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New Journal of Physics

Testing Born’s rule via photoionization of helium

Peter Robert Förderer, Andreas Buchleitner, David Busto, Christoph Dittel

Published Nov 20, 2025• 0 citations
Publisher

Abstract

Abstract State-of-the-art attosecond photoionization experiments are identified as a new platform to test Born’s rule—a postulate of quantum mechanics. A simulation of the so-called Sorkin test under typical experimental conditions infers an achievable measurement precision in the range of the best Sorkin tests to date, demonstrating new opportunities for high-precision tests of Born’s rule via nonlinear matter-wave interferometry. The potential of attosecond photoionization for further fundamental tests of quantum mechanics is discussed.

DOI
10.1088/1367-2630/ae21fd

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Abstract State-of-the-art attosecond photoionization experiments are identified as a new platform to test Born’s rule—a postulate of quantum mechanics. A simulation of the so-called Sorkin test under typical experimental conditions infers an achievable measurement precision in the range of the best Sorkin tests to date, demonstrating new opportunities for high-precision tests of Born’s rule via nonlinear matter-wave interferometry. The potential of attosecond photoionization for further fundamental tests of quantum mechanics is discussed.
We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ( ∼ 10 − 25 s ) currently accessible at high-energy colliders. We focus on targeted tests of the Born rule for spin or polarization probabilities, which offer a particularly clean experimental signal, and which can be described by a simple hidden-variables model of two-state systems proposed by Bell. These probabilities test a remarkable feature of the quantum formalism, whereby expectation values for incompatible experiments are linearly related. Born-rule violations can be parametrized by nonlinear expectation values for quantum measurements of spin or polarization, together with anomalies in ensemble averages, which may then be constrained by experiments. Notable experiments considered here include the recent detection of single photons from top-quark decay, and the indirect measurement of tau-lepton polarization. Repurposing these experiments as tests of the Born rule, however, presents several challenges, which are discussed in this paper.
Born's rule relates detection probabilities to the modulus square of the wave function.It is one of the central principles of quantum mechanics together with that of linear superposition.Single-particle interference is accordingly limited to pairs of quantum paths and higher-order interferences are prohibited.Deviations from Born's law have been quantified via the Sorkin parameter which is proportional to the third-order term.However, while the linearity of quantum theory has been experimentally tested to the level of 10 -20 eV, the Sorkin parameter has only been measured to an accuracy of 2 × 10 -3 in the quantum regime.We here investigate Born's law using many-particle interferences and demonstrate that all interference terms of order (2M + 1) and greater vanish for M particles.We further introduce a family of many-particle Sorkin parameters and show that they are exponentially more sensitive to deviations from Born's rule than their single-particle counterpart.
As a fundamental postulate of quantum mechanics, Born's rule assigns probabilities to the measurement outcomes of quantum systems and excludes multiorder quantum interference. Here we report an experiment on a single spin in diamond to test Born's rule by inspecting the third-order quantum interference. The ratio of the third-order quantum interference to the second order in our experiment is bounded to the scale of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which provides a stringent constraint on the potential breakdown of Born's rule.
Attosecond physics enables the study of ultrafast coherent electron dynamics in matter upon photoexcitation and photoionization, revealing spectacular effects such as hole migration and coherent Auger dynamics in molecules. In the photoionization scenario, there has been a strong focus on probing the physical manifestations of internal quantum coherence within the individual parent ion and photoelectron systems. However, quantum correlations between these two subsystems emerging from attosecond photoionization events have thus far remained much more elusive. In this work, we design theoretically and model numerically a direct probe of quantum entanglement in attosecond photoionization in the form of a Bell test. We simulate from first principles a Bell test protocol for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime predicting robust violation of the Bell inequality. This theoretical result paves the way for the direct observation of entanglement in the context of ultrafast photoionization of many-electron systems. Our work provides a novel perspective on attosecond physics directed toward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics, including in the chemical decomposition pathways of molecular ions. Published by the American Physical Society 2024