Measurements of the birefringence of a single atom strongly coupled to a high-nesse optical resonator are reported, with nonlinear phase shifts observed for intracavity photon number much less than one. A proposal to utilize the measured conditional phase shifts for implementing quantum logic via a quantum-phase gate (QPG) is considered. Within the context of a simple model for the eld transformation, the parameters of the \truth table" for the QPG are determined.PACS numbers: 32.80. 33.55.Ad, 42.65.Pc Although the theory of quantum computation dates back more than a decade to the seminal works of Feynman and Deutsch 1], there has recently been an explosion of new activity driven in large measure by Shor's quantum algorithm 2] for e cient factorization. While most attention has been directed toward theoretical issues, several strategies have also been proposed for laboratory investigations 3]. However, the demands on experimental systems for building quantum computational networks 4] are quite severe, requiring strong coupling between quantum carriers of information (\qubits") in an environment with minimal dissipation. Hence, experimental progress has lagged behind the remarkable theoretical developments in quantum information theory.Within this context, we present a signi cant experimental step toward realizing quantum logic with individual photons as qubits. Moreover, our work bears import for related experimental challenges such as quantum nondemolition (QND) measurement and quantum cryptography. Speci cally, we report the demonstration of conditional dynamics at the single photon level between two frequency-distinct elds in an optical resonator. Our measurements utilize the circular birefringence of an atom strongly coupled to the resonator to rotate the linear polarization of a transmitted probe beam. The phase shift between circular polarization states is conditioned upon the intensity of a pump beam via a Kerr-type nonlinearity, with conditional phase shifts 16 per intracavity photon extracted from our data. To explore further the prospects for quantum logic based on these capabilities, we have experimentally investigated a candidate quantum-phase gate (QPG) and, within the context of a simple model, have extracted relevant phase shifts for the \truth table" of the QPG. In our proposed implementation, \ ying qubits" are single-photon pulses propagating in two frequency-o set channels, with internal states speci ed by polarization.It should be noted at the outset that necessary and sufcient testing procedures have not yet been established for providing direct experimental veri cation that a given \black box" laboratory system can perform quantum logic transformations with su cient delity to implement Deutsch's Quantum Turing be tolerated in experimental systems before the advantages of unitary information processing are lost. However, any laboratory quantum gate must exhibit coherence and demonstrably produce entanglement between qubits. The practical application of such criteria requires the formulat...

The controlled production of single photons is of fundamental and practical interest; they represent the lowest excited quantum states of the radiation field, and have applications in quantum cryptography and quantum information processing. Common approaches use the fluorescence of single ions, single molecules, colour centres and semiconductor quantum dots. However, the lack of control over such irreversible emission processes precludes the use of these sources in applications (such as quantum networks) that require coherent exchange of quantum states between atoms and photons. The necessary control may be achieved in principle in cavity quantum electrodynamics. Although this approach has been used for the production of single photons from atoms, such experiments are compromised by limited trapping times, fluctuating atom-field coupling and multi-atom effects. Here we demonstrate a single-photon source based on a strongly localized single ion in an optical cavity. The ion is optimally coupled to a well-defined field mode, resulting in the generation of single-photon pulses with precisely defined shape and timing. We have confirmed the suppression of two-photon events up to the limit imposed by fluctuations in the rate of detector dark counts. The stream of emitted photons is uninterrupted over the storage time of the ion, as demonstrated by a measurement of photon correlations over 90 min.

In near-field imaging, resolution beyond the diffraction limit of optical microscopy is obtained by scanning the sampling region with a probe of subwavelength size. In recent experiments, single molecules were used as nanoscopic probes to attain a resolution of a few tens of nanometres. Positional control of the molecular probe was typically achieved by embedding it in a crystal attached to a substrate on a translation stage. However, the presence of the host crystal inevitably led to a disturbance of the light field that was to be measured. Here we report a near-field probe with atomic-scale resolution-a single calcium ion in a radio-frequency trap-that causes minimal perturbation of the optical field. We measure the three-dimensional spatial structure of an optical field with a spatial resolution as high as 60 nm (determined by the residual thermal motion of the trapped ion), and scan the modes of a low-loss optical cavity over a range of up to 100 microm. The precise positioning we achieve implies a deterministic control of the coupling between ion and field. At the same time, the field and the internal states of the ion are not affected by the trapping potential. Our set-up is therefore an ideal system for performing cavity quantum electrodynamics experiments with a single particle.

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