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Several novel schemes are studied which pave the way to deterministic quantum logic with photons. In one of such schemes, a weak (quantum) probe pulse, upon propagating through the medium, interacts with the forward and backward components of a weak signal pulse that is dynamically trapped in a photonic band-gap structure. In an alternative scheme, the two pulses propagate in the opposite directions in the EIT medium and interact with each other via strong, long-range dipole-dipole interaction between Rydberg states of the atoms. Both schemes are capable of implementing with high fidelity the conditional phase gate between two single-photon pulses, under physically realistic, experimentally accessible conditions.

We show that the giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor can give rise to the formation of Thirring-type spatial solitons, which are supported solely by cross-phase modulation that couples the two copropagating light beams.

We show that very large nonlocal nonlinear interactions between pairs of colliding slow-light pulses can be realized in atomic vapors in the regime of electromagnetically induced transparency. These nonlinearities are mediated by strong, long-range dipole--dipole interactions between Rydberg states of the multi-level atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of pi even for weakly focused single-photon pulses, thereby allowing a deterministic realization of the photonic phase gate., Comment: 4 pages, 2 figures

We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable $\ensuremath{\pi}$ phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.

We introduce and discuss two schemes for generation and transfer of photon-photon and atom-atom entanglement. First we propose a method to achieve a large conditional phase shift of a probe field in the presence of a single-photon control field whose carrier frequency is within the photonic band gap created by spatially-periodic modulation of the electromagnetically induced transparency resonance. Then we present the concept of a reversible transfer of the quantum state of two internally-translationally entangled fragments, formed by molecular dissociation, to a photon pair. Our scheme allows, in principle, high-fidelity state transfer from the entangled dissociated fragments to light, thereby producing a highly correlated photon pair. This process can be followed by its reversal at a distant node of a quantum network resulting in the recreation of the original two-fragment entangled state. The proposed schemes may have advantageous applications in quantum teleportation, cryptography, and quantum computation.

Giantly enhanced cross-phase modulation with suppressed spectral broadening is predicted between optically-induced dark-state polaritons whose propagation is strongly affected by photonic bandgaps of spatially periodic media with multilevel dopants. This mechanism is shown to be capable of fully entangling two single-photon pulses with high fidelity., Comment: 7 pages, 1 figure

It has been proposed that the adiabatic loading of a Bose-Einstein Condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch, {\it et al.}, Phys. Rev. Lett. {\bf 81}, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force-constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a non-stationary BEC in a harmonic trap., LaTeX 11 Pages, 6 figures

The evolution of nonlinear light fields traveling inside a resonantly absorbing Bragg reflector is studied by use of Maxwell-Bloch equations. Numerical results show that a pulse initially resembling a light bullet may effectively experience negative refraction and anomalous dispersion in the resonantly absorbing Bragg reflector.