subPoissonian

SubPoissonian, more commonly written as sub-Poissonian, refers to a statistical property of light where the photon-number distribution has a variance smaller than the mean. This contrasts with Poissonian statistics, where the variance equals the mean, and with super-Poissonian statistics, where the variance exceeds the mean. In quantum optics, sub-Poissonian photon statistics are a signature of nonclassical light.

A standard way to quantify sub-Poissonian behavior is through the Mandel Q parameter, Q = (⟨n^2⟩ − ⟨n⟩^2 − ⟨n⟩)/⟨n⟩, where n is the photon number. Sub-Poissonian light has Q < 0, Poissonian light has Q = 0, and super-Poissonian light has Q > 0. Another common indicator is the zero-delay second-order coherence, g2(0) = ⟨n(n−1)⟩/⟨n⟩^2, with sub-Poissonian statistics implying g2(0) < 1 and often antibunching behavior.

Physically, sub-Poissonian statistics arise from highly nonclassical states, such as Fock states with a definite photon number or certain conditioned or heralded light sources. Coherent states, like those from an ideal laser, exhibit Poissonian statistics (Q = 0, g2(0) = 1). Sub-Poissonian light is of interest for quantum information processing, quantum communications, and precision measurements, because reduced photon-number fluctuations can improve performance in certain protocols.

Experimentally, observing sub-Poissonian statistics requires high-efficiency photon-number-resolving detection and careful control of detector noise, dark counts, and losses, which can mask nonclassical statistics.