We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.

We propose and experimentally verify a scheme to engineer arbitrary states of traveling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel. The measurement consists of bringing the idler field into interference with two ancilla coherent states, followed by two single-photon detectors, which, in coincidence, herald the preparation event. By varying the amplitudes and phases of the ancillae, we can prepare any arbitrary superposition of zero-one-and two-photon states. PACS numbers:Modern quantum information science relies upon two key concepts -superposition and entanglement. As fundamental tenets of quantum mechanics, they govern the way information can be shared, transferred or measured. This information lives in a Hilbert space, in the form of a quantum state. Consequently, the ability to actively control the coherent dynamics of a quantum state is paramount for quantum information technology. This task forms the essence of quantum state engineering (QSE). In the optical domain, a widely-used approach for QSE involves generating a "primitive" quantum state and then manipulating it, for example, by bringing it into interaction with an ancillary system. Employing appropriate measurements, the ancilla is then traced out, leading to reduction of the overall system to the desired target state, ready to be detected and characterized.In modern quantum optics, the "primitive" is commonly the state of correlated photon pairs produced in spontaneous parametric down conversion (SPDC). Conditional photon detection on one or both channels is then employed to produce the state of interest. This technique has been successfully applied to engineer complex entangled states of dual-rail optical qubits [1], albeit mostly in a postselected manner: we do not know that the state has been prepared until it is detected and destroyed. A fundamental impediment to optical QSE arises because equidistant energy levels of a harmonic oscillator (such as an electromagnetic mode) cannot be individually accessed using classical control signals. Outside the optical domain, this challenge has been addressed in ion traps [8] and high-Q microwave cavities [9] by coupling the oscillator energy eigenstates to a two-level atomic or spin system [10]. Very recently, arbitrary superposition of Fock states were synthesized inside a superconducting cavity by means of coupling to a Josephson phase qubit [11]. However, the loss of coherence in this scheme provides a fundamental limitation to the obtainable accuracy and complexity of the prepared state.While traveling field implementations do not suffer from this kind of decoherence and also automatically satisfy DiVincenzo's criterion of "flying qubits" [12], they are still beset with the problem of inefficiencies and losses. There exist a number of theoretical proposals for implementing optical QSE [reviewed in detail in [13]], for example, using coherent disp...