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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the...
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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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Optimal quantum phase estimation in an atomic gyroscope based on a Bose-Hubbard model.

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    We identified optimal quantum states for atomic gyroscopes. Squeezed entangled states significantly enhance precision, even with moderate losses, outperforming previous methods.

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    Area of Science:

    • Quantum physics
    • Atomic physics
    • Quantum information science

    Background:

    • Atomic gyroscopes utilize quantum states for precise phase estimation.
    • Previous studies explored uncorrelated, BAT, and NOON states for phase uncertainty estimation.
    • The Bose-Hubbard model is a key framework for studying interacting quantum systems.

    Purpose of the Study:

    • To determine the optimal quantum state for an atomic gyroscope.
    • To develop a method for calculating quantum Fisher information for any initial state.
    • To identify states that maximize precision under both lossless and lossy conditions.

    Main Methods:

    • Introduced a Hermitian operator (H) and an equivalent unitary parametrization transformation.
    • Utilized this transformation to calculate quantum Fisher information for arbitrary states.
    • Analyzed performance under both lossless and lossy (dissipative) environments.

    Main Results:

    • Identified Squeezed Entangled States (SES) and Entangled Even Squeezed States (EESS) as optimal probe states.
    • Demonstrated that SES and EESS significantly enhance gyroscope precision.
    • Showed improved performance for moderate loss rates compared to previously studied states.

    Conclusions:

    • SES and EESS represent superior quantum states for atomic gyroscope applications.
    • The developed method provides a universal approach to finding optimal states for quantum sensing.
    • These findings advance the development of high-precision quantum measurement devices.