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...

We have demonstrated an interferometer for atoms. A three-grating geometry is used, in which the interfering beams are distinctly separated in both position and momentum. We used a highly collimated beam of sodium atoms with a de Broglie wavelength of 16 pm and high-quality 0.4-pm-period freestanding gratings which we fabricated using a novel method. The interference signal is 70 counts/s, which allows us to determine the phase to 0.1 rad in 1 min. Applications of atom interferometers are briefly discussed.

The enhanced coupling between atoms and photons inside a high-finesse optical cavity provides a novel basis for optical measurements that continuously monitor atomic degrees of freedom. We describe an experiment in which cavity quantum-electrodynamic effects are utilized for real-time detection of individual atoms falling through an optical cavity after being dropped from a magneto-optical trap. Our technique permits experiments that are triggered by the presence of a single optimally coupled atom within the cavity mode volume.

One of the canonical questions in quantum optics is the nature of the radiative properties of an atom when the normal vacuum fluctuations of the electromagnetic reservoir are replaced by the asymmetric, reduced fluctuations of a squeezed vacuum. While the basic radiative linewidth-narrowing effect has been known for over a decade ͓C. W. Gardiner, Phys. Rev. Lett. 56, 1917 ͑1986͔͒, experimental realizations with operationally definable definitive manifestations of the quantum nature of the squeezed reservoir have been largely lacking from subsequent investigations. This paper presents measurements on an experimentally realized atomsqueezed-light system, in which the squeezed-light output of a subthreshold optical parametric oscillator illuminates an atom strongly coupled to a high-finesse optical resonator. Transmission of a weak probe field incident on the atom-cavity system is investigated both theoretically and experimentally. Alteration of the transmitted probe spectrum has been observed, as has a transmission modulation that depends on the phase of the squeezed field relative to a saturating coherent field ͑displaced squeezing͒. In certain parameter regimes, properties unique to the quantum nature of the squeezed light have been identified in the theoretical treatment, but complications in the experiment prevent their unequivocal measure. It is found that the observed effects of the squeezed light are dramatically reduced relative to the predictions of an idealized theory. This is quantitatively attributed to the effects of atomic beam fluctuations and a simple modeling of the atomic beam as an additional loss mechanism in the theory leads to reasonable agreement with the data.

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