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arXiv:0812.4384 · Physical Review Letters

Measurement of Autler-Townes and Mollow Transitions in a Strongly Driven Superconducting Qubit

Matthias Baur, Stefan Filipp, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, Peter Leek, Alexandre Blais, Andreas J. Wallraff

Published Jun 19, 2009• 188 citations
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Abstract

We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive readout of the qubit coupled off resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited qubit states and dispersive level shifts due to off-resonant drives.

DOI
10.1103/physrevlett.102.243602

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We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive readout of the qubit coupled off resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited qubit states and dispersive level shifts due to off-resonant drives.
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.
The damped and coherently-driven JaynesndashndashndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' 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 experimentally investigated the energy spectrum of two strongly coupled tunable transmon atoms with a coupling energy of 300[Formula: see text]MHz. The energy levels are dispersively probed through a readout resonator coupled to the atoms. The higher excited level energies could be probed by 2-photon or 3-photon processes. The power dependence of the readout transmission showed that the n-photon process satisfies the power law with a power of [Formula: see text]1. We also observed the Autler-Townes splitting, by probing the Rabi frequencies resonant to one of the higher levels driven by an external microwave field. Coherent operations on the atoms reveal that the relaxation time (T1) and dephasing time (T2) are approximately 62[Formula: see text]ns and 51[Formula: see text]ns, respectively.
Routers, switches, and repeaters are essential components of modern information-processing systems. Similar devices will be needed in future superconducting quantum computers. In this work we investigate experimentally the time evolution of Autler-Townes splitting in a superconducting phase qubit under the application of a control tone resonantly coupled to the second transition. A three-level model that includes independently determined parameters for relaxation and dephasing gives excellent agreement with the experiment. The results demonstrate that the qubit can be used as a ON/OFF switch with 100 ns operating time-scale for the reflection/transmission of photons coming from an applied probe microwave tone. The ON state is realized when the control tone is sufficiently strong to generate an Autler-Townes doublet, suppressing the absorption of the probe tone photons and resulting in a maximum of transmission.
Sideband transitions are spectroscopically probed in a system consisting of a Cooper pair box strongly but nonresonantly coupled to a superconducting transmission line resonator. When the Cooper pair box is operated at the optimal charge bias point, the symmetry of the Hamiltonian requires a two-photon process to access sidebands. The observed large dispersive ac-Stark shifts in the sideband transitions induced by the strong nonresonant drives agree well with our theoretical predictions. Sideband transitions are important in realizing qubit-photon and qubit-qubit entanglement in the circuit quantum electrodynamics architecture for quantum information processing.