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Open questions in closed-loop photodetection

Jeffrey H. Shapiro

Published Jan 1, 1987• 0 citations
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The usual open-loop quantum and semiclassical theories of light detection are extended to include closed-loop operation in which there is feedback from the detector to the source. It is shown that the unmistakable signatures of nonclassical light associated with open-loop detection, such as sub-shot-noise spectra and sub-Poisson photo-counts, do not carry over to closed-loopsystems. This behavior is illustrated through quantitatively indistinguishable quantum and semiclassical analyses of two recent closed-loop experiments in which sub-Poisson photocount statistics were produced. It turns out that if the open-loop illumination does not require the use of quantum photodetection theory, then neither does the closed-loop illumination. Conversely, if the open-loop illumination is nonclassical, then the closed-loop behavior must be analyzed quantum mechanically. The use of nonclassical field correlations to obtain light beams that give sub-Poisson open-loop photocounts from these closed-loop arrangements is discussed and generalized into a synthesis procedure for producing light beams with arbitrary open-loop photocount statistics.

Journal of the Optical Society of America B•Oct 1, 1987•119 citations

Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description

Masahito Ueda

A nonequilibrium open-system theory for continuous photodetection processes is developed using a probability-density functional combined with the path-integral technique. Nonunitary time evolution of the system-environment density operator due to measurement back action and continuous measurement is exactly described for three familiar photodetection processes. New exact photocounting formulas are obtained for these three processes; in particular, Mollow's photocounting formula is generalized for a nonequilibrium open system. Distinctive features between a closed system and an open system are presented; for example, the probability distribution for the number of counts is shown to contain complete information about photoelectron statistics for a closed system, whereas it does not for an open system. The obtained formulas are applied to photodetection of a single-mode photon field that interacts linearly with a pump source consisting of a single harmonic oscillator and a reservoir consisting of an infinite number of harmonic oscillators. In the former case, increasing the ratio of the source-field coupling constant to the field-detector coupling constant causes the photon field to cross over from a closed attenuating field to an open stationary field. In the latter case, a quantum-mechanical fluctuation-dissipation theorem in the continuous photodetection context is discussed.

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The Loop Opens: Energy Input as the Physical Mechanism of Quantum Measurement Disturbance

Ryan Weber

We propose a purely physical resolution to the quantum measurement problem. In the Loop Interpretation of the Settling Field framework, a particle is energy at c moving along a closed geometric path it cannot exit — imprisoned by its own speed in the curvature of the vacuum field V(φ) = β(e^{2φ} − 1 − 2φ). The difference between a photon and an electron is not their fundamental nature but the geometry of their path: one open, one closed. E = mc² is not a conversion formula. It is the energy cost of one closed loop of light.Measurement disturbs the particle not because observation selects from a superposition but because injecting energy physically opens the closed loop, momentarily converting the particle to radiant energy. The open path explores all available geometries simultaneously at c, then re-closes at the location of strongest geometric resonance in the combined field of particle and apparatus. What the Copenhagen Interpretation calls wavefunction collapse is a physical sequence: loop opens, explores, re-closes. The Born rule is not a postulate about fundamental indeterminacy. It is a map of resonance condition strengths across the measurement apparatus geometry.This reframing is consistent with all existing quantum mechanical predictions and with the body of optomechanical back-action experiments confirming that disturbance scales quantitatively with measurement energy across two orders of magnitude. Back-action-evading measurement — in which energy is injected in a mode geometrically orthogonal to the loop’s closure condition — is explained without paradox. The quantum Zeno effect follows trivially from repeated loop opening and re-closure without invoking observation as a causal agent.The paper makes one new prediction that distinguishes the Loop Interpretation from both Copenhagen and Many-Worlds: the disturbance-versus-cooperativity curve for quantum back-action measurements should show a stiffness inflection at a characteristic cooperativity C* determined by V’’(φ_n) at the particle’s fold position. For the electron at fold position n = 0.722, below C* disturbance scales sublinearly with cooperativity; above C* it scales superlinearly. Copenhagen and Many-Worlds both predict smooth linear scaling throughout. The test requires no new experiments — only re-analysis of existing published optomechanics datasets on a log-log scale. The Steinberg group at the University of Toronto and the Aspelmeyer group in Vienna are identified as natural experimental contacts.The paper includes a parallel account of seven questions posed simultaneously to Many-Worlds and the Loop Interpretation — what is a particle, what is measurement, what is the wavefunction, why does measurement appear random, what is entanglement, what predictions does each make beyond standard quantum mechanics, and what is each framework’s ontological cost. The comparison is presented without commentary. Many-Worlds makes no predictions beyond Copenhagen and commits to an uncountably infinite proliferation of parallel universes. The Loop Interpretation makes one testable prediction and commits to one real scalar field with one free parameter. Many-Worlds is the right answer to the wrong question. The loop picture dissolves the collapse problem rather than solving it.Three gaps are honestly stated: the precise value of C* requires a full measurement of μ_vac from galaxy cluster weak lensing profiles; the coupling between the electromagnetic probe field and the loop closure geometry requires numerical computation; and the claim that quantum mechanics is deterministic at the zeptosecond scale is a prediction rather than a derivation.

