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Optics Express

Quantum fluctuation recovery through scattering media

Dong Li, Mingle Liao, P. Wang, Feng Huang, Yao Yao

Published Nov 18, 2025• 0 citations
Publisher

Abstract

After transmitting through a disordered medium, a squeezed state would conceivably exhibit excess noise above the shot-noise level. Recent advancements have demonstrated that the technique of single-sided wavefront shaping provides an effective avenue to suppress the excess noise. Nevertheless, the minimum suppressed noise remains above the initial squeezed noise level. Inspired by full-reflection structures enabling novel optical phenomena, we propose an alternative noise-reduction scheme combining a zero-transmission structure with wavefront shaping, which further reduces the excess quantum fluctuations. Intriguingly, when the input is a single-mode squeezed state, the excess fluctuation can be fully erased. Therefore, our approach paves another way for the elimination of the excess noise induced by multiple scattering in disordered media.

DOI
10.1364/oe.574309

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After transmitting through a disordered medium, a squeezed state would conceivably exhibit excess noise above the shot-noise level. Recent advancements have demonstrated that the technique of single-sided wavefront shaping provides an effective avenue to suppress the excess noise. Nevertheless, the minimum suppressed noise remains above the initial squeezed noise level. Inspired by full-reflection structures enabling novel optical phenomena, we propose an alternative noise-reduction scheme combining a zero-transmission structure with wavefront shaping, which further reduces the excess quantum fluctuations. Intriguingly, when the input is a single-mode squeezed state, the excess fluctuation can be fully erased. Therefore, our approach paves another way for the elimination of the excess noise induced by multiple scattering in disordered media.
In diversified optical applications, such as optical imaging and optical metrology, it is evidently significant to pursue low quantum fluctuations of light to promise the enhancement of measurement precision. Recently, it has been demonstrated that the technique of wavefront shaping provides an effective avenue to suppress the excess quantum noise of quadrature-squeezed light through a disordered medium in the presence of one-sided illumination. Nevertheless, the minimum suppressed noise is still above the initial squeezed noise level. Inspired by two-sided modulation enabling novel optical phenomena, we propose an alternative noise-reduction scheme combining two-sided illumination with wavefront shaping. It is clarified that our approach is able to further reduce the excess quantum fluctuation. The exact condition for the reduced noise to reach below the standard quantum limit is given. Intriguingly, the excess noise can be fully erased in certain case. Therefore, our scheme paves another way for elimination of the excess noise induced by multiple scattering in disordered media.
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.
After propagating through a random amplifying medium, a squeezed state commonly shows excess noise above the shot-noise level. Since large noise can significantly reduce the signal-to-noise ratio, it is detrimental for precision measurement. To circumvent this problem, we propose a noise-reduction scheme using wave-front shaping. It is demonstrated that the average output quantum noise can be effectively suppressed even beyond the shot-noise limit. Both the decrease of amplification strength and the increase of input squeezing strength can give rise to a decrease in the suppressed average quantum noise. Our results not only show the feasibility of manipulating the output quantum noise of random amplifying media but also indicate potential applications in quantum information processing in complex environments, such as quantum imaging, quantum communication, and quantum key distribution.
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.
The scheme of optical imaging using scattering lens can provide a resolution beyond the classical optical diffraction limit with a coherent-state input. Nevertheless, due to the shot noise of the coherent state, the corresponding signal-to-noise ratio and resolution are both still shot-noise-limited. In order to circumvent this problem, we theoretically propose an alternative scheme where the squeezed state (with a sub-shot noise) is considered as input and the quantum noise is then suppressed below the shot-noise level. Consequently, when comparing with the previous imaging scheme (using combination of coherent state and scattering lens), our proposal is able to achieve an enhanced signal-to-noise ratio for a given scattering lens. Meanwhile, it is demonstrated that the resolution is also improved. We believe that this method may afford a new way of using squeezed states and enable a higher performance than that of using coherent state and scattering lens.
Propagating quadrature squeezed light through a multiple scattering random medium is found to induce pronounced spatial quantum correlations that have no classical analogue. The correlations are revealed in the number of photons transported through the sample that can be measured from the intensity fluctuations of the total transmission or reflection. In contrast, no pronounced spatial quantum correlations appear in the quadrature amplitudes where excess noise above the shot noise level is found.