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

TL;DR

This paper provides a theoretical analysis of a three-level superconducting quantum system under two-tone driving, focusing on the Autler-Townes effect, decoherence, and dark states, with implications for experimental data interpretation.

Contribution

It introduces analytical solutions for a multi-level superconducting system under two-tone driving, extending models to five levels for better experimental agreement, and analyzes the structure of dark states.

Findings

Analytical solutions describe Autler-Townes splitting in superconducting qubits.

Extending the model to five levels improves agreement with experimental data.

Stationary states are closely related to dark states.

Abstract

We present a detailed theoretical analysis of a multi-level quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as the Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanpaa 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.