The spectral purity of an oscillator is central to many applications, such as detecting gravity waves, defining the second, ground-state cooling and quantum manipulation of nanomechanical objects, and quantum computation. Recent proposals suggest that laser oscillators which use very narrow optical transitions in atoms can be orders of magnitude more spectrally pure than present lasers. Lasers of this high spectral purity are predicted to operate deep in the 'bad-cavity', or superradiant, regime, where the bare atomic linewidth is much less than the cavity linewidth. Here we demonstrate a Raman superradiant laser source in which spontaneous synchronization of more than one million rubidium-87 atomic dipoles is continuously sustained by less than 0.2 photons on average inside the optical cavity. By operating at low intracavity photon number, we demonstrate isolation of the collective atomic dipole from the environment by a factor of more than ten thousand, as characterized by cavity frequency pulling measurements. The emitted light has a frequency linewidth, measured relative to the Raman dressing laser, that is less than that of single-particle decoherence linewidths and more than ten thousand times less than the quantum linewidth limit typically applied to 'good-cavity' optical lasers, for which the cavity linewidth is much less than the atomic linewidth. These results demonstrate several key predictions for future superradiant lasers, which could be used to improve the stability of passive atomic clocks and which may lead to new searches for physics beyond the standard model.

We study the performance and limitations of a coherent interface between collective atomic states and single photons. A quantized spin-wave excitation of an atomic sample inside an optical resonator is prepared probabilistically, stored, and adiabatically converted on demand into a sub-Poissonian photonic excitation of the resonator mode. The measured peak single-quantum conversion efficiency of χ=0.84(11) and its dependence on various parameters are well described by a simple model of the mode geometry and multilevel atomic structure, pointing the way towards implementing highperformance stationary single-photon sources.PACS numbers: 42.50. Dv, 03.67.Hk, 42.50.Fx, 32.80.Pj A quantum-coherent interface between light and a material structure that can store quantum states is a pivotal part of a system for processing quantum information [1]. In particular, a quantum memory that can be mapped onto photon number states in a single spatio-temporal mode could pave the way towards extended quantum networks [2,3] and all-optical quantum computing [4]. While light with sub-Poissonian fluctuations can be generated by a variety of single-quantum systems [5,6,7], a point emitter in free space is only weakly, and thus irreversibly, coupled to an electromagnetic continuum.To achieve reversible coupling, the strength of the emitter-light interaction can be enhanced by means of an optical resonator, as demonstrated for quantum dots in the weak- [8,9], trapped ions in the intermediate- [10], and neutral atoms in the strong-coupling regime [11,12]. By controlling the position of a single atom trapped inside a very-high-finesse resonator, McKeever et al. have realized a high-quality deterministic single-photon source [12]. This source operates in principle in the reversiblecoupling regime, although finite mirror losses presently make it difficult to obtain full reversibility in practice.Alternatively, superradiant states of an atomic ensemble [13] exhibit enhanced coupling to a single electromagnetic mode. For three-level atoms with two stable ground states these collective states can be viewed as quantized spin waves, where a spin-wave quantum (magnon) can be converted into a photon by the application of a phasematched laser beam [3]. Such systems have been used to generate [14,16], store and retrieve single photons [18,19], to generate simultaneous-photon pairs [17,25], and to increase the single-photon production rate by feedback [21,22,23]. The strong-coupling regime between magnons and photons can be reached if the sample's optical depth OD exceeds unity. However, since the failure rate for magnon-photon conversion in these free-space [14,15,16,17,18,19,20,21,22,23] or moderate-finessecavity [24,25] systems has been around 50% or higher, which can be realized with OD ≤ 1, none of the ensemble systems so far has reached the strong, reversible-coupling regime. In this Letter, we demonstrate for the first time the strong-coupling regime between collective spin-wave excitations and a single electromagnetic mode. This is evidenc...

We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output-coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the independent behavior of two disparate oscillators to the phase-locking that is the signature of quantum synchronization. PACS numbers: 05.45.Xt, 42.50.Lc, 37.30.+i, 64.60.Ht Synchronization is an emergent phenomenon that describes coupled objects spontaneously phase-locking to a common frequency in spite of differences in their natural frequencies [1]. It was famously observed by Huygens, the seventeenth century clock maker, in the antiphase synchronization of two maritime pendulum clocks [2]. Dynamical synchronization is now recognized as ubiquitous behavior occurring in a broad range of physical, chemical, biological, and mechanical engineering systems [1,3,4].Theoretical treatments of this phenomenon are often based on the study of phase models [5,6], and as such have been applied to an abundant variety of classical systems, including the collective blinking of fireflies, the beating of heart cells, and audience clapping. The concept can be readily extended to systems with an intrinsic quantum mechanical origin such as nanomechanical resonators [7,8], optomechanical arrays [9], and Josephson junctions [10,11]. When the number of coupled oscillators is large, it has been demonstrated that the onset of classical synchronization is analogous to a thermodynamic phase transition [12] and exhibits similar scaling behavior [13].Recently, there has been increasing interest in exploring manifestations in the quantum realm. Small systems have been considered, e.g., one qubit [14] and two qubits [15] coupled to a quantum dissipative driven oscillator, two dissipative spins [16], two coupled cavities [17], and two micromechanical oscillators [18,19]. Connections between quantum entanglement and synchronization have been revealed in continuous variable systems [19]. It has been shown that quantum synchronization may be achieved between two canonically conjugate variables [20]. Since the phenomenon is inherently non-equilibrium, all of these systems share the common property of competition between coherent and incoherent driving and dissipative forces.In this paper, we propose a modern-day realization of the original Huygens experiment [2]. We consider the synchronization of two active atomic clocks coupled to a common single-mode optical cavity. It has been predicted that in the regime of steady-state superradiance [21-24] a neutral atom lattice clock could produce an ultracoherent optical field with a quality factor (ratio of frequency to linewidth) that approaches 10 18 . We show that two such clocks may exhibit a dynamical phase transition [26][27][28][29] from two disparate oscillators to quantum phase-locked dynamics. ...

We use the vacuum Rabi splitting to perform quantum nondemolition (QND) measurements that prepare a conditionally spin-squeezed state of a collective atomic psuedo-spin. We infer a 3.4(6) dB improvement in quantum phase estimation relative to the standard quantum limit for a coherent spin state composed of uncorrelated atoms. The measured collective spin is composed of the twolevel clock states of nearly 10 6 87 Rb atoms confined inside a low finesse F = 710 optical cavity. This technique may improve atomic sensor precision and/or bandwidth, and may lead to more precise tests of fundamental physics.PACS numbers: 42.50.Pq, 42.50.Dv, 37.30.+i, Large ensembles of uncorrelated atoms are extensively used as precise sensors of time, rotation, and gravity, and for tests of fundamental physics [1][2][3][4]. The quantum nature of the sensors imposes a limit on their ultimate precision. Larger ensembles of N atoms can be used to average the quantum noise as 1/ √ N , a scaling known as the standard quantum limit. However, the ensemble size is limited by both technical constraints and atom-atom collisions-a fundamental distinction from photon-based sensors. Learning to prepare entangled states of large ensembles with noise properties below the standard quantum limit will be key to extending both the precision [5] and/or bandwidth [6] of atomic sensors. More broadly, the generation and application of entanglement to solve problems is a core goal of quantum information science being pursued in both atomic and solid state systems.In this Letter, we utilize the tools of cavity-QED to prepare an entangled ensemble with a 3.4(6) dB improvement in spectroscopic sensitivity over the standard quantum limit. The method does not require single particle addressability and is applied to a spectroscopically large ensemble of N = 7 × 10 5 atoms using a single < 200 µs operation. The gain in sensitivity is spectroscopically equivalent to the enhancement obtained had we created > 10 5 pairs of maximally entangled qubits, demonstrating the power of a top-down approach for entangling large ensembles. The probing of atomic populations via the vacuum Rabi splitting is also of broad interest for nondestructively reading out a wide variety of both atomic and solid state qubits.The large ensemble size is a crucial component. Entangled states of cold, neutral atoms are unlikely to impact the future of quantum sensors and tests of fundamental physics unless the techniques for generating the states are demonstrated to work for the 10 4 to 10 7 neutral atom ensembles typically used in primary frequency standards [7] and atom interferometers [2,4].The approach described here allows quantum-noise limited readout of a sensor with < 0.2 photon recoils/atom, producing little heating of the atomic ensemble. Applied to a state-of-the-art optical lattice clock, the resulting enhanced measurement rates will suppress the dominant aliasing of the local oscillator noise [1,8].The gain in spectroscopic sensitivity demonstrated here is far from the fundamental Hei...