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README.md

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 [![License: MIT](https://img.shields.io/badge/License-MIT-blue.svg)](https://opensource.org/license/mit)
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+🧩 **New (Nov. 5):** We added **CPhO 2025 (Chinese Physics Olympiad)** — the national final theoretical exam to the HiPhO benchmark.
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 🏆 **New (Sep. 16):** We launched "[**PhyArena**](https://phyarena.github.io/)", a physics reasoning leaderboard incorporating the HiPhO benchmark.
 
 ## 🌐 Introduction

data/PanPhO_2025.json

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         "id": "PanPhO_2025_6_10",
         "context": "[Generation of ultrashort electromagnetic pulse] \n\nThe Nobel Prize in Physics 2018 \\& 2023 were awarded to pioneers who contributed to \"Method of generating high-intensity, ultra-short optical pulses\" and \"Generation of attosecond pulses of light for the study of electron dynamics in matter\". Attosecond pulse refers to electromagnetic field with a duration on the order of $10^{-18}$ second. The advent of attosecond technique has made possible the study of ultrafast dynamics in physical, chemical and biological systems at a record high temporal resolution. Thus far, the most widely used method to generate attosecond pulse (Nobel Prize in Physics 2023) is to rely on the interaction of gas molecules and intensive femtosecond laser pulse (Nobel Prize in Physics 2018). In this question, we will explore some important aspects of the short pulse generation.\n\nThe following identity may be useful:\n$\\int_{-\\infty}^{\\infty} e^{-a \\omega^{2}} e^{-i \\omega t} d \\omega = \\sqrt{\\frac{\\pi}{a}} \\exp \\left(-\\frac{t^{2}}{4 a}\\right)$ \n\nPhysical constants: \nElectric charge: $e = 1.60 \\times 10^{-19} \\mathrm{C}$ \nElectron mass: $m_{e} = 9.11 \\times 10^{-31} \\mathrm{kg}$ \nSpeed of light in vacuum: $c = 3.00 \\times 10^{8} \\mathrm{m} / \\mathrm{s}$ \nPlanck constant: $h = 6.63 \\times 10^{-34} \\mathrm{J} \\mathrm{s}$ \n\nPart B: Dispersion \n\nBefore entering the attosecond $(10^{-18} \\mathrm{s})$ regime, it historically took numerous effort of researchers to just generate femtosecond pulses ($1 \\mathrm{fs} = 10^{-15} \\mathrm{s}$), which now can be readily obtained from a standard Ti:sapphire laser and serve as the starting point to generate the even shorter attosecond pulse. One challenge at the time was to devise a laser cavity that can fight against the strong dispersion arise from traversing the Ti:sapphire crystal, an indispensable element in which amplification takes place. The dispersion here means the frequency dependent refractive index in the Ti:sapphire crystal, which has a strong absorption at 2.5 eV.\n\n[figure1]\n\nB1: Assuming the transition responsible for the absorption can be described with a classical model for an oscillating bound electron (mass $m$) oscillating at a characteristic frequency $(\\Omega_{0})$ about a nucleus. In the presence of an external AC E-field of amplitude $E_{0}$ oscillating at single frequency $\\omega$, $X_{0}$ is the largest possible displacement of the electron. The damping force of the oscillator can be described by $f_{d} = -m \\gamma v$ where $v$ is the velocity of the oscillator and $\\gamma$ is a single parameter to describe the total effect from energy loss of all kinds. \n\nPart D: High-harmonic generation of attosecond pulse \n\nTake a short femtosecond pulse from Ti:sapphire laser (center frequency $\\omega_{0}$) and focus it into a gas medium. One could generate light at integer multiples of the driving frequency, often referred to as high-harmonic generation (HHG).",
         "question": "To allow radiation at new frequencies, please modify the oscillator model correspondingly and show your modification is viable.",
-        "test": "In the previous analysis (see B1–B2), the motion of a bound electron under an external AC electric field was modeled as a damped driven linear harmonic oscillator. Specifically, for an electron of mass m, natural frequency Ω₀, and damping coefficient γ, subjected to an electric field E(t) = E₀ e^{-iωt}, the equation of motion was:\n\nm ẍ + mγ ẋ + mΩ₀² x = -e E₀ e^{-iωt}.\n\nThis model describes linear response near resonance and explains absorption and dispersion. To account for high-harmonic radiation, the oscillator model must be extended to include anharmonic terms in the potential, leading to nonlinear response.",
         "marking": [
             "Award 1.0 pt if the answer writes down or correctly explains the modified equation of motion",
             "Award 1.5 pts if the answer shows how the first-order solution leads to $x_1 \\propto E_0 e^{i \\omega_0 t}$",