We show an optical heterodyne spectrometer with picometer resolution and high sensitivity. Moreover, we report the quantum limit of detecting multi-mode light using heterodyne detection, and compare it to a typical down conversion source output.
Optical heterodyne detection-based spectrometers are attractive due to their relatively simple construction and ultrahigh resolution. Here we demonstrate a proof-of-principle single-mode optical-fiber-based heterodyne spectrometer that has picometer resolution and quantum-limited sensitivity around 1550 nm. Moreover, we report a generalized quantum limit of detecting broadband multispectral-temporal-mode light using heterodyne detection, which provides a sensitivity limit on a heterodyne detection-based optical spectrometer. We then compare this sensitivity limit to several spectrometer types and dim light sources of interest such as spontaneous parametric downconversion, Raman scattering, and spontaneous four-wave mixing. We calculate that the heterodyne spectrometer is significantly less sensitive than a single-photon detector and is unable to detect these dim light sources, except for the brightest and narrowest-bandwidth examples.
The distance between two point light sources is difficult to estimate if that distance is below the diffraction (Rayleigh's) resolution limit of the imaging device. A recently proposed technique enhances the precision of this estimation by exploiting the source-separation-dependent coupling of light into higher-order transverse-electromagnetic (TEM) modes, particularly the TEM01 mode of the image. We theoretically analyze the estimation of the source separation by means of homodyne or heterodyne detection with a local oscillator in the TEM01 mode, which is maximally sensitive to the separation in the sub-Rayleigh regime. We calculate the Fisher information associated with this estimation and compare it with direct imaging. For thermal sources, the Fisher information in any mode of the image plane depends nonlinearly on the average received photon number. We show that the per-photon Fisher information surpasses that of direct imaging (in the interesting sub-Rayleigh regime) when the average received photon number per source exceeds two for homodyne detection and four for heterodyne detection.
Laser Doppler Vibrometry (LDV) is a high-precision, non-contact measurement technique that leverages optical interference between a reference beam and a Doppler-shifted measurement beam derived from coherent laser light. By detecting phase variations induced by surface vibrations, LDV has become a widely utilized tool in industrial environments for vibration analysis, structural diagnostics, and quality control. The detection sensitivity of the LDV is fundamentally constrained by the Poissonian statistics of photon arrivals. In heterodyne LDV systems, the enhancement of signal-to-noise ratio (SNR) and measurement resolution under shot-noise-limited conditions typically requires increasing the optical power of the measurement beam. However, this approach becomes infeasible in scenarios with strict constraints on thermal load or optical power. Recent studies have demonstrated that injecting squeezed vacuum states as non-classical light sources can suppress quantum noise while maintaining low optical power, thus surpassing the standard quantum limit. This thesis introduces the principle of the heterodyne LDV combined with squeezed light sources. The first scientific hypothesis proposed herein is that introducing laser light with squeezed quantum uncertainties into industrial heterodyne LDVs enables vibration measurements to exceed the physical resolution limits of traditional LDVs, achieving sub-shot-noise sensitivity. The thesis designed a squeezed-light-enhanced heterodyne LDV, achieving over 3 dB of squeezing within a 40 MHz measurement bandwidth and demonstrating a noise-equivalent displacement resolution reaching 8 fm/√Hz, thereby confirming the first hypothesis. Addressing the limitations imposed by the finite dynamic range of analog-to-digital converters (ADCs) on the SNR of digitally demodulated phase-modulated signals, the thesis proposes a clipping-based synchronous zero-crossing sampling technique and a corresponding second scientific hypothesis: that this sampling scheme enables heterodyne LDV to overcome the digital noise floor defined by the ADC's SNR. Experimental results demonstrate that this sampling and demodulation approach effectively reduces ADC quantization noise, allowing the digital resolution of the demodulated phase-modulated signal to surpass the ADC-imposed SNR limit while preserving the quantum noise-level squeezing, thereby validating the second hypothesis. Compared to previous work, this research constitutes the first experimental verification of squeezed-light-enhanced measurement feasibility in a classical heterodyne LDV operating at a 40 MHz difference frequency, advancing the application of quantum-enhanced precision metrology in industrial vibration testing.