The authors have built a microwave Fabry-Pérot resonator made of diamond-machined copper mirrors coated with superconducting niobium. Its damping time (Tc=130ms at 51GHz and 0.8K) corresponds to finesse 4.6×109, the highest ever reached for in any frequency range. This result opens many perspectives quantum information processing, decoherence nonlocality studies.

Quantum simulation can provide insight into physical systems that are too complex for traditional computing techniques. A new proposal describes how a quantum simulator could be realized using laser-trapped circular Rydberg atoms, whose long lifetimes and stability beneficial simulations lasting up to seconds.

Fock states with photon numbers $n$ up to 7 are prepared on demand in a microwave superconducting cavity by quantum feedback procedure that reverses decoherence-induced jumps. Circular Rydberg atoms used as nondemolition sensors or single-photon emitter absorber actuators. The nature of these actuators matches the correction jumps due relaxation. flexibility this method is suited generation arbitrary sequences states.

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

Using an echo technique proposed by Morigi et al. [Phys. Rev. A 65, 040102 (2002)], we have time-reversed the atom-field interaction in a cavity quantum electrodynamics experiment. The collapse of atomic Rabi oscillation coherent field is reversed, resulting induced revival signal. amplitude this ``echo'' sensitive to nonunitary decoherence processes. Its observation demonstrates existence mesoscopic superposition states between and times.

We analyze the quantum Zeno dynamics that takes place when a field stored in cavity undergoes frequent interactions with atoms. show repeated measurements or unitary operations performed on atoms probing state confine evolution to tailored subspaces of total Hilbert space. This confinement leads non-trivial evolutions and generation interesting non-classical states, including mesoscopic superpositions. elucidate main features mechanism context state-of-the-art electrodynamics experiment. A...

Superconducting atom chips and Rydberg atoms are promising tools for quantum information processing operations based on the dipole blockade effect. Nevertheless, one has to face severe problem of stray electric fields in vicinity chip. We demonstrate a simple method circumventing this problem. Microwave spectroscopy reveals extremely long coherence lifetimes (in millisecond range) qubit stored level superposition close chip surface. This is an essential step development simulations with...

The relaxation of a quantum field stored in high-$Q$ superconducting cavity is monitored by nonresonant Rydberg atoms. field, subjected to repetitive nondemolition photon counting, undergoes jumps between number states. We select ensembles realizations evolving from given Fock state and reconstruct the subsequent evolution their distributions. realize this way tomography process yielding all jump rates damping $n$ states ($0\ensuremath{\le}n\ensuremath{\le}7$) are found increase linearly...

We discuss an implementation of quantum Zeno dynamics in a cavity electrodynamics experiment. By performing repeated unitary operations on atoms coupled to the field, we restrict field evolution chosen subspaces total Hilbert space. This procedure leads promising methods for tailoring nonclassical states. propose realize "tweezers" picking coherent at point phase space and moving it towards arbitrary final position without affecting other nonoverlapping components. These effects could be...

We show that microwave spectroscopy of a dense Rydberg gas trapped on superconducting atom chip in the dipole blockade regime reveals directly dipole-dipole many-body interaction energy spectrum. use this method to investigate expansion cloud under effect repulsive van der Waals forces and breakdown frozen approximation. This study opens promising route for quantum simulation systems information transport chains strongly interacting atoms.

By carefully shaping radio frequency pulses, experiments show how to quickly and efficiently prepare a single atom in one of several desired states, key ability for variety quantum technologies.

Circular Rydberg states are excellent tools for quantum technologies, with large mutual interactions and long lifetimes in the tens of milliseconds range, 2 orders magnitude larger than those laser-accessible states. However, such observed only at zero temperature. At room temperature, blackbody-radiation-induced transfers cancel this essential asset circular states, which have thus been used mostly so far specific, complex cryogenic experiments. We demonstrate here, on a laser-cooled atomic...

A quantum system can be monitored through repeated interactions with meter systems. The state of the at time $t$, represented by density matrix $\ensuremath{\rho}(t)$, then becomes conditioned on information obtained meters until that time. More insight in any $t$ is provided, however, taking into account full detection all interacting both past and future $t$. We present experiments use near-resonant atomic probes to monitor evolution quantized field a cavity. application forward-backward...

We realize a coherent transfer between laser-accessible low-angular-momentum Rydberg state and the circular level with maximal angular momentum. This is induced by radiofrequency field high-purity $\sigma^+$ polarization tuned at resonance on Stark transitions inside hydrogenic manifold. observe over few microseconds more than twenty Rabi oscillations initial level. characterize in details these complex involving many levels find them to be perfect agreement simple theoretical model....

We present an efficient, state-selective, nondemolition atom-counting procedure based on the dispersive interaction of a sample circular Rydberg atoms with mesoscopic field contained in high-quality superconducting cavity. The state-dependent atomic index refraction, proportional to atom number, shifts classical phase. A homodyne translates information from phase intensity. final intensity is readout by sample. This method opens promising routes for quantum processing and nonclassical state...

The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at macroscopic scale. It increasingly difficult to isolate a system from its environment when size increases. Making use weird properties mesoscopic states thus requires efficient means combat decoherence. One option real-time feedback. features components conventional feedback: measurement system's state (sensor), analysis (controller), and feedback action (actuator) aiming target state. random...

Preparation of a so-called circular state in Rydberg atom where the projection electron angular momentum takes its maximum value is challenging due to required amount transfer. Currently available protocols for preparation are either accurate but slow or fast error prone. Here we show how use quantum optimal control theory derive pulse shapes that realize and circularization atom. In particular, present theoretical proposal optimized radio-frequency pulses achieve high fidelity shortest...

The simple resonant Rabi oscillation of a two-level system in single-mode coherent field reveals complex features at the mesoscopic scale, with collapses and revivals. Using slow circular Rydberg atoms interacting superconducting microwave cavity, we explore this phenomenon an unprecedented range interaction times photon numbers. We demonstrate efficient production cat states, which are quantum superposition components nearly opposite phases sizes few tens photons. measure cuts their Wigner...

Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of and, notably, a huge coupling to external fields or other while ionic core retains an optically active electron. However, low angular-momentum states suffer almost immediate autoionization when is excited. Here, we demonstrate that strontium circular in $4D$ metastable level impervious over more than few millisecond time scale....

In many quantum measurements, information is acquired incrementally by the successive interaction of meters with measured system. Adaptive measurements minimize use resources (meters) adjusting measurement settings according to available information. We demonstrate an adaptive for nondestructive photon counting in a cavity, based on Ramsey interferometry Rydberg atoms interacting field. Tuning interferometer real time, we speed up 45%. Such methods are promising metrology, state preparation,...

We present a method for reconstructing the average evolution of photon number distribution field decaying in high-Q cavity. It applies an iterative maximum likelihood state reconstruction algorithm to diagonal elements density operator. is based on quantum non-demolition measurements carried out with atoms crossing cavity one by one. A small set successively detected defines positive operator valued measure (POVM). The performed applying this POVM large ensemble realizations. An optimal...