A novel method of preparing a single photon in temporally-delocalized entangled modes is proposed and analyzed. We show that two single-photon pulses propagating in a driven nonabsorbing medium with different group velocities are temporally split under parametric interaction into wellseparated pulses. As a consequence, the single-photon "time-bin-entangled" states are generated with a programmable entanglement, which is easily controlled by driving field intensity. The experimental study of nonclassical features and nonlocality in generated states by means of balanced homodyne tomography is discussed.
We present a fully quantum mechanical treatment of recent experiments on creation of collective quantum memory and generation of non-classically correlated photon pairs from an atomic ensemble via the protocol of Duan et al. [Nature 414, 413(2001)]. The temporal evolution of photon numbers, photon statistics and cross-correlation between the Stokes and anti-Stokes fields is found by solving the equation of motion for atomic spin-wave excitations. We consider a low-finesse cavity model with collectively enhanced signal-to-noise ratio, which remains still considerably large in the free-space limit. Our results describe analytically the dependence of quantum correlations on spin decoherence time and time-delay between the write and read lasers and reproduce the observed data very well including the generated pulse shapes, strong violation of Cauchy-Schwarz inequality and conditional generation of anti-Stokes single-photon pulse. The theory we developed may serve as a basic approach for quantum description of storage and retrieval of quantum information, especially when the statistical properties of non-classical pulses are studied.
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