# Quantum frequency transducer and its applications

Advanced Devices & Instrumentation

Quantum frequency transducer (QFT) is a lead edge technology born from nonlinear optics, which is a basic tool in quantum information technology. QFT is a technology that the wavelength of a photonic state is coherently converted to another wavelength, while main properties of concerns are well preserved. Some main properties of concerns are single-photon coherence, entanglement, spectrum, and spatial information encoded in the light beam. Two main applications in quantum information science, which are quantum frequency interface (QFI) and frequency conversion detection (FCD). Usually, the wavelengths used for quantum computation and quantum sensing are in the visible wavelength or microwave band, which is rather different from those wavelengths used in the telecom band. Therefore, to build a quantum network and link quantum systems works at different wavelengths, a QFI is indispensable and can transduce quantum state from one wavelength to another wavelength. Another scenario in quantum information science that requires QFT is single-photon detection. Single-photon detectors at infrared wavelength are more complicated and have low performance by comparing to the visible detector counterpart. Converting the single photon from wavelengths with low detection performances to wavelengths with high detection performance can solve this issue well. Stimulated by prerequisites of QFI and FCD, many researches have been performed to update the parameters of QFT. In this review, the theory of QFT is introduced first, which shows the basic parameters and the factors that influence these parameters. Then, important progresses in QFT for used in QFI and FCD are introduced and summarized. Finally, perspectives of the research trends and challenges that remain to be solved are discussed.

By utilizing material with high effective nonlinear coefficient and relatively strong pump, the signal photons wavelength can be transduced to another wavelength by using sum-frequency generation (SFG) or difference-frequency generation (DFG). Under the approximation of an undepleted pump, for every annihilation of a signal photon, a converted photon is generated accordingly. Based on this, the interaction Hamiltonian of QFT can be written, and simple solutions can be obtained in the Heisenberg’s picture. In practical, when calculates the quantum conversion efficiency at different parameters, the coupling equation for nonlinear optics at the slow envelope approximation is required. There are some key parameters that are of great concerns to evaluate the quality of QFT, these key parameters includes: quantum conversion efficiency, photonic noise induced in the conversion processes, acceptance frequency bandwidth and spatial bandwidth. After giving the definition and main dependence factors for each parameter, the important methods and progresses to harness these parameters are introduced.

QFI have been realized for different kinds of photonic states, which ranges from single photon states and entangled states in both up-conversion and down-conversion processes. The photonics states are generated from various quantum systems, which ranges from nonlinear crystal and waveguide, cold atomic ensemble, quantum dots, color centers and trapped irons. The main aim of QFI is to bridge the frequency bandgap between different quantum components such as quantum memories, quantum computation units, quantum sensors and the low loss transmission windows of fibers or free space channels, which can be linked together as a quantum network. When high sensitivity single photon detection is not available in certain wavelength band, by converting its wavelength to a wavelength that has high sensitivity photon detector is an effective way to solve the detection problem at the original wavelength band. The frequency conversion detection (FCD) can be widely used in imaging, spectrum analyze, lidar, quantum key distribution and entanglement swapping.

Although QFT has been developed for decades of years, important progresses in key parameters have been achieved to use QFT for specific application, one needs to balance among the mutual restriction of these parameters. QFT is still a very active area for cutting edge researches, and some possible directions that deserve to be explored are as follows: The quantum optics and quantum spectrum researches can be extended to mid-infrared band based on frequency conversion single-photon detection; by combining QFT with interferometer techniques to develop new optical measurement methods, such as noncontact detection of infrared photons and optical phase amplification; to develop compact QFT devices that can be easily integrated into complex optical detection systems, then only high-performance silicon detector is needed for broadband spectrum detection. As the technique and material science move forwards in QFT, we will view important progresses in these directions in near future.

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