Comment on "Generation of phase states by two-photon Absorption"

Generation and control of a single-photon state and a quantum bit (qubit) state are extensively studied from both viewpoints of fundamental interest and applications to quantum cryptography and communication. A popular method for producing a single-photon state is to use one of the twin photons created by parametric down-conversion as a signal and the other as a trigger [1]. The generation time of a photon pair is randomly distributed according to the Poisson-point process. A single-photon turnstile device, based on simultaneous Coulomb blockade for electrons and holes in a mesoscopic pn junction, was proposed [2] and demonstrated [3] to generate heralded single photons. The repetition rate is limited by a radiative recombination lifetime. Recently, Imamoglu and colleagues [4] proposed “photon blockade,” in which optical tunneling is prevented by Kerr nonlinearity instead. They avoid the usual one-photon absorption using atomic dark resonance. To avoid one-photon loss, a special condition must be satisfied for the pulse intensity and width, which places also a limit on the repetition rate. A 50%–50% beam splitter converts a single-photon state into a quantum entangled state, j10 1 eifj01 p2. The two outputs of the beam splitter are correlated, so that, if one of the two beams is lost to reservoirs, the other is collapsed to either j0 or j1 . Generation of a single qubit state j0 1 eifj1 p2, which is proposed in this paper, is preferred for some applications because there is no need to protect the correlated counterpart. In this paper, we propose a new method for generating phase states j0 1 eifj1 p2, which is the special case of a Pegg-Barnett phase state [5], by two-photon absorption (TPA). The present phase state is considered as a qubit state in the language of quantum information science. Let us consider a series of well-focused short laser pulses to be irradiated on a side of crystal in which TPA is effective. Under these conditions, the radiation field is well confined