State-of-the-art optical oscillators based on lasers frequency stabilized to high finesse optical cavities are limited by thermal noise that causes fluctuations of the cavity length. Thermal noise represents a fundamental limit to the stability of an optical interferometer and plays a key role in modern optical metrology. We demonstrate a novel design to reduce the thermal noise limit for optical cavities by an order of magnitude and present an experimental realization of this new cavity system, demonstrating the most stable oscillator of any kind to date. The cavity spacer and the mirror substrates are both constructed from single crystal silicon and operated at 124 K where the silicon thermal expansion coefficient is zero and the silicon mechanical loss is small. The cavity is supported in a vibration-insensitive configuration, which, together with the superior stiffness of silicon crystal, reduces the vibration related noise. With rigorous analysis of heterodyne beat signals among three independent stable lasers, the silicon system demonstrates a fractional frequency stability of 1 × 10 −16 at short time scales and supports a laser linewidth of <40 mHz at 1.5 µm, representing an optical quality factor of 4 × 10 15 .

The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect twophoton coalescence even for non-perfect photons. 03.67.Mn, 42.50.Xa, 42.50.Dv, 42.65.Dr The quantum nature of light impressively manifests itself in the fourth-order interference of two identical and mutually coherent single photons that impinge simultaneously on a beam splitter (BS). The photons coalesce and both leave the beam splitter in the same direction. Hong et al. first demonstrated this phenomenon with photon pairs from parametric down conversion [1] and Santori et al. used the same effect to show the indistinguishability of independently generated photons that are successively emitted from a quantum dot embedded in a micro cavity [2]. In all experiments performed so far, the photons were short compared to the time resolution of the employed detectors, so that interference phenomena were only observed as a function of the spatial delay between the interfering photons [3].To investigate the temporal dynamics behind this interference phenomenon, we now use an adiabatically driven strongly coupled atom-cavity system as single-photon emitter [4,5,6,7]. Photons are generated by a unitary process, so that their temporal and spectral properties can be arbitrarily adjusted. In fact, the duration of the photons used in our experiment exceeds the time resolution of the employed singlephoton counters by three orders of magnitude. This allows for the first time an experimental investigation of fourth-order interference phenomena in a time-resolved manner with photons arriving simultaneously at the beam splitter [8]. We find perfect interference even if the frequency difference between the two photons exceeds their bandwidths. This surprising result is very robust against all kinds of fluctuations and opens up new possibilities in all-optical quantum information processing [9].The principal scheme of the experiment is sketched in Fig. 1. We consider an initial situation where two single photons in modes A and B impinge simultaneously on a BS. In front of the BS, we distinguish states |1 A,B and |0 A,B , where either a photon is present or where it has been annihilated by transmission through the BS and subsequent detection by detector C or D. Mode A is an extended spatiotemporal photonic field mode, traveling along an optical fiber, which initially carries a photon. The photon in mode B emerges from a strongly coupled atom-cavity system, which is driven in a way that the photon is deterministically generated by a vacuum-stimulated Raman transition between two long-lived S...

Optical clocks show unprecedented accuracy, surpassing that of previously available clock systems by more than one order of magnitude. Precise intercomparisons will enable a variety of experiments, including tests of fundamental quantum physics and cosmology and applications in geodesy and navigation. Well-established, satellite-based techniques for microwave dissemination are not adequate to compare optical clocks. Here, we present phase-stabilized distribution of an optical frequency over 920 kilometers of telecommunication fiber. We used two antiparallel fiber links to determine their fractional frequency instability (modified Allan deviation) to 5 × 10(-15) in a 1-second integration time, reaching 10(-18) in less than 1000 seconds. For long integration times τ, the deviation from the expected frequency value has been constrained to within 4 × 10(-19). The link may serve as part of a Europe-wide optical frequency dissemination network.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10−17 via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10−17 is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

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The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal.PACS 42.50.Dv, 42.50.Ct

We report on the first observation of stimulated Raman scattering from a Λ-type three-level atom, where the stimulation is realized by the vacuum field of a high-finesse optical cavity. The scheme produces one intracavity photon by means of an adiabatic passage technique based on a counterintuitive interaction sequence between pump laser and cavity field. This photon leaves the cavity through the less-reflecting mirror. The emission rate shows a characteristic dependence on the cavity and pump detuning, and the observed spectra have a sub-natural linewidth. The results are in excellent agreement with numerical simulations.PACS numbers: 32.80. Qk, 42.50.Ct, 42.65.Dr, In the last few years, interesting proposals on the generation of non-classical states of light in optical cavities [1,2] and on the controlled generation of single photons from such cavities [3,4] were made. All these schemes are based on a technique known as Stirap (stimulated Raman scattering involving adiabatic passage) [5,6] or a variant thereof, and incorporate the time dependent interaction of an atom with the field mode of an optical cavity. The operation principle is related to that of a Raman laser [7], with the difference that now a single atom interacts with an empty cavity mode. Other schemes for the preparation of Fock states are based on vacuum Rabi oscillations or, more generally, π-pulses in a two-level atom. In these cases, the need of a longlived excited atomic state restricts experiments to the microwave regime [8,9], where the photon remains stored in a high-Q cavity.Here, we report on the experimental realization of an excitation scheme that allows one to emit a visible photon into a well defined mode of an empty cavity. This photon then leaves the cavity in a known direction. Our method is based on the single-photon generation scheme discussed in [4]. It relies on Stirap [5,6], but instead of using two delayed laser pulses, we have only one exciting pump laser, combined with a strong coupling of a single atom to a single cavity mode [10,11]. This strong coupling induces the anti-Stokes transition of the Raman process. Figure 1 depicts the excitation scheme for the 85 Rbatoms used in our experiment. A Λ-type three-level scheme is realized by the two 5S 1/2 hyperfine ground states F = 3 and F = 2, which we label |u and |g , respectively. The F = 3 hyperfine level of the electronically excited state 5P 3/2 forms the intermediate state, |e . The atom interacts with a single-mode of an optical cavity, with states |0 and |1 denoting zero and one photon in the mode, respectively. The cavity resonance frequency, ω C , is close to the atomic transition frequency between states |e and |g , but far-off resonance from the |e to |u transition. Hence, only the product states |e, 0 and |g, 1 are coupled by the cavity. For this transition, the vacuum Rabi frequency,is time dependent since the atom moves with velocity v across the waist w C of the Gaussian cavity mode. Its peak amplitude is given by the atom-cavity coupling coefficient at an an...