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arXiv:2608.24243

Three-slit interference with a which-path memory ancilla: A bright-dark state formulation

Ajay Kumar, Guruprasad Kadam, Anirban Pathak

quant-phSubmitted Aug 25, 2026• Announced Aug 26, 2026• 0 citations• Revised Sep 1, 2026 (v2)
v1 · Aug 25, 2026v2 · Sep 1, 2026
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Abstract

In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy $S_D$ of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence $C_D$ and bright--dark coherence $C_{BD}$. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas $C_D$ is not by itself a basis-independent physical observable, $C_{BD}$ is basis-invariant. We establish that, for two paths, $C_{BD}$ is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths, $M\geq 3$, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.

Comments
13 pages, 1 Figure, updated references

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In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy SDS_DSD​ of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence CDC_DCD​ and bright--dark coherence CBDC_{BD}CBD​. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas CDC_DCD​ is not by itself a basis-independent physical observable, CBDC_{BD}CBD​ is basis-invariant. We establish that, for two paths, CBDC_{BD}CBD​ is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths, M≥3M\geq 3M≥3, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.
Building upon the recently introduced particle interpretation of the double-slit experiment [Phys. Rev. Lett. 134, 133603 (2025)] which attributes interference phenomena to detector-coupled (bright) and detector-uncoupled (dark) states of light, we develop a continuous-mode extension of the bright- and dark-state framework. This extension addresses a conceptual distinction between interference and diffraction, that is, the transition from a finite set of discrete paths to a continuum of modes. Through the construction of a complete detector-oriented basis for single-slit diffraction, we demonstrate that the observed diffraction pattern arises from projection of the photon state onto a single bright mode by identifying the detectable and undetectable modes, with photons detected at intensity minima having zero probability, as they reside in modes spanning an infinite-dimensional dark subspace. Our approach thus provides a unified particle-based explanation of diffraction that connects quantum and classical wave optics, and reveals distinctive quantum signatures in higher-order correlations.
Interference phenomena, such as those observed in Young’s double-slit experiment, are foundational to quantum mechanics, yet their interpretation continues to spark debate. Villas-Boas et al. [Phys. Rev. Lett. 134, 133603 (2025)] propose a quantum-optical framework attributing non-detection in regions of destructive interference to photons occupying ``perfectly dark'' states, which they claim do not interact with a two-level atom sensor due to vanishing coupling in the Jaynes-Cummings Hamiltonian. We argue that this interpretation is fundamentally flawed. Dark states, such as the out-of-phase coherent state ∣α,−α⟩ |\alpha, -\alpha\rangle ∣α,−α⟩, are readily detectable in alternative experimental setups, including dispersive coupling in cavity QED and photon-counting detectors like photomultiplier tubes or avalanche photodiodes, which are sensitive to the photon number operator. This detectability undermines the assertion that dark states are the intrinsic cause of non-detection in destructive interference regions. Instead, the quantum mechanical superposition principle, combined with the Born rule, fully accounts for interference patterns across all detection schemes, as evidenced by well-established experiments such as single-photon double-slit interference, Hong-Ou-Mandel two-photon interference, and cavity QED measurements. By overgeneralizing a detector-specific effect, the dark-state framework introduces an unnecessary and redundant construct, as the standard quantum mechanical formalism already provides a complete and experimentally validated explanation of interference phenomena.
Interference is conventionally attributed to path-accumulated phase differences, with measurement treated as a passive readout. Here we demonstrate that single-particle interference is governed by the relative phase between the prepared quantum state and the detector-defined measurement basis -- a joint quantity that is operationally inaccessible in any conventional interferometer. Using coherently seeded entangled nonlinear biphoton sources, we show that independently scanning the pump phase difference, the seed phase difference, or the signal interferometric phase each produces identical sinusoidal fringes (V≈0.99V\approx0.99V≈0.99) -- a three-scan equivalence impossible in any two-mode interferometer. The fringe visibility is continuously controlled through the idler-state overlap, directly encoding quantum distinguishability without idler detection. The same measurement-defined interference law persists from the single-photon to the high-flux regime. The bright-dark collective-state structure demonstrated here unifies coherent population trapping and electromagnetically induced transparency in atomic ΛΛΛ-systems, discrete photonic interference, and single-slit diffraction within a common framework differing only in dark-subspace dimensionality, establishing measurement-defined photonic modes as a fundamental resource for quantum photonics.
Abstract We introduce a generalized algebraic framework for the bright–dark mode decomposition of a two-path quantum interferometer entangled with a path-sensitive detector. Within this formulation, the loss of interference visibility is reinterpreted not as a destruction of quantum coherence, but as a conserved, coherent redistribution of amplitude between a bright (interfering) sector and a dark (path-informative) sector of the joint quanton–detector state. Unlike previous bright–dark formulations restricted to bosonic field-mode algebra in optical or cavity-QED systems, our approach utilizes the universal SU (2) geometry of the two-path Hilbert space. This allows the formalism to be applied to any single-particle ( N = 1) interferometer, including massive fermions such as electrons or neutrons, where particle statistics introduce no additional constraints. We demonstrate that as detector distinguishability increases, amplitude flows continuously and predictably into the dark sector, providing a quantitative redistribution sum rule that governs the transition from interference to which-path information. This algebraic perspective offers a unified, platform-independent language for characterizing decoherence and complementarity, providing a direct operational framework for monitoring information flow in diverse quantum interferometric platforms.
We present a detailed numerical investigation of the internal encoding of path information in the double-slit experiment within the Unified Dimensional Cohesion Theory (UDCT 4.3) framework. Using the Auxiliary Variable Method, we evolve a geometric memory field concurrently with the wavefunction in a strictly unitary manner. In one-dimensional simulations, we systematically vary the memory coupling strength γ across the range [0, 100] with fixed relaxation time τ = 0.12 and perform quantitative analysis of interference visibility and peak broadening. Visibility is computed using peak detection with prominence thresholding on the final probability density. In two-dimensional simulations with a physically realistic double-slit barrier, we demonstrate that the geometric memory field develops a clear spatial asymmetry between the two slits. This asymmetry is quantified and shown to encode which-path information internally without any external measurement. We compare our wavefunction-based approach with previous trajectory-based formulations (v4.2) and discuss the advantages and limitations of each. Our results provide concrete evidence that geometric memory can serve as a physically grounded internal mechanism for path distinguishability in quantum systems.
We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple-beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease but, under certain conditions, lead to an increase of the fringe contrast. Here we explain this seemingly counterintuitive effect based on a model for a multipath interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multipath situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the l1{l}_{1}l1​ norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multipath interference and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.