Theory of Photon Subtraction for Two-Mode Entangled Light Beams

Abstract

Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation.

Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

“…Recently, the probability representation of quantum states called symplectic tomogram has been developed [6]; see also reviews [7][8][9][10]. In this approach, the system states in conventional quantum mechanics are described by standard probability distributions.…”