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The electronic structure and the optical properties of an excitonic n-string which is a bound state of n Frenkel excitons (n = 2, 3, . . . ) are theoretically clarified. The binding mechanism may be attributed to the electrostatic dipolar interaction among the Frenkel excitons, which is in contrast to the formation mechanism of the otherwise analogous excitonic molecules in a system of Wannier excitons; it makes it possible to form bound states of more than two Frenkel excitons. The effects of the n-string states on the electronic structure and optical properties are studied. The two-photon absorption and the differential transmission spectra are shown to depend strongly on the direction of the induced static dipole moment, which determines whether the interaction between excitons is attractive or repulsive.

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A new method for producing a phase state by two-photon absorption is proposed. We show that such a process conserves the phase of an initial coherent state ja͘ and converts it to jc͘ ͑j0͘ 1 e if j1͒͘͞ p 2, where a jaje if . Therefore, we obtain desirable phase states by controlling the phase of the initial coherent state. Appropriate materials with a reasonable two-photon absorption rate are proposed. PACS numbers: 03.65.Bz, 42.50.Dv, 42.50.Lc 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, ͑j10͘ 1 e if j01͒͘͞ p 2. 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 j0͘ or j1͘. Generation of a single qubit state ͑j0͘ 1 e if j1͒͘͞ p 2, 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 ͑j0͘ 1 e if j1͒͘͞ p 2, 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 to a small volume. Therefore we may expect the TPA rate becomes larger than a single-photon one even when a laser pulse contains two or three photons. We will discuss several possible systems, i.e., atomic gas, exciton-biexciton system, and semiconductors. We choose, e.g., for the last case, the fundamental frequency v well below the exciton frequency, but the two-photon frequency 2v is well above the band-to-band transition frequency. The laser pulses are attenuated dominantly by TPA and each becomes a superposition of single-and zero-photon states with almost equal amplitude....

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