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arXiv:2609.26949

Measurement-based feedback as a flexible tool to control non-Poissonian photon statistics

Ming Li, JunYan Luo, Georg Engelhardt

quant-phSubmitted Sep 22, 2026• Announced Sep 24, 2026• 0 citations
arXivHTMLPDF

Abstract

Non-Poissonian photon statistics are usually traced to nonlinear interactions, nonclassical states, or engineered reservoirs. Here we show that measurement-based feedback can be alternatively deployed to control the Poissonian character of the measurement statistics in an externally-driven linear cavity. Each photon detection triggers a weak displacement operation whose phase determines how the feedback interferes with the coherent cavity field, resulting in a significant cavity response. Full counting statistics and two-time photon correlations show that the feedback phase controls the sign and strength of the induced correlations, continuously tuning the emission statistics between super- and sub-Poissonian regimes. At generic phases, the Mandel parameter responds linearly to the feedback amplitude, whereas at specific phases, the leading response becomes quadratic. The same phase dependence is also found in higher-order cumulants of the emission statistics. These results establish measurement-based feedback as a route to controlling photon statistics in otherwise linear driven-dissipative systems.

Comments
12 pages, 5 figures

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Non-Poissonian photon statistics are usually traced to nonlinear interactions, nonclassical states, or engineered reservoirs. Here we show that measurement-based feedback can be alternatively deployed to control the Poissonian character of the measurement statistics in an externally-driven linear cavity. Each photon detection triggers a weak displacement operation whose phase determines how the feedback interferes with the coherent cavity field, resulting in a significant cavity response. Full counting statistics and two-time photon correlations show that the feedback phase controls the sign and strength of the induced correlations, continuously tuning the emission statistics between super- and sub-Poissonian regimes. At generic phases, the Mandel parameter responds linearly to the feedback amplitude, whereas at specific phases, the leading response becomes quadratic. The same phase dependence is also found in higher-order cumulants of the emission statistics. These results establish measurement-based feedback as a route to controlling photon statistics in otherwise linear driven-dissipative systems.
In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
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We present the quantum theory of optical cavity feedback mediated by homodyne detection, with an arbitrary time delay. We apply this theory to a system with nonclassical dynamics, a sub-Poissonian pumped laser. By using the feedback to phase lock the laser it is possible to produce output light which exhibits perfect quadrature squeezing on resonance, rather than just sub-Poissonian intensity statistics. However, we also show that feedback mediated by homodyne detection (or any other extracavity measurement) cannot produce nonclassical light unless the cavity dynamics can do so without feedback. Furthermore, in systems which already exhibit squeezing, such feedback can only degrade the squeezing in the output. With feedback mediated by an intracavity measurement, these theorems do not apply. We show that an (admittedly unrealistic) intracavity quantum nondemolition quadrature measurement allows arbitrary squeezing to be produced by controlling the amplitude of a coherent driving field.
Abstract We investigate the steady-state photon statistics and quantum properties of a cascade three-level atom coupled to a two-mode squeezed-vacuum reservoir. The mean photon number, photon-number correlations, second-order coherence, and quadrature fluctuations are examined as functions of the stimulated-emission decay constant and the squeezing parameter. The system exhibits two distinct regimes: a squeezing-dominated regime, governed by reservoir-induced correlations, and a cavity-dynamics-dominated regime, characterized by strong gain–loss competition. Enhanced squeezing increases photon generation, intermodal correlations, and intracavity energy through correlated photon-pair injection while reducing vacuum fluctuations. Conversely, stronger stimulated emission induces nonlinear amplification, asymmetric photon distributions, and sequential emission dynamics. A transition from super-Poissonian to sub-Poissonian statistics is observed, indicating the coexistence of photon antibunching and continuous-variable quantum correlations. Furthermore, atom–cavity interactions modify the generalized uncertainty bounds, revealing fundamental limitations on achievable squeezing imposed by higher-order noise processes. These findings demonstrate that engineered reservoirs and cascade atomic systems provide versatile control of nonclassical light for quantum communication, precision metrology, and continuousvariable quantum information processing.
Quantum optics characterizes light through photon correlations, motivating their connection to correlated ab initio molecular electronic structure. In this study, intracavity photon statistics of cavity-coupled molecules are computed from QED coupled-cluster (QED-CCSD-22) densities and validated against exact diagonalization of the Pauli-Fierz Hamiltonian. A change of coordinate origin or dipole convention displaces the ground state coherently, so second-order and higher cumulants of the cavity field are independent of these conventions even for molecular ions. The photon subsystem of QED Hartree-Fock is exactly coherent, so the invariant statistics describe fluctuations beyond this electron-photon product reference. The field fluctuations are super-Poissonian, and their degree of second-order coherence depends primarily on cavity frequency in the tested weak-coupling regime, falling from 18.5 to 4.9 for H2 as the cavity is detuned from 5 to 20 eV. The third cumulant identifies non-Gaussian fluctuations and changes sign under reversal of the coupling direction.