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<p>Quantum tunneling phenomena are fundamentally altered by electromagnetic fields, leading to flux quantization, Berry phases, and novel transport properties. However, traditional solid-state investigations suffer from disorder and decoherence effects that obscure precise measurements. We present a comprehensive theoretical and experimental framework for probing electromagnetic modifications of quantum tunneling using ultracold atoms in synthetic gauge fields. Our approach combines rigorous tight-binding models with Peierls substitution, deriving effective continuum Hamiltonians with momentum-valued vector and scalar potentials. We establish validity regimes for WKB approximations with Langer corrections and implement mode-resolved magnetic tunneling theory. Through exact diagonalization, transfer-matrix simulations, and comprehensive error analysis via covariance matrices, we predict modest but measurable tunneling modifications of 0.3–2.8%, detectable at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2-3\sigma\)</EquationSource> </InlineEquation> confidence levels under realistic experimental constraints. We provide detailed protocols including flux calibration (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Phi /\Phi _0 = 0.12 \pm 0.02\)</EquationSource> </InlineEquation>), coherence windows (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>300 ms), and statistical requirements (320 shots per data point). All major systematic uncertainties are quantified, with emphasis on discrimination protocols and null result interpretation. This work represents a paradigmatic shift toward reproducibility-focused experimental design in quantum simulation through three key innovations: (i) realistic effect predictions accounting for all systematic errors, (ii) explicit null-result interpretation protocols providing scientific value regardless of outcome, and (iii) comprehensive discrimination methods separating genuine electromagnetic effects from competing mechanisms—providing immediate experimental guidance while setting new reproducibility standards for the field.</p>

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Quantum Tunneling in Synthetic Gauge Fields: A Conservative and Reproducible Framework for Ultracold Atoms

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Mahgoub A. Salih,
  • Mohamed Y. Shirgawi

摘要

Quantum tunneling phenomena are fundamentally altered by electromagnetic fields, leading to flux quantization, Berry phases, and novel transport properties. However, traditional solid-state investigations suffer from disorder and decoherence effects that obscure precise measurements. We present a comprehensive theoretical and experimental framework for probing electromagnetic modifications of quantum tunneling using ultracold atoms in synthetic gauge fields. Our approach combines rigorous tight-binding models with Peierls substitution, deriving effective continuum Hamiltonians with momentum-valued vector and scalar potentials. We establish validity regimes for WKB approximations with Langer corrections and implement mode-resolved magnetic tunneling theory. Through exact diagonalization, transfer-matrix simulations, and comprehensive error analysis via covariance matrices, we predict modest but measurable tunneling modifications of 0.3–2.8%, detectable at \(2-3\sigma\) confidence levels under realistic experimental constraints. We provide detailed protocols including flux calibration ( \(\Phi /\Phi _0 = 0.12 \pm 0.02\) ), coherence windows ( \(\sim\) 300 ms), and statistical requirements (320 shots per data point). All major systematic uncertainties are quantified, with emphasis on discrimination protocols and null result interpretation. This work represents a paradigmatic shift toward reproducibility-focused experimental design in quantum simulation through three key innovations: (i) realistic effect predictions accounting for all systematic errors, (ii) explicit null-result interpretation protocols providing scientific value regardless of outcome, and (iii) comprehensive discrimination methods separating genuine electromagnetic effects from competing mechanisms—providing immediate experimental guidance while setting new reproducibility standards for the field.