Quantum Rabi Oscillations in Coherent and in Mesoscopic Cat Field States.

The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.

Coherent Transfer between Low-Angular-Momentum and Circular Rydberg States.

We realize a coherent transfer between a laser-accessible low-angular-momentum Rydberg state and the circular Rydberg level with maximal angular momentum. It is induced by a radio frequency field with a high-purity σ^{+} polarization resonant on Stark transitions inside the hydrogenic Rydberg manifold. We observe over a few microseconds more than 20 coherent Rabi oscillations between the initial Rydberg state and the circular level. We characterize these many-Rydberg-level oscillations and find them in perfect agreement with a simple model. This coherent transfer opens the way to hybrid quantum gates bridging the gap between optical communication and quantum information manipulations with microwave cavity and circuit quantum electrodynamics.

Microwaves Probe Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas.

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

Field locked to a Fock state by quantum feedback with single photon corrections.

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

Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics.

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

Process tomography of field damping and measurement of Fock state lifetimes by quantum nondemolition photon counting in a cavity.

The relaxation of a quantum field stored in a high-Q superconducting cavity is monitored by nonresonant Rydberg atoms. The field, subjected to repetitive quantum nondemolition photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the n photon states (0 < or = n < or = 7) are found to increase linearly with n. The results are in excellent agreement with theory including a small thermal contribution.

Freezing coherent field growth in a cavity by the quantum zeno effect.

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 backaction 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.

Realization of a superconducting atom chip.

We have trapped rubidium atoms in the magnetic field produced by a superconducting atom chip operated at liquid helium temperatures. Up to 8.2x10(5) atoms are held in a Ioffe-Pritchard trap at a distance of 440 microm from the chip surface, with a temperature of 40 microK. The trap lifetime reaches 115 s at low atomic densities. These results open the way to the exploration of atom-surface interactions and coherent atomic transport in a superconducting environment, whose properties are radically different from normal metals at room temperature.

Nondestructive Rydberg atom counting with mesoscopic fields in a cavity.

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

Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence.

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

Coherence-preserving trap architecture for long-term control of giant Ryberg atoms.

We present a way to trap a single Rydberg atom, make it long-lived, and preserve an internal coherence over time scales reaching into the minute range. We propose to trap using carefully designed electric fields, to inhibit the spontaneous emission in a nonresonant conducting structure, and to maintain the internal coherence through a tailoring of the atomic energies using an external microwave field. We thoroughly identify and account for many causes of imperfection in order to verify at each step the realism of our proposal.

Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity.

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 quantum state superpositions at the quantum-classical boundary.

Quantum information in cavity quantum electrodynamics: logical gates, entanglement engineering and 'Schrödinger-cat states'.

In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.

Direct measurement of the Wigner function of a one-photon Fock state in a cavity.

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

Generating and probing a two-photon fock state with a single atom in a cavity.

A two-photon Fock state is prepared in a cavity sustaining a "source mode" and a "target mode," with a single circular Rydberg atom. In a third-order Raman process, the atom emits a photon in the target while scattering one photon from the source into the target. The final two-photon state is probed by measuring by Ramsey interferometry the cavity light shifts induced by the target field on the same atom. Extensions to other multiphoton processes and to a new type of micromaser are briefly discussed.

Coherent control of an atomic collision in a cavity.

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 a nonresonant cavity are entangled by coherent energy exchange. The process, mediated by the virtual emission and absorption of a microwave photon, is characterized by a collision mixing angle 4 orders of magnitude larger than for atoms colliding in free space with the same impact parameter. The final entangled state is controlled by adjusting the atom-cavity detuning. This procedure, essentially insensitive to thermal fields and to photon decay, opens promising perspectives for complex entanglement manipulations.

A complementarity experiment with an interferometer at the quantum-classical boundary.

To illustrate the quantum mechanical principle of complementarity, Bohr described an interferometer with a microscopic slit that records the particle's path. Recoil of the quantum slit causes it to become entangled with the particle, resulting in a kind of Einstein-Podolsky-Rosen pair. As the motion of the slit can be observed, the ambiguity of the particle's trajectory is lifted, suppressing interference effects. In contrast, the state of a sufficiently massive slit does not depend on the particle's path; hence, interference fringes are visible. Although many experiments illustrating various aspects of complementarity have been proposed and realized, none has addressed the quantum-classical limit in the design of the interferometer. Here we report an experimental investigation of complementarity using an interferometer in which the properties of one of the beam-splitting elements can be tuned continuously from being effectively microscopic to macroscopic. Following a recent proposal, we use an atomic double-pulse Ramsey interferometer, in which microwave pulses act as beam-splitters for the quantum states of the atoms. One of the pulses is a coherent field stored in a cavity, comprising a small, adjustable mean photon number. The visibility of the interference fringes in the final atomic state probability increases with this photon number, illustrating the quantum to classical transition.

Step-by-step engineered multiparticle entanglement

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 and process information in nonclassical ways. This implies programmable sequences of operations to generate and analyze the entanglement of complex systems. We have demonstrated such a procedure for two atoms and a single-photon cavity mode, engineering and analyzing a three-particle entangled state by a succession of controlled steps that address the particles individually. This entangling procedure can, in principle, operate on larger numbers of particles, opening new perspectives for fundamental tests of quantum theory.