Frequency conversion is a crucial process in various fields, particularly in nonlinear optics and electronics, enabling applications like laser fabrication and coupling of quantum systems. The need for efficient and wideband microwave frequency conversion is particularly pressing in the context of coupling diverse solid-state qubit systems. Solid-state qubits often have disparate resonant frequencies, hindering the creation of hybrid quantum networks. Coherent conversion of microwave photons is essential for frequency matching, and wideband conversion is crucial for quantum sensing applications. Traditional methods often involve tuning bias fields to align resonant frequencies, which can be problematic due to limitations in tunability, potential interference with the system under study, and challenges in miniaturization. This research proposes a novel method addressing these limitations by leveraging the nonlinear magnetic response in spintronic devices, specifically focusing on a hybrid system of NV centers in diamond and a CoFeB thin film. This approach promises a passive, wideband, and easily integrable on-chip solution for microwave frequency conversion.

Extensive research exists on frequency conversion in nonlinear optics, leading to advancements in laser technology and quantum system coupling. Efforts have focused on microwave-optical photon conversion for long-distance quantum communication. The challenge of frequency matching in solid-state qubits, particularly superconducting and spin qubits with varying microwave resonant frequencies, necessitates efficient coherent microwave frequency conversion. While nonlinear electric response is commonly exploited, the nonlinear magnetic response in spintronic devices remains relatively unexplored, despite promising potential for stronger interactions. Recent studies have demonstrated nonlinear four-wave mixing and high-order harmonic generation in magnetic films, hinting at the possibility of wideband frequency conversion using magnetic nonlinearities. This paper builds upon this prior work, exploring the nonlinear magnetic response from symmetry breaking in domain walls, offering a path towards a more efficient and wideband frequency conversion.

The study utilized a hybrid quantum system comprising NV centers in diamond coupled to a 15 nm CoFeB thin film deposited on a coplanar waveguide (CPW). Two configurations were employed: NV centers in nanodiamonds randomly dispersed on the CPW surface and NV centers in a bulk diamond placed near the CPW. Both configurations showed similar results. The NV centers act as sensors of stray fields generated by spin waves (magnons) excited in the CoFeB film by microwaves propagating through the gold waveguide. A static magnetic field was applied parallel to the microwave propagation, ensuring perpendicular alignment between the microwave and static fields. Optically detected magnetic resonance (ODMR) was used to detect high-order harmonic frequencies induced by the nonlinear magnetic response in the CoFeB film. The ODMR signal, measured as a decrease in photoluminescence (PL) intensity, was analyzed as a function of bias field and pump microwave frequency. Micromagnetic simulations were conducted using Mumax3 software to model different domain configurations and their influence on harmonic generation. Subsequently, multi-wave mixing experiments were performed using two microwave sources, sweeping their frequencies to identify conditions where the sum or difference frequencies (or their harmonics) resonated with the NV centers' ESR frequency. The wideband frequency conversion spectrum was measured, spanning from 100 MHz to 12 GHz (instrumentation limited). Finally, coherent quantum control experiments were conducted by measuring Rabi oscillations driven by harmonic microwave frequencies to assess the coherence of the converted magnons. The conversion efficiency was quantitatively analyzed by examining the Rabi frequencies.

The research successfully demonstrated wideband coherent microwave frequency conversion in a hybrid quantum system. High-order harmonic generation (up to 25th order) was observed, attributed to the strong nonlinear magnetic response from symmetry breaking in the domain walls of the CoFeB thin film. Micromagnetic simulations confirmed the correlation between domain wall length and the intensity of the harmonic response. Multi-wave mixing experiments showed a wide conversion bandwidth (0.1–12 GHz), with flexible combinations of two microwave inputs. The system successfully performed microwave sensing under a fixed magnetic field, eliminating the need for tunable bias fields. Up- and down-conversion protocols were demonstrated for wideband microwave sensing, significantly enhancing the bandwidth of solid-state qubit quantum sensing. Furthermore, coherent quantum control of NV centers was achieved using converted magnons, indicating good coherence preservation during the conversion process. A conversion efficiency of 5.9% was obtained for the third-order conversion, quantified through Rabi frequency analysis.

The findings demonstrate a significant advance in microwave frequency conversion, achieving a wide bandwidth not readily attainable with conventional techniques. The use of nonlinear magnetic response in spintronic devices offers advantages in terms of compactness, integrability, and the avoidance of phase matching issues. The successful implementation of wideband microwave sensing without the need for tunable magnetic fields offers significant advantages for quantum sensing applications, enabling miniaturization and simplified experimental setups. The demonstration of coherent quantum control using frequency-converted magnons highlights the potential for coupling diverse solid-state qubit systems. The observed nonlinear effects are not solely confined to domain walls, implying further enhancement potential by engineering magnetic textures and utilizing advanced materials. This research opens new avenues for the development of nonlinear spintronic devices, offering potential alternatives to traditional semiconductor devices.

This research successfully demonstrated a novel wideband coherent microwave frequency conversion method based on magnon nonlinearity in a hybrid quantum system. The method's capabilities in wideband microwave sensing and coherent quantum control offer significant advancements for quantum sensing and quantum information processing. Future research directions include exploring the potential of other spintronic materials and further optimization of the conversion efficiency by manipulating magnetic textures and device geometry.

The current experimental setup's bandwidth is limited by the available instrumentation; higher frequencies are likely achievable with upgraded equipment. The precise mechanisms contributing to the nonlinear response beyond domain walls require further investigation. A complete theoretical model accounting for all observed phenomena is yet to be developed. Further research is needed to fully understand and optimize the conversion efficiency.