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Future Vanguard: Unpublished IP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).

    Initial formulation of quantum-defect theory (QDT) for van der Waals potential using analytic solutions. Used to relate bound spectrum to scattering and to relate effective range to scattering length.

  • Bo Gao, "Breakdown of Bohr's Correspondence Principle", Phys. Rev. Lett., 83, 4225 (1999).

    Established the fundamental difference between quantum systems bound by -1/rn potential with n≤2 and those with n>2. For the former, the system is more classical for greater principle quantum numbers, while the reverse is true for latter type of systems.

  • 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).

    Used QDT to reveal some of the universal behaviors followed by all weakly-bound diatomic molecules.

  • Bo Gao, "Angular-momentum-insensitive quantum-defect theory for diatomic systems", Phys. Rev. A, 64, 010701 (2001).

    Discovered the angular-momentum-insensitive nature of a properly defined short-range parameter for atom-atom interactions. Essential for describing interaction over a wide range of energies and is the mathematical foundation for a future database of atom-atom interactions.

  • 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 and more realistic 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).

    NIST collaboration: It started the applications of multichannel quantum defect theory (MQDT) in cold-atom physics.

  • 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 to all power-law potentials. The description of interaction using reflection and transmission amplitudes, introduced here, is a fundmental progress with long-lasting impact.

  • Bo Gao, "Analytic description of atomic interaction at ultracold temperatures: The case of a single channel", Phys. Rev. A, 80, 012702 (2009).

    Precise analytic description for all partial waves, including the introduction of a generalized scattering length for all partial waves and an analytic description of shape resonances in all partial waves.

  • Bo Gao, "Universal Properties in Ultracold Ion-Atom Interactions", Phys. Rev. Lett., 104, 213201 (2010).

    The rich structures and universal behaviors of ion-atom systems as dictated by the polarization potential.

  • Bo Gao, "Universal Model for Exoergic Bimolecular Reactions and Inelastic Processes", Phys. Rev. Lett., 105, 263203 (2010).

    An accurate and predictive universal model for exoergic neutral-neutral chemical reactions. It is but a first application of much deeper MQDT for reactions based on reflection and transmission amplitudes.

  • Bo Gao, "Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes", Phys. Rev. A, 83, 062712 (2011).

    Another application of MQDT for reactions based on reflection and transmission amplitudes, applied here to ion-molecule reactions.

  • Bo Gao, "Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance", Phys. Rev. A, 84, 022706 (2011).

    Precise analytic description and rigorous definitions and physical meanings of broad and narrow Feshbach resonances, in all partial waves.

Mathematical & Analytic Solutions

  • Bo Gao, "Multiphoton detachment in a static uniform magnetic field", Phys. Rev. A, 41, 5039 (1990).

    Analytic solution for an electron in a combination of a laser field and a static magnetic field. Important for understanding matter interaction with strong fields.

  • Bo Gao and Anthony F. Starace, "Laser-induced detachment processes in an electric field", Phys. Rev. A, 42, 5580 (1990).

    Analytic solution for an electron in a combination of a laser field and a static electric field. Important for understanding matter interaction with strong 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 analytic solutions for atomic steady states in near-resonant fields. One of the very few nontrivial analytic density-matrix solutions.

  • Bo Gao, "Solutions of the Schrödinger equation for an attractive 1/r6 potential", Phys. Rev. A, 58, 1728 (1998).

    First analytic solution for the van der Waals potential, difficult and unexpected. It provides the foundation for the quantum-defect theory (QDT) for atom-atom interactions.

  • Bo Gao, "Repulsive 1/r3 interaction", Phys. Rev. A, 59, 2778 (1999).

    Another difficult and unexpected analytic solution for a van der Waals-type potential. Its importance will grow even further when incorporated into multichannel quantum defect theory for anisotropic potentials (MQDTA).

  • Bo Gao, "Binding energy and scattering length for diatomic systems", J. Phys. B, 37, 4273 (2004).

    Analytic formulas relating a scattering length to a binding energy, for not only s but also other partial waves.

  • Hao Duan, Li You, and Bo Gao, "Ultracold collisions in the presence of synthetic spin-orbit coupling", Phys. Rev. A, 87, 052708 (2013).

    Analytic solutions for interaction via a synthetic gauge field. It is of interest in condensed matter physics in connection with topological insulators.

  • 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).

    First analytic solution for a two-scale potential. It helps to unified Rydberg and low-lying states through a multiscale QDT (msQDT).

  • 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).

    Exact analytic relationship between the change of density of states and the shape of a potential. It is a stepping stone towards a deeper understanding of complexity of N-body quantum system and their thermodynamic behaviors.

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. This paper, using our variational method, led to accurate results for up to 12th-order perturbation. We have not seen a calculation close to that order after almost 40 years since. Let us know if you have seen one.

  • 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 in medical physics for 2 years.

  • Ming Li, Li You, and Bo Gao, "Multichannel quantum-defect theory for ion-atom interactions", Phys. Rev. A, 89, 052704 (2014).

    MQDT treatment is finally able to reveal all the complexity and glory of ion-atom interactions: Feshbach resonances, diffraction resonances, effects of hyperfine structure, and effects of idential nuclei.

  • Constantinos Makrides and Bo Gao, "Multichannel quantum-defect theory for heteronuclear group-I systems", Phys. Rev. A, 89, 062718 (2014).

    Computationally efficient MQDT formulation of magnetic Feshbach resonances in alkali-metal systems.

  • Ming Li and Bo Gao, "Proton-hydrogen collisions at low temperatures", Phys. Rev. A, 91, 032702 (2015).

    Detailed study of astronomically important proton-hydrogen interaction that included the effects of hyperfine structure for the first time.

  • 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 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 exploration of p-wave Feshbach resonances.

  • 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.