[Paper Review] Spectrally resolved NOON state interference

Rui‐Bo Jin, Ryōsuke Shimizu+6 more|arXiv (Cornell University)|Apr 2, 2021

Quantum optics and atomic interactions1 references4 citations

TL;DR

This paper demonstrates the first experimental observation of spectrally resolved NOON state interference (NOON-SI), where joint spectral intensities (JSIs) are measured across frequency and time domains. Unlike conventional time-domain measurements that lose spectral information, the authors show that interference patterns persist in the frequency domain—especially at non-zero delays—yielding higher Fisher information and improved phase estimation precision beyond the standard NOON-SI limit.

ABSTRACT

NOON state interference (NOON-SI) is a powerful tool to improve the phase sensing precision, and plays an important role in quantum measurement. In most of the previous NOON-SI experiments, the measurements were performed in time domain where the spectral information of the involved photons was integrated and lost during the measurement. In this work, we experimentally measured the joint spectral intensities (JSIs) at different positions of the interference patterns in both time and frequency domains. It was observed that the JSIs were phase-dependent and show odd (even)-number patterns at $0$ ($π$) phase shift; while no interference appeared in time domain measurement, the interference pattern clearly appeared in frequency domain. To our best knowledge, the latter is the first observation of the spectrally resolved NOON state interference, which provides alternative information that cannot be extracted from the time-domain measurement. To explore its potential applications, we considered the interferometric sensing with our setup. From the Fisher information-based analysis, we show that the spectrally resolved NOON-SI has a better performance at non-zero-delay position than its non-spectrally resolved counterpart. The spectrally resolved NOON-SI scheme may be useful for quantum metrology applications such as quantum phase sensing, quantum spectroscopy, and remote synchronization.

Motivation & Objective

• To overcome the limitation of conventional NOON-SI experiments that integrate spectral information in time-domain measurements.
• To explore the role of spectral correlations in NOON state interference by measuring joint spectral intensities (JSIs) in both time and frequency domains.
• To evaluate whether spectrally resolved detection improves phase sensing performance compared to non-spectrally resolved NOON-SI.
• To investigate the potential of spectrally resolved NOON-SI for quantum metrology, spectroscopy, and remote synchronization.

Proposed method

• Utilized a type-II spontaneous parametric down-conversion (SPDC) source at 1584 nm to generate polarization-entangled NOON states.
• Employed a two-dimensional spectral measurement technique using two spectrometers to resolve joint spectral intensities (JSIs) of signal and idler photons.
• Scanned the relative delay between the two paths using a piezoelectric actuator (PZT) and recorded coincidence counts across time and frequency.
• Applied the spectral correlation measurement technique from Gerrits et al. (2015) to achieve high spectral resolution and fast acquisition.
• Theoretical modeling used the joint spectral amplitude $ f(\omega_s, \omega_i) $ to compute Fisher information for both spectrally resolved (SR) and non-spectrally resolved (NSR) cases.
• Fisher information was calculated via $ F_{SR}(\tau) = \int\!\!\!\int |f(\omega_s, \omega_i)|^2 (\omega_s + \omega_i)^2 d\omega_s d\omega_i $, enabling comparison with time-domain visibility.

Experimental results

Research questions

• RQ1 Can interference patterns in NOON state interference be observed in the frequency domain when they vanish in the time domain?
• RQ2 How does the spectral correlation (JSI) of entangled photons evolve with phase delay in NOON-SI?
• RQ3 Does spectrally resolved detection provide higher Fisher information than conventional time-domain detection for phase estimation?
• RQ4 What is the performance advantage of spectrally resolved NOON-SI in estimating phase or time delay over a wide range of delays?
• RQ5 How does the phase-dependent structure of JSIs in NOON-SI differ from the phase-independent JSI in HOM interference?

Key findings

• Interference patterns were clearly observed in the frequency domain, while no interference was visible in the time domain at 10 ps delay, where visibility dropped to 0%.
• The joint spectral intensity (JSI) exhibited odd-numbered patterns at 0 phase shift and even-numbered patterns at π phase shift, indicating phase-dependent spectral structure.
• At non-zero delays, the spectrally resolved Fisher information ($ F_{SR} $) reached its maximum and remained high, outperforming the non-spectrally resolved counterpart ($ F_{NSR} $), which degraded with delay.
• Theoretical analysis confirmed that $ F_{SR} $ achieves the maximum possible Fisher information across all delays, unlike $ F_{NSR} $, which diminishes away from the interference center.
• The spectral correlation structure in NOON-SI splits along the anti-diagonal in the $ \omega_s $-$ \omega_i $ plane, contrasting with the diagonal splitting seen in HOM interference due to sum-frequency vs. difference-frequency interference.
• The two-dimensional spectral resolution enabled by dual spectrometers revealed previously inaccessible spectral information, suggesting potential for higher-precision parameter estimation in quantum metrology and spectroscopy.