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arXiv:2403.08578 · Physical Review A

Coherent competition and control between three-wave mixing and four-wave mixing in superconducting circuits

Miao‐Xiang Liang, Yu-Xiang Qiu, Hai‐Chao Li, Wei Xiong

Published Jan 27, 2025• 0 citations

Abstract

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.

DOI: 10.1103/physreva.111.013716

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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.

We investigate the interplay between six-wave mixing (SWM) and four-wave mixing (FWM) resulting from atomic coherence and polarization beat in a four-level atomic system. The dressed FWM evolution and competition pathways can be controlled by the coupling field to exhibit two FWM and SWM turning points, FWM+SWM, and FWM+FWM interference regions. Quantum interference between two FWM or one FWM and one SWM channels leads to nonlinear signal enhancement and suppression under different conditions. The fifth-order nonlinear response can be obtained by the phase control of the polarization beat between the FWM and SWM signals.

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.

Using phase control between four-wave mixing (FWM) and six-wave mixing (SWM) channels in a four-level atomic system, we demonstrate temporal and spatial interferences between these two nonlinear optical processes. Efficient and coexisting FWM and SWM signals are produced in the same electromagnetically induced transparency window via atomic coherence. The temporal interference has a femtosecond time scale corresponding to the optical transition frequency. Such studies of intermixing between different order nonlinear optical processes with a controllable phase delay can have important applications in high-precision measurements, coherence quantum control, and quantum information processing.

We experimentally investigate the soliton formation and dynamics in the nonlinear propagation of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence in a three-level atomic system, under the competition between focusing and defocusing nonlinearities, as well as between gain and dissipation, due to the third- and fifth-order nonlinear susceptibilities with opposite signs. With multi-parameter controllability and nonlinear competition in the system, fundamental, dipole, and azimuthally-modulated vortex FWM solitons can transform mutually from one to the other. Such investigations have potential applications in optical pattern formation and control, and all-optical communication.

We demonstrate the controllable nonlinear microwave modulation in a cyclically driven three-level superconducting Josephson system. By designing two subtle matched conditions in the △-type atom-field configuration, a new physical mechanism – combined action of nonlinear wave mixing and wave interference – is developed and leads to not only amplification but also attenuation for two microwave signals. Our results show that such a nonlinear manipulation of the signal transition from enhancement to damping can be tuned in a large scope by controlling the relative phase and the driving-field frequency and thus the solid-state Josephson system can act as a phase- and frequency-controlled amplitude modulator. Our study opens up a fascinating perspective for its widespread applications in nonlinear optics and quantum information science.

We demonstrate efficient energy exchange during propagation between four-wave-mixing (FWM) and six-wave-mixing (SWM) signals generated in a four-level inverted-Y atomic system, which fall in the electromagnetically induced transparency window. After an initial growth distance for both FWM and SWM fields in the atomic medium, these two nonlinear optical processes compete and exchange energy between them, and eventually reach their respective steady-state values at long interaction distance. This energy exchange phenomenon can be explained by considering established atomic coherences among various atomic states and quantum interferences between three-photon and five-photon excitation pathways. Understanding these high-order nonlinear optical processes and interplays between them can be very important for correlated FWM (or SWM) photon-pair generations and quantum information processing.