赋能应用的量子 API
通过专有的，尽量解析的算法方案与高性能 C++ 基础设施，搭建前沿量子理论与工业级软件之间的桥梁。
核心技术三角
深度掌握量子力学理论及其数学结构，为它在物理与化学领域的应用提供严谨的理论框架。
自主研发的 1/rⁿ 势能全套解析解系列及与之相应的量子亏损理论 (QDT) ，是处理相互作用的数学基础。
源自 1992-94 年起始的生产级 C++ 基因。确保关键任务不但高效且绝对稳健。
技术前瞻：未公开的知识产权
一系列正在转化为生产力工具的核心技术资产。
新一代薛定谔方程传播子
专为高效数值求解薛定谔方程开发的新型传播算法。
多尺度量子亏损理论 (msQDT)
极大地改善精度和拓宽适用的能量范围。
各向异性势能的量子亏损理论 (MQDTA & msMQDTA)
突破对称性限制，实现对非球面势能的精准多尺度描述。
访问与路线图
意波量子 API 目前仅通过我们的战略咨询服务提供。分级 SaaS 访问与机构授权方案正在开发中。
相关技术细节与演示案例将陆续通过本网站及微信服务号发布。
论文精选
量子物理理论
- Bo Gao, "Quantum-defect theory of atomic collisions and molecular vibration spectra", Phys. Rev. A, 58, 4222 (1998).
Introduced the foundational quantum-defect theory (QDT) for long-range potentials.
- Bo Gao, "Breakdown of Bohr's Correspondence Principle", Phys. Rev. Lett., 83, 4225 (1999).
Demonstrated the non-classical behavior of high-lying states in long-range potentials.
- Bo Gao, "Zero-energy bound or quasibound states and their implications for diatomic systems with an asymptotic van der Waals interaction", Phys. Rev. A, 62, 050702 (2000).
Explored the threshold properties of van der Waals systems.
- Bo Gao, "Angular-momentum-insensitive quantum-defect theory for diatomic systems", Phys. Rev. A, 64, 010701 (2001).
Simplified multichannel problems through angular-momentum-insensitive parameters.
- Haixiang Fu, Yuzhu Wang, and Bo Gao, "Beyond the Fermi pseudopotential: A modified Gross-Pitaevskii equation", Phys. Rev. A, 67, 053612 (2003).
Extended the GPE to account for more complex interaction potentials in BECs.
- Bo Gao, Eite Tiesinga, Carl J. Williams, and Paul S. Julienne, "Multichannel quantum-defect theory for slow atomic collisions", Phys. Rev. A, 72, 042719 (2005).
A unified framework for low-energy scattering and Feshbach resonances.
- Bo Gao, "General form of the quantum-defect theory for -1/rα type of potentials with α > 2", Phys. Rev. A, 78, 012702 (2008).
The definitive generalization of QDT for all power-law potentials.
- Bo Gao, "Analytic description of atomic interaction at ultracold temperatures: The case of a single channel", Phys. Rev. A, 80, 012702 (2009).
Provided precise analytic scattering lengths and effective ranges.
- Bo Gao, "Universal Properties in Ultracold Ion-Atom Interactions", Phys. Rev. Lett., 104, 213201 (2010).
Identified universal scaling laws for ion-atom systems at microkelvin temperatures.
- Bo Gao, "Universal Model for Exoergic Bimolecular Reactions and Inelastic Processes", Phys. Rev. Lett., 105, 263203 (2010).
A predictive model for chemical reaction rates based on universal QDT.
- Bo Gao, "Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes", Phys. Rev. A, 83, 062712 (2011).
Quantized the Langevin model to describe ion-molecule capture.
- Bo Gao, "Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance", Phys. Rev. A, 84, 022706 (2011).
Analytical formulation for Feshbach resonance shapes and shifts.
数学与解析解方案
- Bo Gao, "Multiphoton detachment in a static uniform magnetic field", Phys. Rev. A, 41, 5039 (1990).
Analytic study of magnetic field effects on multiphoton electron detachment.
- Bo Gao and Anthony F. Starace, "Laser-induced detachment processes in an electric field", Phys. Rev. A, 42, 5580 (1990).
Detailed derivation of detachment cross-sections in combined fields.
- Bo Gao, "Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Analytic results", Phys. Rev. A, 48, 2443 (1993).
Provided exact solutions for atomic steady states in near-resonant fields.
- Bo Gao, "Solutions of the Schrödinger equation for an attractive 1/r6 potential", Phys. Rev. A, 58, 1728 (1998).
Derived the first complete set of analytic solutions for the van der Waals potential.
