-tone spectroscopy using independent coupler and probe tones reveals an Autler–Townes splitting in the thermal n = 1 photon peak. The observed effect is explained accurately using the four lowest levels of the dispersively dressed qubit–resonator system and compared to results from numerical simulations of the steady-state master equation for the coupled system.
By applying a coupling microwave field gated by random-telegraph-noise (RTN), we report the experimental demonstration of dynamically modulated Autler-Townes effect (ATE) in an artificial atom---a superconducting transmon qubit---and obtain the distinguished characteristics when a system is affected by RTN. By further applying another coupling microwave filed on the transmon, we use an intense bichromatic field to couple the energy levels. Depending on the detuning of the couplers, remarkable interference patterns emerge in the spectrum, which come from the dressed states induced by the modulated ATE. Numerical calculations agree well with the experimental data.