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Journal of Electronic Research and Application

Temporal SU(1,1) Interferometer Based on Four- Wave Mixing Time Lens and Its Applications in Ultrafast Time-Frequency Manipulation

Tianyu Liu, Zepeng Liu

Published Aug 8, 2025• 0 citations
Publisher

Abstract

Temporal optics, which enables lossless manipulation of ultrafast pulses, offers a new dimension for the regulation of quantum optical fields. In this paper, we established a temporal Fourier transform (TF) system based on a four-wave mixing (FWM) time lens and constructed a full quantum theoretical model for the resulting temporal SU(1,1) interferometer. This interferometer has high temporal resolution, can impose interference in both time and frequency domains, and is sensitive to the phase derivative. By introducing linear time-varying phase modulation, we achieved sub-picosecond precision in temporal autocorrelation measurements and generated ​an optical frequency comb with a fixed interval based on a feedback iteration mechanism. Theoretical analysis reveals ​the crucial regulatory role of time-frequency coupling in quantum interference, providing novel solutions for ultrafast quantum imaging, temporal mode encoding, and the generation of optical frequency quantization.

DOI
10.26689/jera.v9i4.11468

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Temporal optics, which enables lossless manipulation of ultrafast pulses, offers a new dimension for the regulation of quantum optical fields. In this paper, we established a temporal Fourier transform (TF) system based on a four-wave mixing (FWM) time lens and constructed a full quantum theoretical model for the resulting temporal SU(1,1) interferometer. This interferometer has high temporal resolution, can impose interference in both time and frequency domains, and is sensitive to the phase derivative. By introducing linear time-varying phase modulation, we achieved sub-picosecond precision in temporal autocorrelation measurements and generated ​an optical frequency comb with a fixed interval based on a feedback iteration mechanism. Theoretical analysis reveals ​the crucial regulatory role of time-frequency coupling in quantum interference, providing novel solutions for ultrafast quantum imaging, temporal mode encoding, and the generation of optical frequency quantization.
Interferometers are highly sensitive to phase differences and are utilized in numerous schemes. Of special interest is the quantum SU(1,1) interferometer which is able to improve the sensitivity of classical interferometers. We theoretically develop and experimentally demonstrate a temporal SU(1,1) interferometer based on two time lenses in a 4f configuration. This temporal SU(1,1) interferometer has a high temporal resolution, imposes interference on both time and spectral domains, and is sensitive to the phase derivative which is important for detecting ultrafast phase changes. Therefore, this interferometer can be utilized for temporal mode encoding, imaging, and studying the ultrafast temporal structure of quantum light.
Time-lenses can image ultrafast signals in time. Placing them in a 2-f configuration leads to Fourier transform of the input signal and ultrafast spectroscopy. We utilized two time-lenses in a 4-f configuration and formed an interferometer in the time domain. Our time lenses are based on four-wave mixing process, generating an idler beam which serves as the output. The output from the first time-lens is the input to the second time-lens. At the output of the second time-lens, we get an interference between the signal beams of both time-lenses and the idler beams of both time-lenses. This interference is sensitive to ultrafast phase shifts in time and can lead to interfere signals in different times. This interferometer is good for quantum imaging, and studying the temporal structure of entangled photons. In this talk we will demonstrate the interferometer, how we exploit time-lenses for interferometry, the application of the interferometer, and our experimental results.
Quantum interferometers are able to improve the sensitivity of classical interferometers beyond the shot-noise limit. This is done by employing squeezed states of light and destructive interference of the noise in the system. We developed a quantum SU(1,1) interferometer in the time domain. Our nonlinear quantum interferometer creates interference of the input signals at different times and frequencies. We can control the time and frequency differences for investigating the full temporal and spectral structure of the signal. This quantum interferometer can be utilized for sensing ultrafast phase changes, quantum imaging, temporal mode encoding, and studying the temporal structure of entangled photons.
Techniques to control the spectro-temporal properties of quantum states of light at ultrafast time scales are crucial for numerous applications in quantum information science. In this work, we report an all-optical time lens for quantum signals based on Bragg-scattering four-wave mixing with picosecond resolution. Our system achieves a temporal magnification factor of 158 with single-photon level inputs, which is sufficient to overcome the intrinsic timing jitter of superconducting nanowire single-photon detectors. We demonstrate discrimination of two terahertz-bandwidth, single-photon-level pulses with 2.1 ps resolution (electronic jitter corrected resolution of 1.25 ps). We draw on elegant tools from Fourier optics to further show that the time-lens framework can be extended to perform complex unitary spectro-temporal transformations by imparting optimized temporal and spectral phase profiles to the input waveforms. Using numerical optimization techniques, we show that a four-stage transformation can realize an efficient temporal mode sorter that demultiplexes 10 Hermite–Gaussian (HG) modes. Our time-lens-based framework represents a new toolkit for arbitrary spectro-temporal processing of single photons, with applications in temporal mode quantum processing, high-dimensional quantum key distribution, temporal mode matching for quantum networks, and quantum-enhanced sensing with time-frequency entangled states.
Temporal optics has attracted much attention due to its ability for lossless stretching of ultrafast temporal pulses. Concurrently, spatial SU(1,1) interferometers (SUIs) are widely utilized due to their high sensitivity to phase changes. Building on these concepts, we investigate a temporal SUI based on a temporal Fourier transform system, injecting broadband squeezed light for characterization. Our results show that the output spectral characteristics of the interferometer depend on the ratio of the focal group delay dispersion values of the two time lenses (defined as the scaling factor MMM) and the derivative of the applied phase. The scaling factor MMM strongly influences both the bandwidth and the degree of squeezing in the output spectrum. Meanwhile, the phase derivative induces a frequency shift proportional to its magnitude. Furthermore, the output squeezed-state spectrum exhibits concentrated squeezing at both the center frequency and the shifted frequencies. As the scaling factor MMM increases, the proportion of squeezing concentrated at the center frequency increases correspondingly. We also theoretically analyze and numerically calculate the phase sensitivity with respect to the phase derivative and the scaling factor MMM, under both lossless and lossy conditions. This temporal SUI architecture opens new avenues for the control of nonclassical fields in the time-frequency domain and quantum information processing applications.
Interferometers are highly sensitive to phase differences and are utilized in numerous schemes. Quantum interferometers are able to improve the sensitivity of classical interferometers beyond the shot-noise limit. This is done by employing squeezed states of light and destructive interference of the noise in the system. We developed a quantum SU(1,1) interferometer in the time domain. Our nonlinear quantum interferometer creates interference of the input signals at different times and frequencies. We can control the time and frequency differences for investigating the full temporal and spectral structure of the signal. This quantum interferometer can be utilized for sensing ultrafast phase changes, quantum imaging, temporal mode encoding, and studying the temporal structure of entangled photons.