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arXiv:1103.2223 · Physical Review B

Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system

Jian Li, Gheorghe Sorin Paraoanu, Katarina Cicak, Fabio Altomare, Jae I. Park, Raymond W. Simmonds, Mika A. Sillanpää, Pertti Juhani Hakonen

Published Sep 30, 2011• 56 citations

Abstract

We present a detailed theoretical analysis of a multilevel quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanp\"a\"a et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.

DOI: 10.1103/physrevb.84.104527

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We present a detailed theoretical analysis of a multilevel quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanp"a"a et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.

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 the experimental data.

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.

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.

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%

.

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.