Quantum teleportation is analyzed for states of dynamical variables with continuous spectra, in contrast to previous work with discrete (spin) variables. The entanglement fidelity of the scheme is computed, including the roles of finite quantum correlation and nonideal detection efficiency. A protocol is presented for teleporting the wave function of a single mode of the electromagnetic field with high fidelity using squeezed-state entanglement and current experimental capability.[ S0031-9007(97)

We report measurements of cavity-QED effects for the radiative coupling of atoms in a dilute vapor to the external evanescent field of a whispering-gallery mode ͑WGM͒ in a fused silica microsphere. The high Q (5ϫ10 7 ), small mode volume ͑10 Ϫ8 cm 3 ), and unusual symmetry of the microcavity evanescent field enable velocity-selective interactions between fields with photon number of order unity in the WGM and N T ϳ1 atoms in the surrounding vapor. ͓S1050-2947͑98͒50904-3͔PACS number͑s͒: 42.50.CtCavity QED has proven to be a fertile arena in which to study coherent interactions between single atoms and photons ͓1͔. In the optical domain, the cavities employed to achieve strong coupling have been Fabry-Perot microresonators with finesse Fϳ10 5 , as in the initial work of Ref.͓2͔ and continuing to the recent demonstrations of real-time cavity QED with individual atoms ͓3,4͔. By contrast, the whispering gallery modes ͑WGMs͒ of quartz microspheres ͓5͔ offer an alternative avenue to the regime of strong coupling with the potential to surpass Fabry-Perot cavities with respect to certain key parameters in cavity QED. For example, such resonators have the capability of achieving extremely long photon storage lifetimes while maintaining a strong dipole coupling to an atomic ͓6͔, ionic ͓7͔, or molecular ͓8͔ species via the small volume of a single mode, leading to the potential for ratios of coherent coupling to loss mechanisms in excess of 10 3 ͓6͔ . Indeed, quality factors QϷ8ϫ10 9 have been reported for wavelengths 633 nm рр852 nm, corresponding to finesse Fϳ2.2ϫ10 6 ͓9,10͔, which is the highest value on record for an optical resonator.Motivated by these prospects, in this Rapid Communication we report measurements of the interaction of atoms with the external evanescent field of a whispering gallery mode in a domain in which cavity-QED effects become important. More specifically, we study the modifications of cavity transmission due to the coupling of N T ϳ1 cesium atoms in a thermal gas with a single resonant WGM at the level of a few photons in the mode. The possibility for sensitivity to N T ϳ1 atoms in the microsphere's evanescent field in the face of Doppler broadening of roughly 100 times the natural linewidth is a consequence of the features of the microspheres used here, namely, small size ͑with radius aϽ60 m and mode volume V m ϳ10 Ϫ8 cm 3 ) and narrow linewidth ͑with Q 1 ϭ5ϫ10 5 рQрQ 2 ϭ5ϫ10 7 ). Although it is clearly desirable to reduce the Doppler broadening by coupling to cold atoms ͓3,4͔, our current experiments are an exciting initial step towards realizing the potential of WGMs for long-lived coherent dynamics in cavity QED.The actual setup is depicted in Fig. 1 and consists of a grating stabilized diode laser of a few hundred kHz linewidth coupled into a microsphere via frustrated total internal reflection from a prism ͓5͔. The microspheres are fabricated from low-OH fused silica of index nϭ1.452 using an oxygenhydrogen microtorch ͓11͔ and then mounted inside the vacuum system. The range Q 1 →Q 2 is ac...

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Quantum teleportation is analyzed for states of dynamical variables with continuous spectra, in contrast to previous work with discrete (spin) variables. The entanglement fidelity of the scheme is computed, including the roles of finite quantum correlation and nonideal detection efficiency. A protocol is presented for teleporting the wave function of a single mode of the electromagnetic field with high fidelity using squeezed-state entanglement and current experimental capability.[ S0031-9007(97)

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.