Feedback is one of the most powerful techniques for the control of classical systems. An extension into the quantum domain is desirable as it could allow the production of non-trivial quantum states and protection against decoherence. The difficulties associated with quantum, as opposed to classical, feedback arise from the quantum measurement process-in particular the quantum projection noise and the limited measurement rate-as well as from quantum fluctuations perturbing the evolution in a driven open system. Here we demonstrate real-time feedback control of the motion of a single atom trapped in an optical cavity. Individual probe photons carrying information about the atomic position activate a dipole laser that steers the atom on timescales 70 times shorter than the atom's oscillation period in the trap. Depending on the specific implementation, the trapping time is increased by a factor of more than four owing to feedback cooling, which can remove almost all the kinetic energy of the atom in a quarter of an oscillation period. Our results show that the detected photon flux reflects the atomic motion, and thus mark a step towards the exploration of the quantum trajectory of a single atom at the standard quantum limit.

We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 µK. Time-dependent transmission and intensitycorrelation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the 1 s regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.Achieving strong coupling of a single atom to a light mode opens up new avenues for many applications ranging from sensitive detection to quantum information. A solution is feedback cooling. The idea is to observe the moving atom and then, using a fast feedback loop, engineer a suitable dissipative force that slows down the particle [5][6][7]. The performance is mainly limited by the accuracy with which the atomic trajectory can be measured. So far, feedback cooling has only been implemented for charged particles like antiprotons under the name of stochastic cooling [8], for electrons in Penning traps [9], for ions in Paul traps [10] and for micromechanical resonators [11]. A modest increase of the storage time of a single trapped atom has been achieved by means of feedback [12, 13] but cooling has not yet been demonstrated directly.Here we report on measurements performed in a new experimental setup optimized for the demands of feedback cooling. Compared to [13], more than 4 times higher photon detection efficiencies and faster feedback logic were implemented. As a result, we achieve average storage times exceeding 1 s. We deduce a temperature of about 160 µK and observe the improved localization of the atom. We also show that the performance of feedback cooling depends strongly on the amount of available information. Our results demonstrate the versatility of feedback cooling for all kinds of strong-coupling experiments with single atoms where 3D laser cooling is difficult to realize due to the limited optical access. Our85 Rb atoms are trapped inside a Fabry-Perot cavity with two spherical mirrors of different radii of curvature (R 1 = 200 mm, R 2 = 10 mm) and transmission coefficients (T 1 = 2 ppm, T 2 = 16 ppm, L 1 + L 2 ≈ 11 ppm), resulting in a finesse of F ≈ 2 × 10 5 . The cavity has a length of 260 µm, yielding a cavity field decay rate of κ = 2π×1.5 MHz and maximum atom-field coupling constant of g 0 =2π×16 MHz. With an atomic dipole decay rate γ = 2π×3 MHz, this puts our experiment in the strong-coupling regime of cavity quantum electrodynamics (QED).Two circularly polarized lasers at 785 nm and 780 nm are simultaneously coupled into the cavity through the mirror with the lower transmission. They are on resonance with two T EM 00 modes of the cavity separated by four free spectral ranges. The laser at 785 nm stabilizes the cavity length, traps the atom, and actuates the atomic motion. The other laser at 780 nm, called the probe laser, is blue detuned by 40 MHz from the 5S 1/...

Single quantum emitters like atoms are wellknown as non-classical light sources which can produce photons one by one at given times [1], with reduced intensity noise. However, the light field emitted by a single atom can exhibit much richer dynamics. A prominent example is the predicted[2] ability for a single atom to produce quadrature-squeezed light [3], with sub-shotnoise amplitude or phase fluctuations. It has long been foreseen, though, that such squeezing would be "at least an order of magnitude more difficult" to observe than the emission of single photons [4]. Squeezed beams have been generated using macroscopic and mesoscopic media down to a few tens of atoms [5], but despite experimental efforts [6][7][8], single-atom squeezing has so far escaped observation. Here we generate squeezed light with a single atom in a highfinesse optical resonator. The strong coupling of the atom to the cavity field induces a genuine quantum mechanical nonlinearity [9], several orders of magnitude larger than for usual macroscopic media [10][11][12]. This produces observable quadrature squeezing [13][14][15] with an excitation beam containing on average only two photons per system lifetime. In sharp contrast to the emission of single photons [16], the squeezed light stems from the quantum coherence of photon pairs emitted from the system [17]. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emitters [18][19][20][21][22][23].Unlike in a standard Kerr medium, our squeezing does not result from a simple nonlinear polarization of the medium but from a cavity-enhanced atomic coherence which exists for weak coherent driving. Consider a twostate atom with ground and excited states |g and |e . In the absence of a resonator, the amount of squeezing is governed by the atomic coherence, σ = |g e|, and the excited-state occupation probability. The latter pro- * Publication reference: Nature 474, 623-626 (2011), www.nature.com/doifinder/10.1038/nature10170 † Present address: MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands duces incoherent scattering which destroys the squeezing. Therefore, the laser intensity must remain low to preserve the atomic and hence the optical coherence, see Supplementary Information. Under this condition, the optical squeezing is determined by the fluctuations of the atomic coherence, ∆σ 2 = ( σ − σ ) 2 , itself given by ∆σ 2 = − σ 2 owing to the fermionic character of a twostate atom, σ 2 = 0. Note that this sets an upper bound to the amount of squeezing which can be obtained, even when all the light scattered by the atom in all directions is observed.The presence of the cavity introduces two important ingredients as sketched in Fig. 1. First, the cavity mirrors spatially direct the squeezed light towards the detectors thus eliminating the need to observe the full 4π solid angle. Second, the strong coupling to the optical cavity mode makes ...

