The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order HG40 mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order HG30 and HG50 modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using HG00 as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes.The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order HG40 mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order HG30 and HG50 modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using HG00 as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes.

PhotonicsMay 17, 20236 citations

Amplitude Interferometry

William J. Tango

WORLD SCIENTIFIC eBooksMay 19, 20210 citations

A Modification of Jamin's Interferometer

Uzumi Doi

Proceedings of the Physico-Mathematical Society of Japan. 3rd SeriesJan 1, 19200 citations

Transverse distance estimation with higher-order Hermite-Gauss modes

Dilip Paneru, Alessio D'Errico, Ebrahim Karimi

We explore the use of higher-order Hermite-Gauss modes for sensing optically induced transverse displacements. In the small-displacement regime, we show that projective measurements onto the two neighboring spatial modes yield optimal Fisher information, linearly scaling with the mode order $m$ . We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Gaussian mode even at larger separations. This approach enables enhanced displacement sensitivity with only a minimal number of measurements, offering a simple and scalable alternative to conventional Spatial Mode Demultiplexing schemes. We provide a proof-of-principle experimental demonstration using spatial light modulators, showing an order-of-magnitude reduction in estimation variance when employing Hermite-Gauss modes of order $m = 8$ and $m = 17$ . These results highlight the potential of structured light for ultrasensitive displacement sensing and may enable new applications in birefringence measurements with broadband or low-coherence light sources.We explore the use of higher-order Hermite-Gauss modes for sensing optically induced transverse displacements. In the small-displacement regime, we show that projective measurements onto the two neighboring spatial modes yield optimal Fisher information, linearly scaling with the mode order $m$. We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Gaussian mode even at larger separations. This approach enables enhanced displacement sensitivity with only a minimal number of measurements, offering a simple and scalable alternative to conventional Spatial Mode Demultiplexing schemes. We provide a proof-of-principle experimental demonstration using spatial light modulators, showing an order-of-magnitude reduction in estimation variance when employing Hermite-Gauss modes of order $m = 8$ and $m = 17$. These results highlight the potential of structured light for ultrasensitive displacement sensing and may enable new applications in birefringence measurements with broadband or low-coherence light sources.

arXiv:2506.02926Physical Review ADec 5, 20251 citation

High Resolution Interferometry with Steep Dispersion

G. Muller, M. Muller, Andreas Wicht +2 more

European Quantum Electronics Conference (EQEC)Jan 1, 19960 citations

Ultra-sensitive tilt measurement based on exceptional point sensors with Hermite-Gaussian pointer

Zhiyuan Wang, Zijing Zhang

Abstract Parity-time (PT)-symmetric non-Hermitian systems exhibit a heightened sensitivity to external environmental changes, making them a popular choice in the field of quantum sensing. In this study, we designed a small tilt sensor based on the exceptional point (EP) of non-Hermitian systems. The measurement sensitivity of the sensor can be increased by a factor of 10000 times when compared with that of traditional sensors. However, in terms of the measurement precision of the EP sensor, there was no significant improvement because the EP sensor amplified the signal while amplifying the noise. Nonetheless, EP sensors retain clear advantages in specialized scenarios, such as detector saturation events, during which they surpass traditional sensors. Subsequently, we increased the measurement precision of the EP sensor by 2 n + 1 times by using high-order Hermite-Gaussian (HG) light, where n denotes the mode order of the signal light. Finally, we conclude this study with an analysis of the noise in EP sensors based on quantum error theory. Furthermore, we explore how EP sensors can strike a balance between high sensitivity and precision by incorporating a squeezed light field with elevated HG modes.Abstract Parity-time (PT)-symmetric non-Hermitian systems exhibit a heightened sensitivity to external environmental changes, making them a popular choice in the field of quantum sensing. In this study, we designed a small tilt sensor based on the exceptional point (EP) of non-Hermitian systems. The measurement sensitivity of the sensor can be increased by a factor of 10000 times when compared with that of traditional sensors. However, in terms of the measurement precision of the EP sensor, there was no significant improvement because the EP sensor amplified the signal while amplifying the noise. Nonetheless, EP sensors retain clear advantages in specialized scenarios, such as detector saturation events, during which they surpass traditional sensors. Subsequently, we increased the measurement precision of the EP sensor by 2 n + 1 times by using high-order Hermite-Gaussian (HG) light, where n denotes the mode order of the signal light. Finally, we conclude this study with an analysis of the noise in EP sensors based on quantum error theory. Furthermore, we explore how EP sensors can strike a balance between high sensitivity and precision by incorporating a squeezed light field with elevated HG modes.

Physica ScriptaJun 27, 20250 citations

m

. We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Gaussian mode even at larger separations. This approach enables enhanced displacement sensitivity with only a minimal number of measurements, offering a simple and scalable alternative to conventional Spatial Mode Demultiplexing schemes. We provide a proof-of-principle experimental demonstration using spatial light modulators, showing an order-of-magnitude reduction in estimation variance when employing Hermite-Gauss modes of order

m = 8

and

m = 17

. These results highlight the potential of structured light for ultrasensitive displacement sensing and may enable new applications in birefringence measurements with broadband or low-coherence light sources.