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Nonlinear Frequency Generation and Conversion: Materials and Devices

Controlling the quantum noise of intense light

Nicholas Rivera

Published Mar 4, 2026• 0 citations
Publisher

Abstract

In reality, a wide variety of laser sources have fluctuations in excess (and often far in excess) of the coherent state, even when technical noise sources are suppressed. I present recent advances that challenge this paradigm, and show how multimode nonlinearities can be steered towards reducing the noise of intense beams of light down to quantum limits associated with coherent states and squeezed states of light. I will show how multimode correlations and wavefront shaping can suppress excess noise by orders of magnitude: reaching, and even surpassing, the shot-noise limit. We demonstrate these effects for femtosecond pulses propagating in both single-mode fibers and in multi-mode fibers. Our ability to control noise is aided by a general theory framework that we have developed, called quantum sensitivity analysis, which lets us predict how quantum noise is transformed by nonlinear and multimode systems.

DOI
10.1117/12.3088581

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In reality, a wide variety of laser sources have fluctuations in excess (and often far in excess) of the coherent state, even when technical noise sources are suppressed. I present recent advances that challenge this paradigm, and show how multimode nonlinearities can be steered towards reducing the noise of intense beams of light down to quantum limits associated with coherent states and squeezed states of light. I will show how multimode correlations and wavefront shaping can suppress excess noise by orders of magnitude: reaching, and even surpassing, the shot-noise limit. We demonstrate these effects for femtosecond pulses propagating in both single-mode fibers and in multi-mode fibers. Our ability to control noise is aided by a general theory framework that we have developed, called quantum sensitivity analysis, which lets us predict how quantum noise is transformed by nonlinear and multimode systems.
Nonlinear optical effects such as frequency conversion form the basis for many practical light sources. In a variety of settings, the performance of such sources is limited by quantum noise. In many nonlinear systems, this quantum noise gets strongly amplified, as a result of the large sensitivity of the nonlinear dynamics to changes in the initial conditions - a feature common to many nonlinear systems. Here, we develop a general theory of quantum noise resulting from nonlinear dynamics initiated by many-photon Gaussian quantum states. The theory provides guidelines to find the optimal quantum state to inject to maximally suppress the noise at the output. As a concrete example of the concept and theory, we consider the nonlinear optical phenomenon of supercontinuum generation by a femtosecond pulse, a famously noise-generating process, which is important in a range of applications in materials characterization and life science. By seeding supercontinuum generation with pulsed squeezed vacuum, one can achieve order-of-magnitude magnitude reduction of intensity and phase noise simultaneously, over a broad band of wavelengths, passively, and with no change in spectrum. The large magnitude and bandwidth of this effect is challenging to achieve by other means of stabilization, pointing to a promising approach for controlling quantum noise in a variety of nonlinear systems.
Optical fibers offer considerable advantages over bulk nonlinear media for the generation of squeezed states. This thesis reports on experimental investigations of reducing quantum noise by means of squeezing in nonlinear fiber optic interferometers. Fibers have low insertion loss which allows for long interaction lengths. High field intensities are easily achieved in the small cores of single mode fibers. Additionally, the nonlinear process employed is self phase modulation or the Kerr effect, whose broad band nature requires no phase matching and can be exploited with ultra-short pulses of high peak intensity. All these advantageous features of fibers result in easily obtained large nonlinear phase shifts and subsequently large squeezing parameters. By the self phase modulation process a correlation is produced between the phase and amplitude fluctuations of the optical field. The attenuated or squeezed quadrature has a lower noise level than the initial level associated with the coherent state field before propagation. The resulting reduced quantum noise quadrature can be utilized to improve the sensitivity of a phase measuring instrument such as an interferometer.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
This research focuses on advanced noise suppression technologies for high-precision measurement systems, particularly addressing the limitations of classical noise reducing approaches. The noise level of laser sources is a crucial factor that directly affects the measurement sensitivity in applications such as gravitational wave detection and biomedical imaging. Classical feedback control technologies are effective but often encounter a bottleneck resulting from the classical noise suppression limits. To cope with these challenges, a novel method integrating quantum squeezed light with classical feedback control systems to reduce intensity noise is proposed in this work. By employing an amplitude-squeezed light field, a quantum-enhanced feedback control model is developed, thereby theoretically examining the influence of both the feedback loop gain and the degree of squeezing on the noise suppression performance. The results show that the injection of squeezed light significantly reduces the intensity noise, approaching the shot noise limit (SNL), thereby improving the system sensitivity beyond the classical noise reduction boundaries. Specifically, –10 dB squeezed state injection into the feedback system yields an additional noise suppression of approximately 8.97 dB, exceeding what is achievable using classical feedback alone. This demonstrates that the potential of the proposed method can enhance measurement precision close to the quantum noise limits without increasing the laser power. The analysis highlights the asymmetric noise suppression effects between the inner feedback loop and outer feedback loop. Although the outer loop benefits significantly from the squeezed light injection and achieves noise levels that are unattainable by classical feedback methods, the inner loop shows relatively minor improvements. This asymmetry is attributed to the inherent characteristics of quantum squeezing and the limitations of the feedback loop design. Further investigation into the individual noise components reveals that the primary contributors to the intensity noise include input noise, photodetector noise, and beam splitter-induced vacuum fluctuations. The injection of squeezed light effectively mitigates these vacuum fluctuations, which are typically a major noise source in high-precision laser systems. Theoretical research results show that the use of squeezed light in feedback control systems can effectively enhance noise suppression, equivalent to a nine fold increase in detected optical power, without the physical drawbacks of increasing laser power such as thermal noise. In conclusion, this study provides a theoretical validation of combining quantum squeezed states with classical feedback control to exceed classical noise suppression limits. The integration of a –10 dB squeezed state demonstrates a significant noise reduction, showing that this hybrid approach could revolutionize noise management in precision measurement applications. The results pave the way for further exploring quantum-enhanced control technologies in fields such as gravitational wave detection, quantum communication, and advanced optical sensing, providing a pathway for improving sensitivity and noise suppression without increasing additional power requirements.
After multiple scattering of quadrature-squeezed light in a disordered medium, the quadrature amplitudes of the scattered modes present excess noise above the shot-noise level [Opt. Express14, 6919 (2006)OPEXFF1094-408710.1364/OE.14.006919]. A natural question is raised as to whether there exists a method of suppressing the quadrature fluctuation of the output mode. The answer is affirmative. In this work, we prove that wavefront shaping is a promising method to reduce the averaged quantum noise of quadrature amplitudes of the scattered modes. This reduction is owing to the destructive interference of quantum noise. Specifically, when the single-mode squeezed states are considered as inputs, the averaged quantum fluctuation can always be reduced, even below the shot-noise level. These results may have potential applications in quantum information processing, e.g., sub-wavelength imaging using the scattering superlens with squeezed-state sources.