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Annual Meeting Optical Society of America

Squeezing more out of a laser

Carlton M. Caves

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Machida and Yamamoto used negative feedback from a conventional photodetector to stabilize a laser's intensity and thus to obtain sub-shot-noise photon statistics within the feedback loop. Out-of-Ioop light extracted at a beam splitter, however, displayed super-shot-noise statistics. This behavior can be understood both quantum mechanically and semiclassically. Quantum mechanically the culprit is the vacuum field that enters the beam splitter’s second input port. I describe a technique for extracting sub-shot-noise light by replacing the culprit vacuum field with squeezed light generated by a nonlinear device—a squeezer—that is pumped by a portion of the laser light. Moreover, even if the unstabilized laser is shot-noise-limited, the extracted light can have a better intensity SNR; this signal-to-noise improvement requires both feedback and squeezing.

DOI
10.1364/oam.1987.me3

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Squeezing more out of a laser

Carlton M. Caves

A laser's intensity can be stabilized by negative feedback from a conventional photodetector. I propose extraction of sub-shot-noise light from the feedback loop at a beam splitter by illuminating the back side of the beam splitter with squeezed-state light.

Optics Letters•Nov 1, 1987•20 citations

Mechanism of suppressing noise intensity of squeezed state enhancement

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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.

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Sub-Shot Noise Interferometry and Quantum Imaging

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Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).

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Amplitude squeezing in a semiconductor laser using quantum nondemolition measurement and negative feedback

Y. Yamamoto, N. Imoto, S. Machida

A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^${)}^{2}$〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^${)}^{2}$〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^${)}^{2}$〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.

Physical Review A•May 1, 1986•205 citations
Machida and Yamamoto used negative feedback from a conventional photodetector to stabilize a laser's intensity and thus to obtain sub-shot-noise photon statistics within the feedback loop. Out-of-Ioop light extracted at a beam splitter, however, displayed super-shot-noise statistics. This behavior can be understood both quantum mechanically and semiclassically. Quantum mechanically the culprit is the vacuum field that enters the beam splitter’s second input port. I describe a technique for extracting sub-shot-noise light by replacing the culprit vacuum field with squeezed light generated by a nonlinear device—a squeezer—that is pumped by a portion of the laser light. Moreover, even if the unstabilized laser is shot-noise-limited, the extracted light can have a better intensity SNR; this signal-to-noise improvement requires both feedback and squeezing.
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.
We have produced amplitude-squeezed light whose noise is reduced by ~10 dB below the quantum noise limit in four different feedback systems. In our experimental method we have directly compared the noise power spectrum of the laser diode with the quantum noise limit in the low-frequency region, where the classical noise is stronger than the quantum noise. In addition to the well-known methods for extracting the out-loop beams from the feedback system by use of a 50:50 beam splitter, a polarizing beam splitter, or the leakage light from the rear side of a laser diode, we also have tried to use the spatial coherence of the laser light. We also have examined the vacuum fluctuations that prohibited the out-loop beam from being amplitude squeezed. In all these systems we have verified that the noise power spectrum for the in-loop beam is reduced below the quantum noise limit but not that for the out-loop beam; the difference arises mainly because vacuum fluctuations enter each system differently.
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25 , 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.
Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).
A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^)2{)}^{2})2〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.