| Summary: | In this thesis, I present the results of three experiments utilizing entanglement to improve metrology in an optical lattice clock atom Ytterbium-171. Furhtermore, I present a novel interpretation of the Madelung Theory of Quantum Mechanics, namely that of a particle-fluid decomposition and it's consequences.
In more detail, in one experiment, we demonstrate near-unitary squeezing of the collective spin state of ~10³ atoms in an optical lattice clock atom wiht a measured metrological gain of 6.5(4) d limited by readout detection. Without the readout limit, the generated stated themselves offer an inferred metrological gain of 12.9(6) d, limited by the curvature of the Bloch sphere. An interferometer is used to leverage this squeezing into an entanglement enhanced quantum measurement that improves the precision by 3.7(2) over the standard quantum limit (SQL).
In the third experiment, we utilized the ability to reverse the sign of our squeezing Hamilitonian, to circumvent our readout limit, as well as the SQL. Essentially, by squeezing, acquiring a phase shift, and unsqueezing, we obtain SIgnal Amplification by Time-reversed INteraction (SATIN). These results represented the greatest phase sensitivity improvement beyond the SQL, 11.8(5) dB, demonstrated to date in any full Ramsey interferometer. Furhtermore, Heisenberg Scaling in the sensitivity ∞ 1/N was achieved.
The second part of the thesis focuses on the Newtonian-Madelung-Takabayasi Theory of Quantum Mechanics, a classical and gauge-independent picture of quantum mechanics. This forumlation emphasizes the importance of a fifth fundamental force, the gradient of the quantum potential, which allows for the stability of matter and helps demonstrate a clear transition from classical to quantum regimes. This fifth force summarizes effects, that in the canonical theory, look like zero-point motion.
In the spin-0 case, most essential consequences are elucidated: notably, energy conservation in configuration space is derived via the Lagrangian and Noether's theorem, and a classical quantum-boundary is defined. The model is used to predict a relativistic clock shift that agrees with canonical theory to first order in v²/c².
The Madelung Fluid theory is applied to a toy quantum field theory (QFT) for the first time. This generates a classical set of equations, that contain QFT dynamics. It was not yet proven to be entirely equivalent to the starting QFT. Like how the NMT illustrated a hidden fifth fundamental force, the NMT version of QFT illustrates a new fundamental source of radiation. This illustrates an axiom we could utilize as a starting point to quantize any classical field theory, possibly including GR.
Lastly, the connection between classical and quantum mechanics is investigated through the Koopman Theorem and it's importance for understanding fundamental questions about quantum mechanics. The Koopman theorem points to a hypothesis, i.e., the converse of the Koopman theorem is true, that converse might explain why this Newtonian-Madelung-Takabayasi (NMT) picture exists. If this converse were true, it would tell us that this NMT picture (or some other classical picture) could be fundamental, i.e., mathematically guaranteed, rather than happen stance. However, the details of this relationship require more details not yet known.
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