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In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
Embedding materials in optical cavities has emerged as an intriguing perspective for controlling quantum materials, but a key challenge lies in measuring properties of the embedded matter. Here, we propose a framework for probing strongly…
Obtaining insight into the constituents of dark matter and their interactions with normal matter has inspired a wide range of experimental efforts. Several approaches, particularly those involving searches for ultralight bosonic dark matter…
We suggest a general scheme for quantum state engineering based on conditional measurements carried out on entangled twin-beam of radiation. Realistic detection schemes such as {\sc on/off} photodetection, homodyne detection and joint…
Quantum states and measurements exhibit wave-like --- continuous, or particle-like --- discrete, character. Hybrid discrete-continuous photonic systems are key to investigating fundamental quantum phenomena, generating superpositions of…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
We describe a scheme, operating in a manner analogous to a reversed Raman output coupler, for measuring the phase-sensitive quadrature statistics of an atom laser beam. This scheme allows for the transferral of the atomic field statistics…
Homo- and heterodyne detection are fundamental techniques for measuring propagating electromagnetic fields. However, applying these techniques to stationary fields confined in cavities poses a challenge. As a way to overcome this challenge,…
We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne…
We propose an experimental apparatus to reveal the quantum coherence manifested in downward quantum jumps of amplitude bistability. The underlying coherent superposition of macroscopic quantum states is translated into the statistical…
The quantum spin states of atomic ensemble are of special interesting for both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an…
We consider light scattering from ultracold atoms trapped in an optical lattice into a cavity. The measurement of photons leaking out the cavity provides a quantum nondemolition (QND) access to various atomic variables. Depending on the…
We report an algorithm, based on quantum optics formulation, where a coherent state is used as the elementary quantum resource for the image representation. We provide an architecture with constituent optical elements in linear order with…
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of…
In cavity optomechanics, nanomechanical motion couples to a localized optical mode. The regime of single-photon strong coupling is reached when the optical shift induced by a single phonon becomes comparable to the cavity linewidth. We…
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in…
This paper discusses work developed in recent years, in the domain of quantum optics, which has led to a better understanding of the classical limit of quantum mechanics. New techniques have been proposed, and experimentally demonstrated,…
Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical…