We demonstrate single-atom resolution, as well as detection sensitivity more than 20 dB below the quantum projection noise limit, for hyperfine-state-selective measurements on mesoscopic ensembles containing 100 or more atoms. The measurement detects the atom-induced shift of the resonance frequency of an optical cavity containing the ensemble. While spatially-varying coupling of atoms to the cavity prevents the direct observation of a quantized signal, the demonstrated measurement resolution provides the readout capability necessary for atomic interferometry substantially below the standard quantum limit, and down to the Heisenberg limit. PACS numbers:The rapidly progressing field of quantum metrology takes advantage of entangled ensembles of particles to improve measurement sensitivity beyond the standard quantum limit (SQL) arising from quantum projection noise for measurements on uncorrelated particles. Spinsqueezed states [1,2] improve the measurement signalto-noise ratio by redistribution of quantum noise, while GHZ states [3][4][5] enhance the signal via faster-evolving collective phase. GHZ states enable measurement at the Heisenberg limit, where noise-to-signal ratio scales with atom number N as 1/N [5].In both cases, very-high-precision readout is necessary to realize metrological gain. The performance of an entangled interferometer is determined not by the intrinsic fluctuations of the quantum system after detection noise subtraction, but by the full observed noise including detection noise [6][7][8][9][10][11]. Thus, the best observed spin squeezing of 6 dB [7] in a spin-1 2 system, and 8 dB of spin-nematic squeezing in a spin-1 system [11], were both limited by detection. For GHZ states, read-out of the collective phase requires a measurement of the parity of the population difference between two atomic states [5]. A state-selective measurement of atom number with singleatom resolution, which can be used to implement parity detection, therefore represents an important enabling technique for metrology beyond the SQL.An optical cavity can be used both to collect photons in a single mode [12][13][14][15][16][17][18][19][20][21][22], and to generate entangled states via light-mediated atom-atom interactions [7,23,24]. With respect to atom detection, counting of up to 4 atoms [12][13][14][15][16][17][18] and high-fidelity readout of the hyperfine state of a single neutral atom [19][20][21] have been achieved using cavity transmission measurements. Larger ensembles containing up to N = 70 atoms have been measured with atom detection variance (∆N ) 2 = 6 [25]. Spinsqueezed states of atoms in a cavity have also been prepared [7,22,26], and have enabled an atomic clock operating with variance a factor of 3 below the standard quantum limit [27].Single-atom resolution has also been achieved via fluorescence detection in free space. In optical lattices, the parity of site occupation has been measured for up to 5 atoms per lattice site without internal-state discrimination [28][29][30]. For strongly trapped ions...

We report on a simple, compact, and robust 780 nm distributed Bragg reflector laser with subkilohertz intrinsic linewidth. An external cavity with optical path length of 3.6 m, implemented with an optical fiber, reduces the laser frequency noise by several orders of magnitude. At frequencies above 100 kHz the frequency noise spectral density is reduced by over 33 dB, resulting in an intrinsic Lorentzian linewidth of 300 Hz. The remaining lowfrequency noise is easily removed by stabilization to an external reference cavity. We further characterize the influence of feedback power and current variation on the intrinsic linewidth. In this Letter, we present a tunable, long-externalcavity DBR laser with a 3000-fold reduction of its intrinsic linewidth to 300 Hz. This is achieved by implementing a 3.6 m long external cavity using an optical fiber. The system exhibits noise suppression of over 33 dB at frequencies of 100 kHz and above. Low-frequency noise due to mechanical or thermal fluctuations in the feedback path can be controlled by stabilizing the laser to a reference cavity using an active servo loop. Feedback-induced mode instability [16] is avoided by operating within a 13 dB wide range of feedback power.We use a 780 nm DBR laser (Photodigm PH780DBR120T8-S) with 120 mW maximum output power as our source. The laser diode has a front facet reflectivity close to 1%, effective gain region length of 1.8 mm, and DBR reflectivity of 60% (all values are nominal values provided by manufacturer). The diode is temperature stabilized to slightly below room temperature. Throughout our measurements, we operated the laser at 100 mA (16 mW total output power). A beam splitter deflects 10% of the laser power into a 2 m long polarization-maintaining optical fiber that constitutes the feedback path (Fig. 1). An aperture is added before the angled fiber to block unwanted backreflection from the fiber tip. A mirror mounted on a piezoelectric transducer (PZT) reflects the light back into the fiber, and a quarterwave plate in combination with a polarizing beam splitter is used to adjust the feedback power. A maximum −30 dB fractional power can be reflected back into the laser. (Henceforth we denote the fractional feedback power incident on the laser collimator as p, which may be less than the fractional power that is mode matched into the active region of the laser diode.) The externalcavity laser is set up on a 12 00 × 18 00 aluminum baseplate and enclosed by a plastic case to reduce environmental perturbations.In general, the effect of external cavity optical feedback depends on the feedback power, cavity length, and the phase of the feedback light, as summarized by Tkach Fig. 1. Schematic setup for the long-external-cavity laser and the frequency noise characterization. M, mirror; AP, aperture; PM fiber, polarization-maintaining fiber; QWP, quarter-wave plate; BS, beam splitter; PBS, polarization beam splitter; APD, avalanche photodiode; PZT, piezoelectric transducer.

Deterministic photon-photon interactions are a long-standing goal in optical science. Using an atomic ensemble inside a cavity, we demonstrate the mutual cross modulation of two continuous light beams at the level of individual photons. The originally uncorrelated beams derived from independent lasers become anticorrelated, as evidenced by an equal-time cross-correlation function g ð2Þ ¼ 0.89ð1Þ, showing that one photon in one beam extinguishes a photon in the other beam with a probability of 11(1)%. With further technical improvements, our approach should enable the nondestructive continuous detection of traveling optical photons.