The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization, but can instead be reconstructed from an ensemble of copies through measurements on different realizations. Reconstructing the state of a set of trapped particles shielded from their environment is an important step in the investigation of the quantum-classical boundary. Although trapped-atom state reconstructions have been achieved, it is challenging to perform similar experiments with trapped photons because cavities that can store light for very long times are required. Here we report the complete reconstruction and pictorial representation of a variety of radiation states trapped in a cavity in which several photons survive long enough to be repeatedly measured. Atoms crossing the cavity one by one are used to extract information about the field. We obtain images of coherent states, Fock states with a definite photon number and 'Schrödinger cat' states (superpositions of coherent states with different phases). These states are equivalently represented by their density matrices or Wigner functions. Quasi-classical coherent states have a Gaussian-shaped Wigner function, whereas the Wigner functions of Fock and Schrödinger cat states show oscillations and negativities revealing quantum interferences. Cavity damping induces decoherence that quickly washes out such oscillations. We observe this process and follow the evolution of decoherence by reconstructing snapshots of Schrödinger cat states at successive times. Our reconstruction procedure is a useful tool for further decoherence and quantum feedback studies of fields trapped in one or two cavities.

Feedback loops are central to most classical control procedures. A controller compares the signal measured by a sensor (system output) with the target value or set-point. It then adjusts an actuator (system input) to stabilize the signal around the target value. Generalizing this scheme to stabilize a micro-system's quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the sensor measurements cause a random back-action on the system. An optimal compromise uses weak measurements, providing partial information with minimal perturbation. The controller should include the effect of this perturbation in the computation of the actuator's operation, which brings the incrementally perturbed state closer to the target. Although some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations that permanently stabilize quantum systems around a target state have not yet been realized. Here we have implemented such a real-time stabilizing quantum feedback scheme following a method inspired by ref. 13. It prepares on demand photon number states (Fock states) of a microwave field in a superconducting cavity, and subsequently reverses the effects of decoherence-induced field quantum jumps. The sensor is a beam of atoms crossing the cavity, which repeatedly performs weak quantum non-demolition measurements of the photon number. The controller is implemented in a real-time computer commanding the actuator, which injects adjusted small classical fields into the cavity between measurements. The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms. Our experiment demonstrates that active control can generate non-classical states of this oscillator and combat their decoherence, and is a significant step towards the implementation of complex quantum information operations.

The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in which this observable becomes precisely known. Its value is random, with a probability determined by the initial system's state. The evolution induced by measurement (known as 'state collapse') can be progressive, accumulating the effects of elementary state changes. Here we report the observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity. Atoms behaving as microscopic clocks cross the cavity successively. By measuring the light-induced alterations of the clock rate, information is progressively extracted, until the initially uncertain photon number converges to an integer. The suppression of the photon number spread is demonstrated by correlations between repeated measurements. The procedure illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities.

The spin of light in subwavelength-diameter waveguides can be orthogonal to the propagation direction of the photons because of the strong transverse confinement. This transverse spin changes sign when the direction of propagation is reversed. Using this effect, we demonstrate the directional spontaneous emission of photons by laser-trapped caesium atoms into an optical nanofibre and control their propagation direction by the excited state of the atomic emitters. In particular, we tune the spontaneous emission into the counter-propagating guided modes from symmetric to strongly asymmetric, where more than % of the optical power is launched into one or the other direction. We expect our results to have important implications for research in quantum nanophotonics and for implementations of integrated optical signal processing in the quantum regime.

The realization of nanophotonic optical isolators with high optical isolation even at ultralow light levels and low optical losses is an open problem. Here, we employ the link between the local polarization of strongly confined light and its direction of propagation to realize low-loss nonreciprocal transmission through a silica nanofiber at the single-photon level. The direction of the resulting optical isolator is controlled by the spin state of cold atoms. We perform our experiment in two qualitatively different regimes, i.e., with an ensemble of cold atoms where each atom is weakly coupled to the waveguide and with a single atom strongly coupled to the waveguide mode. In both cases, we observe simultaneously high isolation and high forward transmission. The isolator concept constitutes a nanoscale quantum optical analog of microwave ferrite resonance isolators, can be implemented with all kinds of optical waveguides and emitters, and might enable novel integrated optical devices for fiber-based classical and quantum networks.

The main objective of quantum simulation is an in-depth understanding of many-body physics, which is important for fundamental issues (quantum phase transitions, transport, …) and for the development of innovative materials. Analytic approaches to many-body systems are limited, and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms, and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1=2 arrays, providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes, combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization, make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultracold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the detection of arbitrary spin observables with single-site resolution. The proposed simulator realizes an XXZ spin-1=2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kilohertz. All the model parameters can be dynamically tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder, or Floquet time crystals. The proposed platform already presents unrivaled features for quantum simulation of regular spin chains. We discuss extensions towards more general quantum simulations of interacting spin systems with full control on individual interactions.

