{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"915fb20c-0cc3-51b0-9f3f-6bc118a07775","task_key":"train--Challenge~5f27~5fmain","task_revision_id":"1","upstream_id":"Challenge_27_main","short_description":"Consider a one-axis twisting interaction described by the Hamiltonian…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the value of $\\\\xi^2_{\\\\rm opt}$ in decibel.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    xi_opt_2: float, the Wineland spin squeezing parameter optimized over time $t$ ($\\\\xi^2_{\\\\rm opt}$) in dB\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    xi_opt_2 = ...\\n    # ---------------------------------------------------------------\\n\\n    return xi_opt_2\",\"problem_description\":\"# Problem setup:\\nConsider a one-axis twisting interaction described by the Hamiltonian $\\\\hat{H}=\\\\chi\\\\hat{S}^z\\\\hat{S}^z$, where $\\\\hat{S}^z=\\\\sum_{j=1}^N \\\\hat{S}^z_j$ is the total spin operator constructed by summing over $N$ spin-$1/2$ operators. Apart from the one-axis twisting interaction, we also add dissipation terms: single-particle dephasing terms described by Lindblad jump operator $\\\\hat{L}_{z,j}=\\\\sqrt{\\\\gamma_z}\\\\,\\\\hat{S}^z_j$ and spin-particle spin-flip terms described by Lindblad jump operators $\\\\hat{L}_{+,j}=\\\\sqrt{\\\\gamma}\\\\hat{S}^+_j$ and $\\\\hat{L}_{-,j}=\\\\sqrt{\\\\gamma}\\\\hat{S}^-_j$. The Wineland spin-squeezing parameter is defined as $\\\\xi^2\\\\equiv N \\\\min \\\\langle\\\\Delta S_{\\\\perp}^2\\\\rangle/|\\\\langle\\\\hat{\\\\mathbf{S}}\\\\rangle|^2$, where $\\\\hat{\\\\mathbf{S}}$ is the total spin vector, and $\\\\min \\\\langle\\\\Delta S_{\\\\perp}^2\\\\rangle$ denotes the minimum variance in directions perpendicular to the Bloch vector.\\n\\n# Main problem:\\n\\nConsidering the initial state as a coherent spin state pointing in the $+x$ direction, calculate the Wineland spin-squeezing parameter optimized over time $t$ (labelled by $\\\\xi^2_{\\\\rm opt}$) based on the following parameters: $N=10^6$, $\\\\chi=1.0\\\\times 10^{-6}$, $\\\\gamma=0.01$, $\\\\gamma_z=0.01$. You should express the numerical result in terms of decibels and keep up to three significant figures.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}