- Bo Gao, "Repulsive 1/r3 interaction", Phys. Rev. A, 59, 2778 (1999).
Analytic treatment of the repulsive dipole-dipole interaction threshold.
- Bo Gao, "Binding energy and scattering length for diatomic systems", J. Phys. B, 37, 4273 (2004).
Generalized the universal relation between scattering length and binding energy.
- Hao Duan, Li You, and Bo Gao, "Ultracold collisions in the presence of synthetic spin-orbit coupling", Phys. Rev. A, 87, 052708 (2013).
Analyzed scattering modifications induced by synthetic gauge fields.
- Bo Gao, "Quantum-defect theory for -1/r4-type interactions", Phys. Rev. A, 88, 022701 (2013).
Comprehensive analytic framework for ion-atom polarization potentials.
- Haixiang Fu, Mingzhe Li, Meng Khoon Tey, Li You, and Bo Gao, "Multiscale quantum-defect theory and its application to atomic spectrum", New J. Phys., 18, 103016 (2016).
Unified Rydberg and low-lying states through a multiscale potential.
- Bo Gao, "Relation between the change of density of states and the shape of the potential in two-body interactions", Phys. Rev. A, 95, 042704 (2017).
Connected thermodynamics directly to potential energy profiles.
计算与数值创新
- Bo Gao and Anthony F. Starace, "Variational Calculation of Multiphoton Ionization Processes for the H Atom", Phys. Rev. Lett., 61, 404 (1988).
An illustrative application of a new variational method for computing high-order perturbation in quantum mechanics.
- Bo Gao and Anthony F. Starace, "Variational principle for high-order perturbations...", Phys. Rev. A, 39, 4550 (1989).
It is difficult and rare to compute perturbations beyond the second order in quantum mechanics. I developed variational method to enable both efficient and accurate calculations of high-order perturbations. The second paper had results for 12th order perturbation. I have not seen a calculation close to that order after almost 40 years since.
- B. Gao, S. Langer, and P. M. Corry, "Application of the time-dependent Green's function...", Int. J. Hyperthermia, 11, 267 (1995).
Not only innovative in math and numerical method but is also one of the earliest C++ applications in production use at William Beaumont Hospital, Royal Oak, Michigan, where BG was a postdoc for 2 years.
- Ming Li, Li You, and Bo Gao, "Multichannel quantum-defect theory for ion-atom interactions", Phys. Rev. A, 89, 052704 (2014).
Computational implementation for polarization potentials.
- Constantinos Makrides and Bo Gao, "Multichannel quantum-defect theory for heteronuclear group-I systems", Phys. Rev. A, 89, 062718 (2014).
Numerical prediction of resonance locations in mixed systems.
- Ming Li and Bo Gao, "Proton-hydrogen collisions at low temperatures", Phys. Rev. A, 91, 032702 (2015).
Detailed study of charge transfer at the quantum limit.
- Yue Cui, Min Deng, Li You, Bo Gao, and Meng Khoon Tey, "Broad Feshbach resonances in alkali-metal systems", Phys. Rev. A, 98, 042708 (2018).
Tsinghua collaboration: Computational efficiency of MQDT formulation made possible of an exhaustive study of magnetic Feshbach resonances in most alkali-metal species.
实验协作成果
- Shen Dong et al., and Bo Gao, "Observation of broad p-wave Feshbach resonances in 85Rb-87Rb mixtures", Phys. Rev. A, 94, 062702 (2016).
Tsinghua collaboration: Combined theoretical and experimental explorations of p-wave Feshbach resonance.
- Yue Cui et al., Bo Gao, Meng Khoon Tey, and Li You, "Observation of Broad d-Wave Feshbach Resonances...", Phys. Rev. Lett., 119, 203402 (2017).
Tsinghua collaboration: Use d-wave Feshbach resonance to explore d-wave coupling in a many-body quantum system.
- Jiaming Li, Ji Liu, Le Luo, and Bo Gao, "Three-Body Recombination near a Narrow Feshbach Resonance in 6Li", Phys. Rev. Lett., 120, 193402 (2018).
Sun Yat-sen collaboration: Innovative interpretation and analysis of a difficult case of 3-body chemical reaction with the introduction of the concept of direct and indirect processes.
- J. D. Hood et al., B. Gao, and K.-K. Ni, "Multichannel interactions of two atoms in an optical tweezer", Phys. Rev. Research, 2, 023108 (2020).
Harvard collaboration: Provided the first theoretical analysis of multichannel atomic interaction in optical tweezers, enabling precision control of molecule formation and atom-atom interactions.