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Related Concept Videos

Quantum Numbers02:43

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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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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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
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Related Experiment Video

Updated: Jan 29, 2026

Three-Dimensional Ultrasonic Needle Tip Tracking with a Fiber-Optic Ultrasound Receiver
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Quantum-limited fiber-optic phase tracking beyond �� range.

Lidan Zhang, Kaimin Zheng, Fang Liu

    Optics Express
    |February 9, 2019
    PubMed
    Summary

    This study presents a fiber-based phase tracking system using adaptive homodyne detection. The novel system achieves a significantly wider tracking range and quantum-limited performance for high-precision fiber sensing applications.

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    Area of Science:

    • Optics and Photonics
    • Quantum Metrology
    • Fiber Optic Sensing

    Background:

    • Accurate phase tracking is crucial for advanced fiber optic sensing.
    • Existing systems often have limited tracking ranges and performance.

    Purpose of the Study:

    • To demonstrate a novel fiber-based phase tracking system.
    • To achieve quantum-limited performance and a broad tracking range.

    Main Methods:

    • Experimental demonstration of a fiber-based system.
    • Utilizing adaptive homodyne detection.
    • Employing an improved phase-locked loop.

    Main Results:

    • Successful tracking of random phase signals within -2.4 to +2.4 radians.
    • Achieved a significantly larger tracking range compared to previous methods.
    • Demonstrated quantum-limited performance at a photon flux of approximately 10^6.

    Conclusions:

    • The developed system offers superior phase tracking capabilities.
    • Potential applications include high-precision, real-time sensing of temperature and strain.
    • The adaptive homodyne detection technique enhances system performance.