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Optics Letters

Coexistence of three-wave, four-wave, and five-wave mixing processes in a superconducting artificial atom

Hai‐Chao Li, Guo-Qin Ge, Haiyang Zhang

Published Mar 12, 2015• 5 citations
Publisher

Abstract

We present a theoretical study of multiwave mixing in a driven superconducting quantum qubit (artificial atom) with a cyclic Ξ-type three-level structure. We first show that three-wave mixing (3WM), four-wave mixing (4WM), and five-wave mixing (5WM) processes can coexist in the microwave regime in such an artificial system due to the absence of selection rules. Because of electromagnetically induced transparency suppression of linear absorption in a standard Ξ-type configuration, the generated 4WM is enhanced greatly and its efficiency can be as high as 0.1% for only a single artificial atom. We also show that Autler-Townes splitting occurs in the 3WM and 5WM spectra and quantum interference has a significant impact on the total signal intensity being a coherent superposition of these two signals.

DOI
10.1364/ol.40.001133

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We present a theoretical study of multiwave mixing in a driven superconducting quantum qubit (artificial atom) with a cyclic Ξ-type three-level structure. We first show that three-wave mixing (3WM), four-wave mixing (4WM), and five-wave mixing (5WM) processes can coexist in the microwave regime in such an artificial system due to the absence of selection rules. Because of electromagnetically induced transparency suppression of linear absorption in a standard Ξ-type configuration, the generated 4WM is enhanced greatly and its efficiency can be as high as 0.1% for only a single artificial atom. We also show that Autler-Townes splitting occurs in the 3WM and 5WM spectra and quantum interference has a significant impact on the total signal intensity being a coherent superposition of these two signals.
Exploring intermixing and interplay between different frequency-mixing processes has always been one of the interesting subjects at the interface of nonlinear optics with quantum optics. Here we investigate coherent competition and control between three-wave mixing (TWM) and four-wave mixing (FWM) in a cyclic $\mathrm{\ensuremath{\Delta}}$-type three-level superconducting quantum system. In the weak control-field regime, strong competition leads to an alternating oscillation between TWM and FWM signals and this oscillation is a signature of strong energy exchange between these two nonlinear processes. In particular, such oscillation is absent from conventional multiwave mixing in atomic systems. Surprisingly, synchronous TWM and FWM processes are demonstrated in the strong control-field regime and, at the same time, their efficiencies can be as high as 42 and 47%, respectively. Our paper shows that these competitive behaviors between TWM and FWM can be manipulated by tuning the control-field intensity.
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.
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.
The dressed four- and six-wave mixings in a V-type four-level system are considered. Under two different dressed conditions, two- and three-photon resonant Autler–Townes splittings, accompanied by enhancement and suppression of wave mixing signal, are obtained analytically. Meanwhile, an electromagnetic induced transparency of multi-wave mixing is presented, which shows multiple peaks and asymmetric effects caused by one-photon, two-photon and three-photon resonances, separately. The slow light propagation multiple region of multi-wave mixing signal is also obtained.
We demonstrate Autler-Townes (AT) splitting of four-wave mixing in an electromagnetically induced transparency window, which results from the destructive interference between a three-photon process and a five-photon process. The primary and secondary AT splittings are achieved via induced atomic coherence in a four-level Y-type atomic system. Theoretical calculations fit well with the experimentally measured results. Such controlled multichannel splitting of nonlinear optical signals can have potential applications in optical communication and quantum information processing.