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arXiv:2302.11884 · ACS Photonics

Order-Invariant Two-Photon Quantum Correlations in PT-Symmetric Interferometers

Tom A. W. Wolterink, Matthias Heinrich, Stefan Scheel, Alexander Szameit

Published Sep 12, 2023• 3 citations
arXivHTMLPDF

Abstract

Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. Yet, surprisingly few systematic properties of these crucial algebraic objects are known. As such, predicting the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. In this work, we identify sequences of concatenated two-mode linear optical transformations whose two-photon behavior is invariant under reversal of the order. We experimentally verify this systematic behavior in parity-time-symmetric complex interferometer arrangements of varying compositions. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways, even in small-scale non-Hermitian networks.

DOI
10.1021/acsphotonics.3c00439

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Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. Yet, surprisingly few systematic properties of these crucial algebraic objects are known. As such, predicting the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. In this work, we identify sequences of concatenated two-mode linear optical transformations whose two-photon behavior is invariant under reversal of the order. We experimentally verify this systematic behavior in parity-time-symmetric complex interferometer arrangements of varying compositions. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways, even in small-scale non-Hermitian networks.
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Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.
With their conceptual description of Parity-Time symmetry in 1998 [1], Bender and Boettcher inaugurated a new field of studies with fascinating implications on topology [2] and exceptional point dynamics [3], to name a few. Typically, PT-symmetric Hamiltonians exhibit real eigenvalues below a certain threshold, whereas above, the PT-symmetry is spontaneously broken as the eigenvalue spectrum becomes complex. Entirely passive configurations based solely on differential losses [7] allow the physics of PT symmetry to be carried over to a quantum-optical context [6] and explored therein [4]. Here we study the ways in which the degree of loss systematically impacts the characteristics of quantum correlations between interfering photons by analyzing the two-photon correlations in PT-symmetric directional couplers.
Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or postselection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum information enables us to infer information about symmetries of multiphoton networks and states and to observe arbitrary degrees of WWW-state entanglement between a small number of photons with a fixed interferometer. These results are therefore of profound interest for future applications of universal inner-mode-resolved linear optics across fundamental science and quantum technologies with photons with experimentally different spectral properties.