We investigate phase shifts in the strong coupling regime of single-atom cavity quantum electrodynamics (QED). On the light transmitted through the system, we observe a phase shift associated with an antiresonance and show that both its frequency and width depend solely on the atom, despite the strong coupling to the cavity. This shift is optically controllable and reaches 140 • -the largest ever reported for a single emitter. Our result offers a new technique for the characterization of complex integrated quantum circuits.The strongly coupled atom-cavity system plays a central role in research on fundamental quantum optics. Important achievements to date include the creation of single photon sources [1,2] and non-classical microwave states [3,4], single-atom squeezing [5], the observation of novel photon statistics [6][7][8] and the nondestructive detection of microwave and optical photons [9,10]. More complex interacting systems based on this basic element are now attracting much attention in quantum information and simulation. Recent achievements in this direction include the coupling of a single qubit to two cavities [11], the interaction of multiple qubits with a single cavity bus [12,13], and the exchange of quantum states between single qubits in remote cavities [14,15]. Integrated quantum circuits are promising candidates for on-chip quantum computation [16][17][18][19][20] and large strongly coupled networks have been proposed for simulating quantum phase transitions [21][22][23]. However, in such strongly interacting systems, the couplings no longer represent merely a perturbation of the subsystem dynamics, necessitating a holistic analysis of the coupled system. This makes the characterization of strongly coupled quantum circuits a challenging task [24,25].In this Letter, we propose a new technique for characterizing complex quantum circuits, which emerges from an analysis of the phase of light transmitted through a strongly coupled single-atom-cavity system. In particular, we report on the observation of an antiresonant phase shift caused by destructive interference between the coherent drive and the field radiated by the atom. The signature of the antiresonance is a large negative phase shift which depends solely on the atom, despite the strong coupling to the resonator. This is in sharp contrast to the normal modes [26,27], which depend on properties of both atom and cavity as well as the coupling strength [28]. Our measurement paves the way for individual components of strongly interacting quantum systems to be characterized via measurements performed only on the overall coupled system.Previous work on phase spectroscopy in cavity QED has focused on the so-called "bad-cavity" limit in which the cavity decay rate exceeds the coupling strength, κ > ∼ g, and only modest phase shifts were observed [29,30]. Phase changes due to strongly coupled atoms were seen in Ref. [31], but the antiresonance phase shift was not observed. The presence of a transmission dip at the atomic frequency (associated with th...

The quantum dynamics of a strongly driven, strongly coupled single-atom-cavity system is studied by evaluating time-dependent second-and third-order correlations of the emitted photons. The coherent energy exchange, first, between the atom and the cavity mode, and second, between the atom-cavity system and the driving laser, is observed. Three-photon detections show an asymmetry in time, a consequence of the breakdown of detailed balance. The results are in good agreement with theory and are a first step towards the control of a quantum trajectory at larger driving strength.Open quantum systems far from thermal equilibrium hold great promise for the investigation of fundamental physics and the implementation of practical devices [1, 2]. The versatility of such systems comes from two features: the coherent evolution induced by the driving and the dissipation enabling a transfer of information to an observer. These two characteristics affect each other, and the deterministic evolution is interrupted by unpredictable quantum jumps [3, 4]. Monitoring such a quantum trajectory is a challenge, in particular when many quantum states must be discriminated from each other. A model system in this context is provided by optical cavity quantum electrodynamics (QED) in the regime of strong lightmatter coupling, where atomic and photonic observables have been tracked in real time [5][6][7][8] and controlled by means of feedback [9][10][11]. However, these experiments were performed at low excitation. Stronger driving and, hence, faster probing would allow one to track the system more closely and explore high-intensity effects like the coherent coupling of the system with the drive laser or the dynamical polarization of the dressed states [12,13]. Moreover, higher excited states containing several photons should be discernible by characteristic patterns of multiple-photon emissions [14], which can be asymmetric in time due to the predicted breakdown of detailed balance [15]. In this Letter we explore such patterns for a strongly driven atom-cavity system, when the excitation rate exceeds the dissipative rates.We consider a system where the atom-cavity coupling strength g 0 exceeds the atomic polarization decay rate γ and the cavity field decay rate κ. The internal dynamics, described by the Jaynes-Cummings Hamiltonian, is complemented by driving with a probe laser of strength η [31] and dissipation due to spontaneous emission and cavity decay. By monitoring the photon stream from the cavity, one can evaluate different observables such as the average photon number, a † a , or the average number of photon pairs, a †2 a 2 . The first is interesting, e.g., in the context of normal-mode spectroscopy [16,17], while insight into quantum effects can be obtained by regarding photon pairs [14,18]. Due to the interplay of the different dynamical processes, both observables are expected