Malitesta, Marco (2024) Entanglement-enhanced multi-parameter sensing in optical and atom Mach-Zehnder interferometry. [Tesi di dottorato]

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This Thesis is divided into five chapters. The first two chapters provide the theoretical background necessary for presenting the results of my research. The first chapter contains a general overview of optical and atom interferometry, introducing the angular momentum and phase space representation for states in the bosonic Fock space. Gaussian unitaries are revised with particular emphasis on linear interferometers and the squeezing operation; the distinction between quadrature squeezing and spin squeezing is explained in detail. The second chapter is divided into two parts dealing with single- and multi-parameter quantum estimation theory, respectively. Various estimators are described, the Fisher information (FI), the quantum Fisher information (QFI) and the associated lower bounds are defined, and their properties discussed; the same concepts are then generalized to the multi-parameter scenario, highlighting similarities and differences with the one-parameter case. New results are discussed in the last three chapters. In the third chapter, I consider an array of d optical Mach-Zehnder interferometers (MZIs) for the estimation of d relative phases. Each MZI has two inputs, of which the first is fed a coherent state and the second is connected to one of the output ports of a d-mode passive linear optical device (a quantum circuit, QC) taking a generic pure state as input in one port. I derive a formula for the quantum Fisher information matrix (QFIM) of such a scheme, then study its FI both with analytical and numerical methods and show that the quantum Cramér-Rao bound (QCRB) is saturated by local particle-counting measurements, so no recombination of output photons is required. The scheme presented in the third chapter is examined in further detail in the fourth chapter, which addresses the case when the input of the QC is a squeezed-vacuum state. A formula for the sensitivity obtained with the method of moments is derived and compared with the QCRB. I show that, d denoting the number of phase shifts to estimate, an “entangled” strategy based on the splitting of a single squeezed-vacuum state with a QC can achieve up to a d-fold enhancement in sensitivity over a strategy relying on d independent squeezed states. Finally, the impact of noise and losses on the sensitivity is analysed and discussed. In the fifth and last chapter, a similar scheme is proposed aimed at differential phase estimation in atom interferometry. In this case, a spin-coherent state undergoes one-axis twisting dynamics, producing a spin-squeezed state on which a mode-swapping linear operation is subsequently performed. The optimal sensitivity of the scheme and its robustness to fluctuations of the unknown values of the phases are analysed numerically by simulating the evolution of the atomic state along the interferometer. Results are compared to the predictions of an approximate analytical model, establishing an analogy with optical interferometry.

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