Quantum API for Applications

Bridging frontier quantum theory and industrial-scale software through proprietary analytic solutions and high-performance C++ infrastructure.

The Technical Trinity

Quantum Physics & Chemistry

A deep mastery of quantum mechanical theory and its mathematical structures, providing a rigorous theoretical framework for its applications in physics and chemistry.

Mathematical Foundations

Our complete set of analytical solutions for 1/rⁿ potentials and the corresponding Quantum Defect Theory (QDT) provide the essential mathematical foundation for treating particle interactions.

Industrial Computation

Built on a foundation of production-grade C++ dating back to 1992, ensuring that mission-critical tasks are both highly efficient and exceptionally robust.

Future Vanguard: Unpublished IP

A suite of core technical assets currently under transition to our production API.

Next-Gen Schrödinger Propagators

Novel algorithms designed for hyper-efficient numerical solutions of the Schrödinger equation.

Multiscale QDT (msQDT)

Vastly improving precision and significantly broadening the applicable energy range.

QDT for Anisotropic Potentials (MQDTA & msMQDTA)

Breaking symmetry limits for precise multiscale descriptions of non-spherical potentials.

Access & Roadmap

The Yibo Quantum API is currently available exclusively through our strategic consulting engagements. Tiered SaaS access and institutional licensing are currently in development.

Detailed results and demonstrations will be released via this website and our WeChat service account.

Inquire for Early Access

Selected Publications

Quantum Physics Theory

  • 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.

Mathematical & Analytic Solutions

  • 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.

Computational & Numerical Innovation

  • 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.

Experimental Collaborations

  • 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.