How does a quantum system interact with a travelling pulse of quantum radiation, prepared, e.g., in a number state or a coherent state of light? You may think that this problem has been text book material for decades along with detailed solutions for the case of simple, few level systems. But, in fact, it has not. While crucial for multiple effects in quantum optics and for the entire concept of flying and stationary qubits, quantum optics textbooks do not provide a formal description applicable to this foundational and elementary interaction process. After the introduction of a new (and simple) theoretical formalism that, accounts for the interaction of travelling pulses of quantized radiation with a local quantum system, I shall discuss applications of the theory to quantum pulses of optical, microwave and acoustic excitations and show examples of relevance to recent experiments with qubits and non-linear resonators.

{"references": ["Wikipedia contributors, \"Jaynes\u2013Cummings model - Schr\u00f6dinger picture dynamics\", Wikipedia (retrieved 2020-05-10)", "Alexander Holm Kiilerich and Klaus M\u00f8lmer, \"Input-Output Theory with Quantum Pulses\", Physical Review Letters 123, 123604 (2019), DOI:10.1103/PhysRevLett.123.123604", "Alexander Holm Kiilerich and Klaus M\u00f8lmer, \"Quantum interactions with pulses of radiation\", arXiv:2003.04573 (2020)", "Kevin A. Fischer, Rahul Trivedi, Vinay Ramasesh, Irfan Siddiqi, and Jelena Vu\u010dkovi\u0107, \"Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system\", Quantum 2, 69 (2018), DOI:10.22331/q-2018-05-28-69"]}