A microscopic quantum system under continuous observation exhibits at random times sudden jumps between its states. The detection of this quantum feature requires a quantum non-demolition (QND) measurement repeated many times during the system's evolution. Whereas quantum jumps of trapped massive particles (electrons, ions or molecules) have been observed, this has proved more challenging for light quanta. Standard photodetectors absorb light and are thus unable to detect the same photon twice. It is therefore necessary to use a transparent counter that can 'see' photons without destroying them. Moreover, the light needs to be stored for durations much longer than the QND detection time. Here we report an experiment in which we fulfil these challenging conditions and observe quantum jumps in the photon number. Microwave photons are stored in a superconducting cavity for times up to half a second, and are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms, highly correlated in the same state, are interrupted by sudden state switchings. These telegraphic signals record the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons should open new perspectives for the exploration of the quantum-to-classical boundary.

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.

We have built a microwave Fabry-Perot resonator made of diamond-machined copper mirrors coated with superconducting niobium. Its damping time (Tc = 130 ms at 51 GHz and 0.8 K) corresponds to a finesse of 4.6 × 10 9 , the highest ever reached for a Fabry-Perot in any frequency range. This result opens many perspectives for quantum information processing, decoherence and non-locality studies.PACS numbers: 42.50. Pq, Since Bohr-Einstein's photon box thought experiment, storing a photon for a long time has been a dream of physicists. Cavity quantum electrodynamics (CQED) in the microwave domain comes closest to this goal. Photons are trapped in a superconducting cavity and probed by atoms crossing the field one at a time. Experiments with circular Rydberg atoms and Fabry-Perot resonators have led to fundamental tests of quantum theory and various demonstrations of quantum information procedures [1]. The open geometry of the cavity is essential to allow a perturbation-free propagation of long-lived atomic coherences through the mode. With this cavity structure, however, the field energy damping time T c is very sensitive to geometrical mirror defects, limiting T c to ≃ 1 ms in previous experiments. We report here the realization of a Fabry-Perot resonator at ω/2π = 51 GHz, with T c = 130 ms. The cavity quality factor Q is 4.2 × 10 10 and its finesse 4.6 × 10 9 , the highest ever achieved in any frequency domain for this geometry. This important step opens the way to many CQED experiments. Quantum non-demolition detection of a single photon [2] and generation of mesoscopic non-local quantum superpositions [3] are now accessible. Long term storage of single photon fields opens bright perspectives for quantum information processing. These high-Q cavities are also promising for the stabilization of microwave oscillators or for the search of exotic particles [4].A picture of the cavity C with the top mirror removed is shown in Fig. 1. The mirrors have a diameter D 0 = 50 mm. The distance between their apexes is L = 27.57 mm. Their surface is toroidal (radii of curvature 39.4 and 40.6 mm in two orthogonal planes). The two TEM 900 modes near 51.099 GHz with orthogonal linear polarizations are separated by 1.2 MHz. This large frequency splitting is essential to ensure that atoms are efficiently coupled to a single mode only. The mirrors are electrically insulated. A static electric field parallel to the cavity axis is applied between them to preserve the circular states and to tune the atomic transition via the Stark effect [1]. The 1 cm spacing between mirror edges is partly closed by two guard rings improving the static field homogeneity in C. The atoms of a thermal beam enter and exit the cavity through two large ports (1 cm × 2 cm) so that they never come close to metallic surfaces, preserving them from patch effect stray fields. This ensures a good transmission of atomic coherences through the cavity [2]. Four piezoelectric actuators are employed to translate one of the mirrors and to tune the cavity (within ±5 MHz) wit...

We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase-entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large Schrödinger cat states at the quantum-classical boundary.

Fundamental quantum fluctuations caused by the Heisenberg principle limit measurement precision. If the uncertainty is distributed equally between conjugate variables of the meter system, the measurement precision cannot exceed the standard quantum limit. When the meter is a large angular momentum, going beyond the standard quantum limit requires non-classical states such as squeezed states or Schrödinger-cat-like states. However, the metrological use of the latter has been so far restricted to meters with a relatively small total angular momentum because the experimental preparation of these non-classical states is very challenging. Here we report a measurement of an electric field based on an electrometer consisting of a large angular momentum (quantum number J ≈ 25) carried by a single atom in a high-energy Rydberg state. We show that the fundamental Heisenberg limit can be approached when the Rydberg atom undergoes a non-classical evolution through Schrödinger-cat states. Using this method, we reach a single-shot sensitivity of 1.2 millivolts per centimetre for a 100-nanosecond interaction time, corresponding to 30 microvolts per centimetre per square root hertz at our 3 kilohertz repetition rate. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques and could have important practical applications: detection of individual electrons in mesoscopic devices at a distance of about 100 micrometres with a megahertz bandwidth is within reach.

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.

In a quantum world, a watched arrow never moves. This is the Quantum Zeno Effect [1]. Repeatedly asking a quantum system "are you still in your initial state ?" blocks its coherent evolution through measurement back-action. Quantum Zeno Dynamics (QZD) [2,3] leaves more freedom to the system. Instead of pinning it to a single state, it sets a border in its evolution space. Repeatedly asking the system "are you beyond the border ?" makes this limit impenetrable. Since the border can be designed by choosing the measured observable, QZD allows one to tailor dynamically at will the system's Hilbert space. Recent proposals, particularly in the Cavity Quantum Electrodynamics (CQED) context [4,5], highlight the interest of QZD for quantum state engineering tasks [6][7][8][9][10][11], which are the key to quantum-enabled technologies and quantum information processing. We report the observation of QZD in the 51-dimension Hilbert space of a large angular momentum J = 25. Continuous selective interrogation limits the evolution of this angular momentum to an adjustable multi-dimensional subspace. This confined dynamics leads to the production of non-classical 'Schrödinger cat' states [12,13], quantum superpositions of angular momentums pointing in different directions. These states are promising for sensitive metrology of electric and magnetic fields. This QZD approach could also be generalized to cavity and circuit QED experiments [4,5,13], replacing the angular momentum by a photonic harmonic oscillator.Quantum Zeno dynamics modifies the classical motion of a system by its observation in a quantum context [4][5][6][7][8][9][10][11]. However, an actual projective quantum measurement is not mandatory, and QZD can be equivalently attained by performing a pulsed unitary acting only on the states at the border ("Bang Bang" control) or even by applying a strong continuous coupling to these states. This has been predicted theoretically [3] and verified in a recent experiment [14]. In that experiment, however, the evolution of the system is restricted to a dimension 2 subspace. The dynamics is simply that of a spin 1/2, and do not exhibit the most striking features of QZD [4].In this Letter we implement QZD in a large atomic angular momentum J = 25 ('spin' or top), represented as an arrow pointing on a generalized Bloch sphere. In the 51-dimensional Hilbert space, we isolate tailorable multi-dimensional manifolds. We show how QZD induces a very non-classical dynamics inside the Zeno subspace, leading to the generation of Schrödinger cat spin states [12], in which the arrow points at the same time in two different directions. As spin-squeezed states [15], which are the focus of an intense attention, these cat states lead to quantum-enabled metrological applications [13].The angular momentum projection on the polar axis of the generalized Bloch sphere is quantized, taking the values J − k, with k = 0 . . . 2J (the corresponding eigenstates being |J, J − k ). The dynamical evolution from the initial state |J, J (North pole of the Bl...