After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in physics. We performed experiments with Rydberg atoms and microwave photons cavity tested mechanics situations increasing complexity. Entanglement resulted either from resonant exchange energy between the field or dispersive shifts affecting when were not resonant. With two (two one atom photon), we realized new versions...

A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time few photon coherent field trapped in high $Q$ microwave cavity. the equivalent an `` $\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}$'' system which ``meter'' pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' phenomenon transforming...

We have observed the Rabi oscillation of circular Rydberg atoms in vacuum and small coherent fields stored a high Q cavity. The signal exhibits discrete Fourier components at frequencies proportional to square root successive integers. This provides direct evidence field quantization weights yield photon number distribution field. investigation excited levels atom-cavity system reveals nonlinear quantum features extremely low strengths.

Pairs of atoms have been prepared in an entangled state the Einstein-Podolsky-Rosen (EPR) type. They were produced by exchange a single photon between high $Q$ cavity. The atoms, superposition involving two different circular Rydberg states, separated distance order 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more and opens way new tests nonlocality mesoscopic quantum systems.

A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described detail. It based on detection dispersive phase shift produced field wave function nonresonant atoms crossing cavity. This can be measured atomic interferometry, using Ramsey separated-oscillatory-field method. The information acquired detecting sequence modifies step step, until it eventually collapses into Fock state. At same...

After quantum particles have interacted, they generally remain in an entangled state and are correlated at a distance by quantum-mechanical links that can be used to transmit process information nonclassical ways. This implies programmable sequences of operations generate analyze the entanglement complex systems. We demonstrated such procedure for two atoms single-photon cavity mode, engineering analyzing three-particle succession controlled steps address individually. entangling can,...

Following a recent proposal by S. B. Zheng and G. C. Guo (Phys. Rev. Lett. 85, 2392 (2000)), we report an experiment in which two Rydberg atoms crossing non-resonant cavity are entangled coherent energy exchange. The process, mediated the virtual emission absorption of microwave photon, is characterized collision mixing angle four orders magnitude larger than for colliding free space with same impact parameter. final state controlled adjusting atom-cavity detuning. This procedure,...

We have built the first quantum oscillator working on two-photon stimulated emission of radiation. It oscillates continuously a degenerate transition between levels 40S and 39S rubidium atoms. The oscillation is sustained in Q\ensuremath{\simeq}${10}^{8}$ niobium superconducting cavity at 68.415 87 GHz. At threshold, this new maser system operates with only few atoms tens photons time cavity.

We have realized a quantum phase gate operating on bits carried by single Rydberg atom and zero- or one-photon field in high- $Q$ cavity. The operation is based the dephasing of atom-field state produced full cycle Rabi oscillation. angle, conditioned to initial state, can be adjusted over wide range tuning atom-cavity frequency difference. demonstrate that preserves qubit coherence generates entanglement. This an essential tool for nondestructive measurement photons manipulation many-qubit...

We describe a new quantum nondemolition method to monitor the number N of photons in microwave cavity. propose coupling field quasiresonant beam Rydberg atoms and measuring resulting phase shift atom wave function by Ramsey separated-oscillatory-fields technique. The detection sequence reduces into Fock state. With realistic atom-cavity systems, small-photon-number states down N=0 could be prepared continuously monitored.

We have studied by phase modulation spectroscopy the whispering-gallery modes (Mie resonances) of 60 to 200 μm diameter microspheres obtained fusing with a CO2 laser end high-transmission silica fibre. An evanescent wave at 780 nm was produced total internal reflection phase-modulated semiconductor diode beam in glass prism. It coupled into Mie mode microsphere positioned fixed distance from prism face. The spectrum measuring phase-to-amplitude conversion as its carrier frequency scanned....

Implementing the ideas of Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], we present an experimentally feasible scheme for teleportation unknown atomic state between two high-Q cavities containing a nonlocal quantum superposition microwave field states. This experiment provides alternative tests nonlocality involving high-order correlations.

We have measured the complete Wigner function W of vacuum and a single-photon state for field stored in high-Q cavity. This experiment implements direct Lutterbach Davidovich method [L. G. L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)]] is based on dispersive interaction single circular Rydberg atom with cavity field. The nonclassical nature exhibited by region negative values. Extensions to other states are discussed.

The quantum information carried by a two-level atom was transferred to high- $Q$ cavity and, after delay, another atom. We realized in this way memory made of field superposition 0 and 1 photon Fock states. measured the ``holding time'' corresponding decay intensity or amplitude at single level. This experiment implements step essential for processing operations.

We present several schemes for preparing and detecting coherent superpositions of classically distinct states the electromagnetic field in one or two high-Q cavities. These proposals are based on two-atom correlation measurements, to be performed circular Rydberg atoms interacting dispersively with cavity fields. Changing time interval between detected allows a monitoring decay quantum coherence due dissipation. \textcopyright{} 1996 The American Physical Society.

Using a single circular Rydberg atom, we have prepared two modes of superconducting cavity in maximally entangled state. The share photon. This entanglement is revealed by second atom probing, after delay, the correlations between modes. experiment opens interesting perspectives for quantum information manipulation and fundamental tests theory.

We have measured by Ramsey interferometry the dispersive light shifts produced on circular Rydberg states very weak nonresonant microwave fields in a single cavity mode. This experiment yields an absolute measurement of mean photon numbers with sensitivity 0.1. The vacuum induced Lamb shift, equal to shift ``half photon,'' has been observed, providing direct and zero-point field fluctuations

A continuous-wave maser operating on a two-photon transition between Rydberg levels is expected to oscillate with about one atom and few tens of microwave photons at any time in its superconducting cavity. We analyze detail the characteristics this new microscopic quantum electronics device presently under construction our laboratory.

We describe the blueprint of an experiment in which decoherence a mesoscopic superposition radiation states (``Schr\"odinger cat'') becomes reversible process. When high $Q$ cavity containing Schr\"odinger cat is coupled to another resonator, quantum coherence first decays rapidly, then exhibits sharp revivals with period energy exchange between two cavities. The interpretation this emphasizes link and complementarity leads illuminating quantitative usual irreversible phenomenon.