•Apr 16, 2026•0 citations

On the concepts of photons and photodetection

Seng‐Tiong Ho

Nuclear Physics B - Proceedings Supplements•Mar 1, 1989•1 citation
The usual open-loop quantum and semiclassical theories of light detection are extended to include closed-loop operation in which there is feedback from the detector to the source. It is shown that the unmistakable signatures of nonclassical light associated with open-loop detection, such as sub-shot-noise spectra and sub-Poisson photo-counts, do not carry over to closed-loopsystems. This behavior is illustrated through quantitatively indistinguishable quantum and semiclassical analyses of two recent closed-loop experiments in which sub-Poisson photocount statistics were produced. It turns out that if the open-loop illumination does not require the use of quantum photodetection theory, then neither does the closed-loop illumination. Conversely, if the open-loop illumination is nonclassical, then the closed-loop behavior must be analyzed quantum mechanically. The use of nonclassical field correlations to obtain light beams that give sub-Poisson open-loop photocounts from these closed-loop arrangements is discussed and generalized into a synthesis procedure for producing light beams with arbitrary open-loop photocount statistics.
A nonequilibrium open-system theory for continuous photodetection processes is developed using a probability-density functional combined with the path-integral technique. Nonunitary time evolution of the system-environment density operator due to measurement back action and continuous measurement is exactly described for three familiar photodetection processes. New exact photocounting formulas are obtained for these three processes; in particular, Mollow's photocounting formula is generalized for a nonequilibrium open system. Distinctive features between a closed system and an open system are presented; for example, the probability distribution for the number of counts is shown to contain complete information about photoelectron statistics for a closed system, whereas it does not for an open system. The obtained formulas are applied to photodetection of a single-mode photon field that interacts linearly with a pump source consisting of a single harmonic oscillator and a reservoir consisting of an infinite number of harmonic oscillators. In the former case, increasing the ratio of the source-field coupling constant to the field-detector coupling constant causes the photon field to cross over from a closed attenuating field to an open stationary field. In the latter case, a quantum-mechanical fluctuation-dissipation theorem in the continuous photodetection context is discussed.
We propose a purely physical resolution to the quantum measurement problem. In the Loop Interpretation of the Settling Field framework, a particle is energy at c moving along a closed geometric path it cannot exit — imprisoned by its own speed in the curvature of the vacuum field V(φ) = β(e^{2φ} − 1 − 2φ). The difference between a photon and an electron is not their fundamental nature but the geometry of their path: one open, one closed. E = mc² is not a conversion formula. It is the energy cost of one closed loop of light.Measurement disturbs the particle not because observation selects from a superposition but because injecting energy physically opens the closed loop, momentarily converting the particle to radiant energy. The open path explores all available geometries simultaneously at c, then re-closes at the location of strongest geometric resonance in the combined field of particle and apparatus. What the Copenhagen Interpretation calls wavefunction collapse is a physical sequence: loop opens, explores, re-closes. The Born rule is not a postulate about fundamental indeterminacy. It is a map of resonance condition strengths across the measurement apparatus geometry.This reframing is consistent with all existing quantum mechanical predictions and with the body of optomechanical back-action experiments confirming that disturbance scales quantitatively with measurement energy across two orders of magnitude. Back-action-evading measurement — in which energy is injected in a mode geometrically orthogonal to the loop’s closure condition — is explained without paradox. The quantum Zeno effect follows trivially from repeated loop opening and re-closure without invoking observation as a causal agent.The paper makes one new prediction that distinguishes the Loop Interpretation from both Copenhagen and Many-Worlds: the disturbance-versus-cooperativity curve for quantum back-action measurements should show a stiffness inflection at a characteristic cooperativity C* determined by V’’(φ_n) at the particle’s fold position. For the electron at fold position n = 0.722, below C* disturbance scales sublinearly with cooperativity; above C* it scales superlinearly. Copenhagen and Many-Worlds both predict smooth linear scaling throughout. The test requires no new experiments — only re-analysis of existing published optomechanics datasets on a log-log scale. The Steinberg group at the University of Toronto and the Aspelmeyer group in Vienna are identified as natural experimental contacts.The paper includes a parallel account of seven questions posed simultaneously to Many-Worlds and the Loop Interpretation — what is a particle, what is measurement, what is the wavefunction, why does measurement appear random, what is entanglement, what predictions does each make beyond standard quantum mechanics, and what is each framework’s ontological cost. The comparison is presented without commentary. Many-Worlds makes no predictions beyond Copenhagen and commits to an uncountably infinite proliferation of parallel universes. The Loop Interpretation makes one testable prediction and commits to one real scalar field with one free parameter. Many-Worlds is the right answer to the wrong question. The loop picture dissolves the collapse problem rather than solving it.Three gaps are honestly stated: the precise value of C* requires a full measurement of μ_vac from galaxy cluster weak lensing profiles; the coupling between the electromagnetic probe field and the loop closure geometry requires numerical computation; and the claim that quantum mechanics is deterministic at the zeptosecond scale is a prediction rather than a derivation.