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arXiv:1605.08832 · Physical Review A

Method for identifying electromagnetically induced transparency in a tunable circuit quantum electrodynamics system

Qichun Liu, Tie-Fu Li, Xiao-Qing Luo, Hu Zhao, Wei Xiong, Ying-Shan Zhang, Zhen Chen, Jianshe Liu, Wei Chen, Franco Nori, J. S. Tsai, J. Q. You

Published May 31, 2016• 62 citations

Abstract

Electromagnetically induced transparency (EIT) has been realized in atomic systems, but fulfilling the EIT conditions for artificial atoms made from superconducting circuits is a more difficult task. Here we report an experimental observation of the EIT in a tunable three-dimensional transmon by probing the cavity transmission. To fulfill the EIT conditions, we tune the transmon to adjust its damping rates by utilizing the effect of the cavity on the transmon states. From the experimental observations, we clearly identify the EIT and Autler-Townes splitting (ATS) regimes as well as the transition regime in between. Also, the experimental data demonstrate that the threshold ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{AIC}}$ determined by the Akaike information criterion can describe the EIT-ATS transition better than the threshold ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{EIT}}$ given by the EIT theory.

DOI: 10.1103/physreva.93.053838

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Electromagnetically induced transparency (EIT) has been realized in atomic systems, but fulfilling the EIT conditions for artificial atoms made from superconducting circuits is a more difficult task. Here we report an experimental observation of the EIT in a tunable three-dimensional transmon by probing the cavity transmission. To fulfill the EIT conditions, we tune the transmon to adjust its damping rates by utilizing the effect of the cavity on the transmon states. From the experimental observations, we clearly identify the EIT and Autler-Townes splitting (ATS) regimes as well as the transition regime in between. Also, the experimental data demonstrate that the threshold

{\mathrm{\ensuremath{\Omega}}}_{\mathrm{AIC}}

determined by the Akaike information criterion can describe the EIT-ATS transition better than the threshold

{\mathrm{\ensuremath{\Omega}}}_{\mathrm{EIT}}

given by the EIT theory.

Autler-Townes splitting (ATS) and electromagnetically induced transparency (EIT) both yield transparency in an absorption profile, but only EIT yields strong transparency for a weak pump field due to Fano interference. Empirically discriminating EIT from ATS is important but so far has been subjective. We introduce an objective method, based on Akaike's information criterion, to test ATS vs EIT from experimental data for three-level atomic systems and determine which pertains. We apply our method to a recently reported induced-transparency experiment in superconducting-circuit quantum electrodynamics.

We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in a driven three-level superconducting artificial system which is a dressed-state system resulting from the coupling of a superconducting charge qubit (an artificial atom) and a transmission line resonator. In the frame of the dressed-state approach and steady-state approximation, we study the linear absorption of the dressed artificial system to a weak probe signal in depth. In light of the spectrum-decomposition method and some other restrictions, we obtain the explicit conditions for the dressed-state realization of EIT and ATS and present a corresponding "phase diagram". In contrast to usual bare systems, these conditions given in the dressed system have an extra dependency on the qubit-resonator parameters. And by varying the qubit's Josephson coupling energy we demonstrate a transition from EIT to ATS.

Autler-Townes splitting (ATS) and electromagnetically-induced transparency (EIT) both yield transparency in an absorption profile, but only EIT yields strong transparency for a weak pump field due to Fano interference. Empirically discriminating EIT from ATS is important but so far has been subjective. We introduce an objective method, based on Akaike's information criterion, to test ATS vs. EIT from experimental data and determine which pertains. We apply our method to a recently reported induced-transparency experiment in superconducting circuit quantum electrodynamics.

Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two phenomena that can affect the transmission of a probe field in the presence of a stronger field, both yielding transparency in the absorption profile. Being able to discriminate these two similar but distinct phenomena is of vital importance. Here we propose a scheme to describe the EIT and ATS phenomena in a plasmonic system. The proposed system consists of one radiative resonator and one subradiant resonator in metal-insulator-metal waveguide, and the transition is observed from the ATS model to the EIT model through three qualitative regions as the coupling strength decreases. In addition, we apply the method proposed by Anisimov to the induced transparency spectrum in our model, and numerically discerning EIT from ATS based on the Akaike's information criterion in a clear way.

Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler-Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a ?-type three-level system. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more appropriate for the modulated experiments. The proposed experiments are readily implemented in atomic gases, artificial atoms in superconducting quantum devices, or three-level meta-atoms in meta-materials.