We show that the recently demonstrated technique for generating stationary pulses of light [Nature 426, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to dramatically enhance the nonlinear interaction between weak optical pulses. In particular, we show that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of several purely linear optical processes. The resulting process may enable coherent interactions between single photon pulses.Techniques that could facilitate controlled nonlinear interactions between few-photon light pulses are now actively explored [1]. Although research into fundamental limits of nonlinear optics has been carried out over the last three decades, there is renewed interest in these problems in part due to e.g. potential applications in quantum information science [2]. In general, such interactions between few-photon pulses are difficult to achieve, as they require a combination of large nonlinearity, low photon loss and tight confinement of the light beams [3]. In addition, long atom-photon interaction times are required. Simultaneous implementation of all of these requirements is by now only feasible in the context of cavity QED [4].In this Letter we describe a novel method for achieving nonlinear interaction between weak light pulses. Our method is based on a recently demonstrated technique [5,6] in which light propagating in a medium of Rb atoms was converted into an excitation with localized, stationary electromagnetic energy, which could be held and released after a controllable interval. This is achieved by using Electromagnetically Induced Transparency (EIT) [7] to coherently control the pulse propagation. We show here that this method can be extended to confine stationary pulses in all three spatial dimensions. This, in turn, can be used to strongly enhance the nonlinear interaction between weak pulses of light. Specifically we demonstrate that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of linear optical processes and atomic state manipulations. Coherent, controlled nonlinear processes at optical energies corresponding to a single light quanta appear feasible.Before proceeding, we note that the present work is closely related to recent studies on the resonant enhancement of nonlinear optical phenomena via EIT [8,9,10,11]. The essence of these studies is to utilize steep atomic dispersion associated with narrow EIT resonances. In such a system, a small AC Stark shift associated with a weak off-resonant pulse of signal light, produces a large change in refractive index for a resonant probe pulse. In order to fully take advantage of this process, long interaction times between signal and probe pulses must be ensured. Although the latter can be achieved by reducing the group velocities of two interacting pulses by equal amounts [12], in practice this results only in a modest increase of the nonlinear optical effici...

We describe a technique for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The technique is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse. Spatio-temporal control over the pulses is obtained by exploiting long-lived coherent memory for photon states and electromagnetically induced transparency (EIT) in an optically dense atomic medium. Using photon counting experiments we observe generation and shaping of few-photon sub-Poissonian light pulses. We discuss prospects for controlled generation of high-purity n-photon Fock states using this technique.PACS numbers: 42.50. Gy, 42.50.Dv, In recent years much effort has been directed toward generating quantum-mechanical states of the electromagnetic field with a well-defined number of light quanta (i.e., photon-number or Fock states). In addition to being of fundamental interest, these states represent an essential resource for the practical implementation of many ideas from quantum information science such as quantum communication [1]. Over the past decade, tremendous progress has been made in generating singlephoton states by using photon pairs in parametric downconverters [2], single emitters [3,4], and single atoms in high-finesse cavities [5,6]. While parametric downconversion techniques have recently been used to generate multi-photon states [7], it remains experimentally challenging to implement schemes that allow for simultaneous control over both photon number and spatiotemporal properties of the pulse.In this Letter we describe a novel technique for generating pulses of light with controllable, well-defined photon numbers, propagation direction, timing, and pulse shapes by exploiting long-lived coherent memory for photon states in an optically dense atomic medium [8]. We experimentally demonstrate key elements of this technique in photon-counting experiments. This approach combines different aspects of earlier studies on "light storage" [9,10] and Raman preparation and retrieval of atomic excitations [11,12,13]. It is particularly important in the contexts of long-distance quantum communication [14], and EIT-based quantum nonlinear optics [15,16,17].In our approach we first optically pump a large ensemble of N atoms with a three-state "lambda" configuration of atomic states (see Fig.1a) in the ground state |g . Spontaneous Raman scattering [18] is induced by a weak, off-resonant laser beam with Rabi frequency Ω W and detuning ∆ W , referred to as the write laser. This twophoton process flips an atomic spin into the metastable state |s while producing a correlated frequency-shifted photon (a so-called Stokes photon). Energy and momentum conservation ensure that for each Stokes photon emitted in certain direction there exists exactly one flipped spin quantum in a well-defined spin-wave mode. The number of spin wave quanta and the number of photons in the Stokes field thus exhibit strong correlations...

Temporal Ramsey fringes that are due to light scattering by coherently prepared rubidium atoms diffusing through a cell containing neon as a buffer gas have been observed. The effect leads to increasing magneto-optical rotation of cw light polarization at weak magnetic fields.