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arXiv:2509.16090

Effects of time dependence in the second order coherence of pulsed light

Joscelyn van der Veen, Daniel F. V. James

Published Sep 19, 2025• 0 citations
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Abstract

For light in a single temporal mode, the time dependence is associated entirely with the deterministic pulse shape rather than the quantum state. This means the second order coherence of light can no longer be understood as the temporal distribution of photons. We calculate the distribution of photon arrival time differences for pulsed light and find that it is inherently strongly bunched in terms of photocount arrival time differences. We further show how to account for the pulse shape when determining the second order coherence that characterizes quantum states.

DOI
10.48550/arxiv.2509.16090

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For light in a single temporal mode, the time dependence is associated entirely with the deterministic pulse shape rather than the quantum state. This means the second order coherence of light can no longer be understood as the temporal distribution of photons. We calculate the distribution of photon arrival time differences for pulsed light and find that it is inherently strongly bunched in terms of photocount arrival time differences. We further show how to account for the pulse shape when determining the second order coherence that characterizes quantum states.
For light in a single temporal mode, the time dependence is associated entirely with the deterministic pulse shape rather than the quantum state. This means the second order coherence of light can no longer be understood as the temporal distribution of photons. We calculate the distribution of photon arrival time differences for pulsed light and find that it is inherently strongly bunched in terms of photocount arrival time differences. We further show how to account for the pulse shape when determining the second order coherence that characterizes quantum states.
For light in a single temporal mode, the time dependence is associated entirely with the deterministic pulse shape rather than the quantum state. This means the second order coherence of light can no longer be understood as the temporal distribution of photons. We calculate the distribution of photon arrival time differences for pulsed light and find that it is inherently strongly bunched in terms of photocount arrival time differences. We further show how to account for the pulse shape when determining the second order coherence that characterizes quantum states.
From the nonclassicality of photon superbunching to the basic property of intensity, we characterize light with correlation and coherence functions. The correlation functions for nonstationary sources, such as short pulses, depend deterministically on the time dependent shape of the field and change the probability of the ensemble in time. We start from the fundamental principles of detection and show how nonstationary fields result in a coherence function that depends not only on the statistics of the field but also on the field shape. This means that observations of bunching and superbunching with ultrafast sources are not indicative of the quantum state of the field.
From the nonclassicality of photon superbunching to the basic property of intensity, we characterize light with correlation and coherence functions. The correlation functions for nonstationary sources, such as short pulses, depend deterministically on the time dependent shape of the field and change the probability of the ensemble in time. We start from the fundamental principles of detection and show how nonstationary fields result in a coherence function that depends not only on the statistics of the field but also on the field shape. This means that observations of bunching and superbunching with ultrafast sources are not indicative of the quantum state of the field.
From the nonclassicality of photon superbunching to the basic property of intensity, we characterize light with correlation and coherence functions. The correlation functions for nonstationary sources, such as short pulses, depend deterministically on the time dependent shape of the field and change the probability of the ensemble in time. We start from the fundamental principles of detection and show how nonstationary fields result in a coherence function that depends not only on the statistics of the field but also on the field shape. This means that observations of bunching and superbunching with ultrafast sources are not indicative of the quantum state of the field.
To fully utilize the energy-time degree of freedom of photons for optical quantum-information processes, it is necessary to control and characterize the temporal quantum states of the photons at extremely short time scales. For measurements of the temporal coherence of the quantum states beyond the time resolution of available detectors, two-photon interference with a photon in a short-time reference pulse may be a viable alternative. In this paper, we derive the temporal measurement operators for the bunching statistics of a single-photon input state with a photon from a weak coherent reference pulse. It is shown that the effects of the pulse shape of the reference pulse can be expressed in terms of a spectral filter selecting the bandwidth within which the measurement can be treated as an ideal projection on eigenstates of time. For full quantum tomography, temporal coherence can be determined by using superpositions of reference pulses at two different times. Moreover, energy-time entanglement can be evaluated based on the two-by-two entanglement observed in the coherences between pairs of detection times.