Quantum communication and metrology in curved spacetime

In this thesis we study relativistic effects on quantum systems. Quantum physics in curved spacetime is reviewed in a first place, with a focus on continuous variables formalism, quantum metrology techniques, and the relativistic treatment of polarised photons. Then, three topics of interest are studied. The first one is the phononic gravitational wave detector, where resonant mode-mixing and particle creation are triggered in a Bose-Einstein condensate by the passing of a gravitational wave, which can then be measured thanks to quantum metrology techniques. The theory for the phonons’ transformation is developed in details in different resonance scenarios and some sources of noise are considered, like shaking of the cavity where the condensate is trapped and thermal noise. The second topic adressed is quantum communication and metrology in space. In this part, we describe quantum experiments involving communications between Earth and satellites using frequency modes of photons. The propagated and measured photons encode parameters of the spacetime background that can be measured using quantum metrology. Several satellite schemes are discussed, such as satellite to satellite radial communications in Kerr spacetime or Earth to satellite communications in Schwarzschild spacetime. The last topic of this thesis is the evolution of helicity states of photons in a relativistic picture. Two experiments are considered: one where the photons propagate between Earth and satellites through the curved spacetime background surrounding the Earth. The other experiment looks at quantum states of polarised photons as seen by centrifuged observers. For each of these parts, we provide the theory for novel experimental proposals, within the frameworks of either (or both) quantum communications and quantum metrology, that, we believe, would lead to a better understanding in the overlap of quantum mechanics and the relativity theories