HOMI: A Cross-Disciplinary Research Concept

• HOMI is a polysemous term spanning quantum optics and beyond, defined by key applications such as Hong–Ou–Mandel interference in two-photon experiments.
• In quantum optics, it characterizes two-photon interference patterns that enable spectral analysis and improved time estimation through Fourier-transform techniques.
• In machine learning, HCI, and embedded vision, HOMI denotes innovative strategies for high-order label learning, model-informed optimization, and ultra-fast AI platforms.

HOMI is a polysemous research term. In quantum optics it denotes Hong–Ou–Mandel interference, the two-photon interference effect observed when two indistinguishable photons impinge on a 50:50 beam splitter. In other literatures it names “High-Rank and High-Order MultI-label learning,” “Human-in-the-Loop Optimization with Model-Informed Priors,” and “HOMI: Ultra-Fast EdgeAI platform for Event Cameras”; separate historical literature uses Homi as the given name of Homi J. Bhabha (Jin et al., 2017, Si et al., 2022, Liao et al., 9 Oct 2025, H et al., 18 Aug 2025, Singh, 2009).

Usage	Domain	Representative source
Hong–Ou–Mandel interference	Quantum optics	(Jin et al., 2017)
High-Rank and High-Order MultI-label learning	Machine learning	(Si et al., 2022)
Human-in-the-Loop Optimization with Model-Informed Priors	HCI and Bayesian optimization	(Liao et al., 9 Oct 2025)
Ultra-Fast EdgeAI platform for Event Cameras	Embedded vision systems	(H et al., 18 Aug 2025)
Homi J. Bhabha	History of physics	(Singh, 2009)

1. Hong–Ou–Mandel interference in quantum optics

In the quantum-optical literature, HOMI is a hallmark two-photon interference effect. Two photons enter a balanced 50:50 beam splitter from opposite input ports; when the photons are perfectly indistinguishable and arrive simultaneously, they interfere so that they always exit together from the same output port, and the coincidence rate drops to ideally zero. In the multimode SPDC treatment, the biphoton state is written as

$$\left| \psi_2 \right\rangle = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} d\omega_s\, d\omega_i \; f_2(\omega_s ,\omega_i)\, \hat a_s^\dag(\omega_s)\hat a_i^\dag(\omega_i)\left| 00 \right\rangle,$$

and, for a symmetric and real joint spectral amplitude, the HOM coincidence probability becomes

$$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$

This expression shows that the HOM pattern is governed by the joint spectral intensity and, specifically, by the frequency difference $\omega_s-\omega_i$ (Jin et al., 2017).

The central observable is the HOM dip. At $\tau=0$, the cosine term reaches its maximal contribution, and the coincidence channel is ideally extinguished. As $|\tau|$ increases, the cosine oscillates and averages out, so the coincidence rate rises toward the distinguishable-photon limit. The envelope and detailed lineshape depend on the spectral structure of the biphoton wavefunction, which is why HOMI is routinely used as a probe of indistinguishability, temporal overlap, and spectral correlations (Jin et al., 2017).

A distinct but closely related setting is HOM interference between independent photon sources. In that case, the interfering photons are generated in two independent sources rather than in a single SPDC source, so high visibility requires temporal indistinguishability, spectral indistinguishability, identical polarization states, identical spatial modes, and suppression of multi-pair emission. The relevant four-fold coincidence probability depends on the overlap of the two joint spectral amplitudes $f_1$ and $f_2$, making HOMI-IPS a fundamental block for quantum gate, Shor’s algorithm, and Boson sampling (Jin et al., 2015).

2. Spectral analysis, e-WKT, and complete characterization

A major theoretical development treats HOMI as the quantum counterpart of Fourier-transform spectroscopy. The extended Wiener–Khinchin theorem defines projected spectra

$$F_2^{\pm}(\omega_{\pm}) \equiv \frac{1}{2} \int d\omega_{\mp}\; |f_2(\omega_s,\omega_i)|^2,$$

with $\omega_{\pm}=\omega_s\pm\omega_i$, and relates them to second-order correlation functions through

$$F_2^{\pm}(\omega_{\pm}) = \frac{1}{2\pi} \int d\tau \, G_2^{\pm}(\tau) e^{i\omega_{\pm} \tau}.$$

Within this framework, HOMI corresponds to the minus branch: the time-domain HOM interferogram yields the difference-frequency spectrum $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$0, while NOON-state interference yields the sum-frequency spectrum $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$1. Experimentally, the reported HOMI pattern had a triangular envelope with FWHM $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$2, visibility $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$3, and a Fourier-transform-derived difference-frequency bandwidth $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$4, in excellent agreement with the anti-diagonal TSI projection of $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$5 (Jin et al., 2017).

A later proposal combines NOONI and HOMI in a single interferometer. Its central normalized coincidence rate is

$$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$6

so the same time-domain interferogram carries both $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$7, the Fourier signature of the frequency-difference spectrum, and $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$8, the Fourier signature of the frequency-sum spectrum. The stated aim is complete spectral characterization of an arbitrary two-photon state with exchange symmetry from a single quantum interferogram, with direct relevance to quantum Fourier-transform spectroscopy and quantum metrology (Li et al., 2023).

This usage shifts HOMI from a test of photon bunching to a spectral analysis tool. The concrete significance is that spectral correlation information can be obtained from time-domain quantum interferences by Fourier transform, without direct two-dimensional spectral scans of the biphoton state (Jin et al., 2017).

3. Multimode, spectral-domain, and gate-characterization extensions

In multimode frequency-entangled states, HOMI acquires a structured “comb-like” form. For a joint spectral amplitude that is a sum over $$P(\tau) = \frac{1}{2} \left[ 1 - \int d\omega_s d\omega_i \, |f(\omega_s,\omega_i)|^2 \cos[(\omega_s - \omega_i)\tau] \right].$$9 discrete frequency modes, the coincidence probability reduces to

$\omega_s-\omega_i$0

where $\omega_s-\omega_i$1 is the envelope factor inherited from single-mode HOMI and $\omega_s-\omega_i$2 is the details factor. This establishes the paper’s mapping between multi-mode HOM interference and multi-slit interference, with multiple spectral modes playing the role of multiple slits. Within the same analysis, the square root of the maximal Fisher information increases linearly with the number of modes, indicating a direct metrological advantage for time estimation (Guo et al., 2023).

Spectrally resolved HOMI between independent sources makes the delay-dependent interference structure visible in the joint spectrum itself. Using a fast fiber spectrometer, the correlated spectral intensity was measured as a function of delay, revealing spectral fringes that are hidden in time-domain coincidence counts alone. In the heralded single-photon case, the measured raw visibility was $\omega_s-\omega_i$3, and post-processing spectral filtering improved it to $\omega_s-\omega_i$4 for a 2 ns window and $\omega_s-\omega_i$5 for a 1 ns window. The same work emphasizes that time-domain HOM dips alone cannot diagnose subtle spectral mismatch across many independent sources (Jin et al., 2015).

HOMI also appears in frequency-domain gate characterization. A dual-$\omega_s-\omega_i$6 EIT four-wave-mixing frequency beam splitter can act as a frequency-mode Hadamard gate, and the proposed characterization route uses HOMI as quantum process tomography. In that setting, the normalized cross correlation

$\omega_s-\omega_i$7

is measured from the HOM dip of two weak coherent pulses at $\omega_s-\omega_i$8 and $\omega_s-\omega_i$9, which yields $\tau=0$0 and a reported fidelity $\tau=0$1 for the frequency-mode Hadamard gate (Chang et al., 2019).

4. Machine-learning and optimization usages of HOMI

In machine learning, HOMI denotes “High-Rank and High-Order MultI-label learning.” The method is motivated by the claim that the label matrix is generally a full-rank or approximate full-rank matrix, making low-rank factorization inappropriate. Instead of a latent low-rank embedding, it models explicit label self-representation in the original label space: $\tau=0$2 while jointly learning a linear predictor $\tau=0$3 and a Laplacian regularizer based on the local geometric structure of the input. The full objective combines prediction loss, manifold regularization, a high-order label correlation term, and $\tau=0$4 regularization, and the paper reports comparative studies over twelve benchmark data sets validating the effectiveness of the proposed algorithm (Si et al., 2022).

In HCI and Bayesian optimization, HOMI denotes “Human-in-the-Loop Optimization with Model-Informed Priors.” Here the framework augments human-in-the-loop optimization with a training phase where the optimizer learns adaptation strategies from diverse, synthetic user data generated with predictive models before deployment. The paper instantiates the framework with NAF$\tau=0$5, a Bayesian optimization method featuring a neural acquisition function trained with reinforcement learning. In the mid-air keyboard optimization study, the learned optimizer is evaluated against Transfer Acquisition Function and Continual Bayesian Optimization, and the reported user study shows significantly better performance for NAF$\tau=0$6 at iterations 2 and 3, while all methods improve over time and later converge (Liao et al., 9 Oct 2025).

These two usages share a methodological pattern rather than a subject matter. In both, HOMI names a strategy for encoding structure that standard baselines treat only implicitly: high-order label correlations in one case, and model-informed adaptation strategies in the other (Si et al., 2022, Liao et al., 9 Oct 2025).

5. Systems, robotics, and related nomenclature

In embedded vision, “HOMI: Ultra-Fast EdgeAI platform for Event Cameras” denotes a complete end-to-end platform built around a Prophesee IMX636 event sensor chip, a Xilinx Zynq UltraScale+ MPSoC FPGA chip, and an in-house developed AI accelerator. The platform supports constant-time and constant-event modes for histogram accumulation, linear and exponential time surfaces, and reports $\tau=0$7 accuracy on the DVS Gesture dataset in high-accuracy operation and a throughput of $\tau=0$8 fps in low-latency configuration. The hardware-optimised pipeline uses only $\tau=0$9 of the available LUT resources on the FPGA, leaving headroom for multi-task deployments and more complex architectures (H et al., 18 Aug 2025).

Adjacent embodied-AI nomenclature includes “HALOMI: Learning Humanoid Loco-Manipulation with Active Perception from Human Demonstrations” and “Humanoid Manipulation Interface” (HuMI). HALOMI extends Universal Manipulation Interface with egocentric sensing, a manifold-constrained controller, ego-view alignment, and controller-aware reference trajectory adaptation, and reports an average success rate of $|\tau|$0 across three quantitatively evaluated tasks on a Unitree G1 humanoid robot (Zhao et al., 17 Jun 2026). HuMI is a robot-free demonstration framework for humanoid whole-body manipulation that reports a $|\tau|$1 increase in data collection efficiency compared to teleoperation and a $|\tau|$2 success rate in unseen environments (Nai et al., 6 Feb 2026).

A separate household-data paper characterizes “HOMI/HOMER-style work” as work about rich household environments, realistic human routines, and long-term human–robot interactions, but its proposed framework is named HumanAI rather than HOMI (Singh et al., 6 Feb 2026). This suggests that, outside quantum optics, the string HOMI often functions less as a stable concept than as a project-specific acronym or naming motif.

6. Homi as a proper name: Homi J. Bhabha

A separate historical literature uses Homi as the given name of Homi Jehangir Bhabha (1909–1966), whom one paper describes as the architect of modern science and technology in India. In physics, his major contributions include theory of positron-electron scattering, now known as Bhabha scattering, the Bhabha–Heitler theory of cosmic ray showers, and the prediction of heavier electrons; institutionally, he founded Tata Institute of Fundamental Research and the Laboratories of Atomic Energy Establishment at Trombay (Singh, 2009).

Within the history of cosmic-ray physics in the 1930s, Bhabha appears as one of the theorists whose work helped turn cosmic-ray research into a testing ground for quantum electrodynamics. His 1933 paper on absorption and showers was explicitly linked to Bruno Rossi’s experiments, and the 1937 Bhabha–Heitler cascade theory explained shower formation on the basis of the quantum electrodynamics cross-sections calculated by Bethe and Heitler. The same historical account also identifies Bhabha as a participant in the international network linking Rossi, Fermi, Pauli, Heitler, and Bethe (Bonolis, 2013).

In postwar Indian science, Bhabha was the decisive institutional figure in establishing radio astronomy at TIFR. A historical study of the Tata Institute’s radio astronomy group states that he made the decisive offer to start a radio astronomy project in early 1962, thereby turning a loose international network of young Indian radio astronomers into a concrete program that later led to the Ooty Radio Telescope and the Giant Metrewave Radio Telescope (Goss, 2014).

Taken together, these usages show that HOMI is not a unitary concept. It is a cross-disciplinary label whose most technically developed meaning is Hong–Ou–Mandel interference, but whose acronymic reuse in machine learning, optimization, embedded systems, and robotics, and whose overlap with the proper name Homi, make contextual disambiguation essential.