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Review of Scientific Instruments

A study of crosstalk in quantum degeneracy coincidence measurements

Arjun Krishnan U M, Raúl Puente, M. A. H. B. Md Yusoff, Sam Keramati, Herman Batelaan

Published Apr 1, 2025• 0 citations
Publisher

Abstract

For a continuous beam, particles that arrive at random times show a flat second-order correlation function, g(2), as measured by a flat coincidence spectrum. A reduction in the likelihood for two particles in such a continuous beam to arrive at the same time is called antibunching, observed as a dip in the otherwise flat coincidence spectrum. For a pulsed beam, the coincidence spectrum consists of a series of equal height peaks, where the "dip" manifests as a reduction in the height of the zero-delay time peak. For electrons, such a dip is an experimental signature of Coulomb repulsion and Pauli pressure. This paper discusses another effect that can produce a similar signature but that does not originate from the properties of the physical system under scrutiny. Instead, the detectors and electronics used to measure those coincidences suffer significantly even from weak crosstalk. A simple model that explains our experimental observations is given. Furthermore, we provide an experimental approach to correct this type of crosstalk.

DOI
10.1063/5.0250020

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For a continuous beam, particles that arrive at random times show a flat second-order correlation function, g(2), as measured by a flat coincidence spectrum. A reduction in the likelihood for two particles in such a continuous beam to arrive at the same time is called antibunching, observed as a dip in the otherwise flat coincidence spectrum. For a pulsed beam, the coincidence spectrum consists of a series of equal height peaks, where the "dip" manifests as a reduction in the height of the zero-delay time peak. For electrons, such a dip is an experimental signature of Coulomb repulsion and Pauli pressure. This paper discusses another effect that can produce a similar signature but that does not originate from the properties of the physical system under scrutiny. Instead, the detectors and electronics used to measure those coincidences suffer significantly even from weak crosstalk. A simple model that explains our experimental observations is given. Furthermore, we provide an experimental approach to correct this type of crosstalk.
The interference between quantum amplitude for two electrons, emitted from two source points, to be detected at two detection points, is a direct result of quantum exchange statistics. Such interference is observed in the coincidence probability, compared with that of statistically independent electrons, by computing the time correlation function from the arrival times of the electrons. When the two detectors are separated by a distance less than the coherence length, the coincidence probability is suppressed for electrons (antibunching) due to the Pauli principle, even though they do not interact with each other. However, electrons are charged particles. The Coulomb potential, which governs the scattering of one charged particle by another, is so long ranged. It is obvious that we must consider the Pauli principle and the Coulomb interactions simultaneously. This paper deals with basic experimental and theoretical investigations of the antibunching behavior of electrons in a free beam by considering the Pauli principle and the direct Coulomb interaction between two individual electrons. The experimentally found dependences are described in a model which considers the Coulomb scattering and theoretical values of correlation signals evaluated by analytical calculations agree with those determined by experiment. A study of the time correlation function from the arrival times of the electrons will lead to an understanding of the physical processes that take place in electron guns.
Correlations between successive detections in beams of free electrons are studied with a transmission electron microscope. For incoherent illumination of the detectors, a certain random coincidence probability is observed, indicative for uncorrelated arrival times of the electrons. When the illumination is changed from incoherent to coherent, a reduction of the random coincidence probability is observed, indicative for antibunching in the arrival times of the electrons. However, the amount of reduction is larger than the theoretically expected value calculated from the Pauli principle, forbidding more than one identical fermion to occupy the same quantum state. For a certain coherent illumination of the detectors, where we use magnetic lenses in electron microscopes for magnifications of the coherence length, we find an enhanced coincidence probability, indicative for bunching in the arrival times of the electrons. This originates from correlations in beams of free electrons due to Coulomb interactions.
We report an experimental observation of correlated-photon statistics using a single detector. The usual coincidence dip in a two-photon polarization interferometer is accompanied by a dip in single-photon detection rates. Surprisingly, a dip in the singles rate is also observed when the interferometer is aligned for a coincidence peak, or anti-dip. This effect is explained by taking into account all possible photon number states that reach the detector, rather than considering just the state post-selected by the coincidence measurement.
We report experimental observations of correlated-photon statistics in the single-photon detection rate. The usual quantum interference in a two-photon polarization interferometer always accompanies a dip in the single-detector counting rate, regardless of whether a dip or a peak is seen in the coincidence rate. This effect is explained by taking into account all possible photon number states that reach the detector, rather than considering just the state postselected by the coincidence measurement. We also report an interferometeric scheme in which the interference peak or dip in the coincidence corresponds directly to a peak or a dip in the single-photon detection rate.
We introduce the pair second-order correlation function gpairs(2)=⟨(P†)2P2⟩/⟨P†P⟩2g_{\textrm{pairs}}^{\left(2\right)}=\left\langle \left(P^{\dagger}\right)^{2}P^{2}\right\rangle /\left\langle P^{\dagger}P\right\rangle ^{2}gpairs(2)​=⟨(P†)2P2⟩/⟨P†P⟩2, defined through the pair operator P†=a†b†P^{\dagger}=a^{\dagger}b^{\dagger}P†=a†b†, to characterize second-order correlations and pair bunching and antibunching in photon-pair creation processes. This quantity directly probes correlations between pair-generation events within a single two-mode quantum state, providing access to the intrinsic pair-generation process beyond conventional single-mode or heralded second-order correlations, which do not directly capture correlations between pair events. Values of gpairs(2)g_{\textrm{pairs}}^{\left(2\right)}gpairs(2)​ greater than, equal to, or less than unity correspond respectively to pair bunching, Poissonian pair statistics, and pair antibunching. Using the Cauchy--Schwarz inequality, we further show that all classical two-mode fields described by a positive Glauber--Sudarshan \ensuremath{P}-function satisfy gpairs(2)≥1g_{\textrm{pairs}}^{\left(2\right)}\geq1gpairs(2)​≥1, so that pair antibunching is classically forbidden and constitutes an unambiguous signature of nonclassicality. We evaluate gpairs(2)g_{\textrm{pairs}}^{\left(2\right)}gpairs(2)​ for several representative quantum states and show, in particular, that even arbitrarily weak two-mode squeezed vacuum states exhibit pair bunching. Comparison with heralded second-order correlations highlights the complementary information provided by these observables. The proposed correlation function is experimentally accessible via standard coincidence measurements, requires no phase reference or state reconstruction, and remains invariant under uniform loss.
The feasibility of observing two-electron interference is considered. The detection of antibunching in an intensity cross-correlation function using coincidence-delay measurement would be the most feasible experiment. The data acquisition time to observe electron antibunching in a coherent field-emission beam is estimated by taking into account the transversal coherence with a possible experimental configuration. With the available measurement system in an optimized condition, the data acquisition time is found to be $\ensuremath{\sim}{10}^{2}$ h, being considered to be the permissible duration of measurement time.