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Advanced Quantum Technologies

Multiple Photon Subtraction on Light with Tunable Intensity Correlations

Minju Kim, 김석진, Seongjin Hong, Yong‐Su Kim

Published Apr 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We present a unified theoretical and experimental investigation of multiple‐photon subtraction on intensity‐modulated optical fields with negative binomial photon statistics. Using an electro‐optic modulator, we generate fields with tunable from 1.00 to 2.85, spanning coherent, thermal, and super‐thermal regimes. Our theoretical framework based on the negative binomial distribution reveals that ‐photon subtraction transforms the coherence parameter as , providing explicit predictions for all photon statistics. Through systematic experiments with heralded photon‐number resolving detection, we demonstrate excellent quantitative agreement between theory and experiment. The results confirm that a beam splitter with photon‐number resolving detector implementation faithfully reproduces ideal photon subtraction for , while zero‐photon subtraction represents a distinct conditional measurement. This work provides a unified reference for understanding photon subtraction across all intensity correlation regimes.

DOI
10.1002/qute.202500946

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ABSTRACT We present a unified theoretical and experimental investigation of multiple‐photon subtraction on intensity‐modulated optical fields with negative binomial photon statistics. Using an electro‐optic modulator, we generate fields with tunable from 1.00 to 2.85, spanning coherent, thermal, and super‐thermal regimes. Our theoretical framework based on the negative binomial distribution reveals that ‐photon subtraction transforms the coherence parameter as , providing explicit predictions for all photon statistics. Through systematic experiments with heralded photon‐number resolving detection, we demonstrate excellent quantitative agreement between theory and experiment. The results confirm that a beam splitter with photon‐number resolving detector implementation faithfully reproduces ideal photon subtraction for , while zero‐photon subtraction represents a distinct conditional measurement. This work provides a unified reference for understanding photon subtraction across all intensity correlation regimes.
Recently Parigi et al. ( Science , 317 (2007) 1890 ) measured the statistics of a photon-subtracted and a photon-added thermal field. They showed that the measurements agree with the theoretical predictions of the beam splitter (BS) model. We show the equivalence of the quantum trajectory approach and the BS model in photon subtraction by deriving the BS model from the generalized photon counting operators. Our photon counting operators, corresponding to measurements using a resolving detector and a nonresolving detector, are generalization of the standard quantum jump approach. Our model is exact from weak quantum fields to the classical limit of strong fields. We show that our generalized photon counting operators reproduce exactly the results of the BS model when the reflection probability of the beam splitter is equated with the absorption probability of a photon in the standard quantum jump model of cavity field damping. Our theory can explain the recent experimental results of Parigi et al. and shows how similar experiments can be made to test the photon subtraction for the whole range of electromagnetic field intensities ranging from quantum to classical limit. We propose new experiments to test the generalized photon counting operators in the intermediate regime between the quantum and classical limits.
Abstract We study feasible and effective techniques to improve the efficiency and fidelity of photon subtraction in order to enable practical quantum resource engineering based on it. We use thermal light for our investigation and consider non-negligible beam splitting beyond the conventional setup, also taking into account photon detection errors. We find that the output is still a photon-subtracted thermal state when a non-negligible amount of light is reflected from the input beam and measured by the photon detector, but it has an effective mean photon number different than that of the input. It enables a strategy for achieving a target photon-subtracted thermal state by employing a stronger input light and leads to substantial improvement in the probability of successful photon subtraction events. We calculate the fidelity of the output state and analyze how it worsens with larger beam splitting ratios and photon counting errors. Using our understanding of the limiting factors in the conventional routine, we propose a new method for photon subtraction that can achieve high-fidelity output with decent efficiency, and using only mediocre photon detectors. We experimentally verify our solutions that are valuable for improving photon subtraction and lowering the experimental barrier.
Thermal states of light are widely used in quantum optics due to their correlation properties. As is well known, their correlation properties and the photon-number distribution as a whole are strongly dependent on the mode number selected by the detection scheme. The same changes can be caused by photon subtraction. Therefore, we describe the general case of the multimode thermal state after a multiphoton subtraction, when the photon-number statistics is registered by the detector selecting a part of the initial modes. We present an analytical form of the obtained photon-number distribution and its general properties and check them in the experiment.
We demonstrate the effect of multiple-photon subtraction on the generation of conditional states in the pulsed regime. Our experimental scheme relies on a beam splitter (BS) and a pair of linear photodetectors that are able to resolve up to tens of photons. We use a single-mode thermal field at the input port of the BS to test the reliability of our scheme, and we show good agreement with the theory by fully characterizing the conditional outgoing states in terms of photon-number statistics and non-Gaussianity.
Thermal radiation played a pivotal role in the preliminary development of quantum physics where it helped resolve the apparent incongruity of the ultraviolet catastrophe. In contemporary physics, thermal state generation and manipulation finds new application in fields such as quantum imaging and quantum illumination and as a practical realization of Maxwell's demon. These applications often go hand in hand with photon subtraction operations which probabilistically amplify the mean photon number (MPN) of thermal light as a result of its super-Poissonian photon statistics. In this article, we introduce an operation for thermal states of light based on a generalized photon subtraction scheme. Displaced-photon subtraction (DPS) makes use of coherent state displacement followed by a subsequent anti-displacement in combination with single-photon detection to probe the MPN of a thermal state. We find regimes in which the output of a successful DPS is amplified, unchanged, or attenuated relative to the unconditioned output state. The regime of operation is controlled via the magnitude of the coherent displacement. A theoretical description of generalized photon subtraction of a displaced thermal state is derived via a two-mode moment-generating function (MGF) and used to describe generalized DPS. We perform a proof of principle experimental implementation of DPS for the case of a balanced beam splitter for which results demonstrate good agreement with the model.