Tapered optical fibers with a nanofiber waist are versatile tools for interfacing light and matter. In this context, laser-cooled atoms trapped in the evanescent field surrounding the optical nanofiber are of particular interest: They exhibit both long ground-state coherence times and efficient coupling to fiber-guided fields. Here, we demonstrate electromagnetically induced transparency, slow light, and the storage of fiber-guided optical pulses in an ensemble of cold atoms trapped in a nanofiber-based optical lattice. We measure a slow-down of light pulses to group velocities of 50 m/s. Moreover, we store optical pulses at the single photon level and retrieve them on demand in the fiber after 2 µs with an overall efficiency of (3.0 ± 0.4) %. Our results show that nanofiber-based interfaces for cold atoms have great potential for the realization of building blocks for future optical quantum information networks.PACS numbers: 42.50. Gy, 37.10.Jk, 42.50.Ct Storing classical light pulses in optical memories is an important capability for the realization of all-optical signal processing schemes. Similarly, quantum information processing and communication require quantum memories in which quantum states of light can be faithfully stored [1,2]. Such memories are crucial elements of future large-scale quantum optical networks [3]. They are key to quantum repeaters [4] which are indispensable when it comes to the exchange of quantum information over long-distances [5][6][7]. Furthermore, quantum memories can be used to effectively turn a probabilistic single-photon source into an on-demand source [8].A classical light pulse was stored for about one minute in a rare-earth-doped crystal using dynamical decoupling techniques [9]. Similar storage times were achieved with an ensemble of ultracold atoms in a free-space optical lattice [10]. For optical network-based applications, efficient and long-lived fiber-integrated optical memories are desirable and currently constitute an active field of research [11][12][13]. Recently, weak coherent light pulses were stored using a hollow-core photonic-crystal fiber filled with thermal cesium vapor [12]. In this case, the highest measured memory efficiency was 27 % and the memory lifetime was about 30 ns. In another recent work, photons at a wavelength of about 1.5 µm were stored and retrieved with an efficiency of 1 % after 5 ns using a cryogenically cooled erbium-doped fiber [13]. There, it was also demonstrated that photonic entanglement is preserved during storage and retrieval. The performance of these fiber-integrated quantum memories could be significantly improved if decoherence mechanisms such as the motion of the atoms or the coupling to the solid-state environment were suppressed.Here, we make use of a nanofiber-based optical interface [14] to store fiber-guided light in an ensemble of * Schneeweiss@ati.ac.at † Arno.Rauschenbeutel@ati.ac.at trapped neutral atoms. The laser-cooled cesium atoms are confined in a one-dimensional optical lattice that is realized in the evane...

We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a field injected in the cavity by a classical source. This manifestation of the Quantum Zeno effect illustrates the back action of the photon number determination onto the field phase. The residual growth of the field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the measurement process and opens perspectives for active quantum feedback.PACS numbers: 03.65. Ta, 03.65.Xp, 42.50.Pq The 'Quantum Zeno' effect is a spectacular manifestation of the measurement back action. The coherent evolution of a quantum system is inhibited by repeated projective measurements performed at short time intervals. This effect, theoretically discussed in [1,2, 3], has been observed on the evolution of two-level systems such as molecules [4], trapped ions [5], cold atoms [6] as well as on polarization of light [7]. We describe here the observation of the Zeno effect on a harmonic oscillator. The build-up of a coherent field in a high-Q superconducting cavity coupled to a classical source is inhibited by watching repeatedly the photon number. The measurements use circular Rydberg atoms as non-destructive probes [8,9]. The system free evolution is here a run-away coherent classical process, instead of the two-level quantum dynamics considered in [4,5,6,7]. When watching the system, we record single trajectories and the field state evolution is obtained by a statistical analyzis of these data. This study sheds light on the relationship between the Zeno effect and the measurement back action.We first revisit the basics of the Zeno effect in the context of our experiment. A classical source is resonantly coupled to the cavity. The evolution due to the source-cavity coupling during a time T is described by the displacement operator, where α = λT , a (a † ) are the photon annihilation (creation) operators and λ is the complex amplitude of the source. At this stage, we neglect relaxation, assuming T ≪ T c , where T c is the cavity damping time. The initially empty cavity contains at time T the coherent state |α = D(α)|0 (|0 is the vacuum). The average photon number, n = |α| 2 = |λ| 2 T 2 , runs away quadratically with T . This evolution can be split into small steps of duration ∆t ≪ T . The final displacement results from the coherent accumulation of successive injection pulses, * Present address: Johannes Gutenberg Universität, Institut für Physik, Staudingerweg 7, D-55128 Mainz, Germany † Electronic address: brune@lkb.ens.fr each being described by the translation operator D(λ∆t).We now watch the field evolution. In order to separate the field probing from its coupling with the source, we alternate measurements with injection pulses of duration ∆t, such that |λ|∆t ≪ 1. After the first pulse, the cavity contains a cohe...