Photon-added coherent states using the continuous-mode formalism

The addition of a photon into the same mode as a coherent state produces a nonclassical state that has interesting features, including quadrature squeezing and a sub-Poissonian photon-number distribution. The squeezed nature of photon-added coherent (PAC) states potentially offers an advantage in quantum sensing applications. Previous theoretical works have employed a single-mode treatment of PAC states. Here, we use a continuous-mode approach that allows us to model PAC state pulses. We study the properties of a single-photon and coherent state wavepacket superimposed with variable temporal and spectral overlap. We show that, even without perfect overlap, the state exhibits a sub-Poissonian number distribution, second-order quantum correlations and quadrature squeezing for a weak coherent state. We also include propagation loss in waveguides and study how the fidelity and other properties of PAC state pulses are affected.