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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 with a few photon coherent field trapped in a high Q microwave cavity. The mesoscopic superposition was the equivalent of an "atom 1 measuring apparatus" system in which the "meter" was pointing simultaneously towards two different directions -a "Schrödinger cat." The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement. [S0031-9007(96)01848-0] The transition between the microscopic and macroscopic worlds is a fundamental issue in quantum measurement theory [1]. In an ideal model of measurement, the coupling between a macroscopic apparatus ("meter") and a microscopic system ("atom") results in their entanglement and produces a quantum superposition state of the "meter 1 atom" system. Such a superposition is however never observed. Schrödinger has illustrated vividly this problem, replacing the meter by a "cat" [2] and considering the dramatic superposition of dead and alive animal "states." Although such a striking image can only be a metaphor, quantum superpositions involving "meter states" are often called "Schrödinger cats." Following von Neumann [3], it is postulated that an irreversible reduction process takes the quantum superposition into a statistical mixture in a "preferred" basis, corresponding to the eigenvalues of the observable measured by the meter. From then on, the information contents in the system can be described classically. The nature of this reduction has been much debated, with recent theories stressing the role of quantum decoherence [4,5]. According to these approaches, the meter coordinate is always coupled to a large reservoir of microscopic variables inducing a fast dissipation of macroscopic coherences.The simplest model of a quantum measurement involves a two-level atom (e, g) coupled to a quantum oscillator (meter or cat). An oscillator in a coherent state [6] is indeed defined by a c number a, represented by a vector in phase space (jaj p n where n is the mean number of oscillator quanta). Quantum fluctuations make the tip of this vector uncertain, with a circular gaussian distribution of radius unity [ Fig. 1(a)]. Consider the ideal measurement where the "atom-meter" interaction entangles the phase of the oscillator (6f) to the state of the atom, leading to the combined stateWhen the "distance" D 2 p n sin f between the meter states is larger than 1, a Schrödinger cat is obtained [ Fig. 1(b)].Decoherence is modeled by coupling the oscillator to a reservoir, which damps its energy in a characteristic time T r . When D ¿ 1, decoherence is found to occur within a time scale 2T r ͞D 2 [7,8]. This result illustrates the basic feature of the quantum to classical transition [4]. Mesoscopic superpositions made of a few quanta are ex...

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

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.

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Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen ( EPR) type. They were produced by the exchange of a single photon between the atoms in a high Q cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems.[S0031-9007 (97)03502-3] PACS numbers: 03.65. -w, 32.80. -t, 42.50. -pOne of the most puzzling aspects of quantum mechanics, its nonseparability, is illustrated vividly by the famous Einstein-Podolsky-Rosen (EPR) paradox [1]. A pair of particles flying apart from each other is predicted by quantum mechanics to yield measurement results incompatible with our intuitive conceptions about locality and reality. Such a nonclassical behavior is expected from any system made of two parts whose wave function cannot be written, in any basis, as a direct product of independent substates. The system parts are then said to be entangled. The study of entanglement has been given a firm conceptual ground by Bell who derived inequalities that Nature should obey if locality and reality were respected and which are violated by quantum mechanics [2]. Many experiments since Bell's paper have demonstrated violations of these inequalities and have vindicated quantum theory [3][4][5][6][7].In most EPR experiments so far [3,4,6,7], pairs of photons flying apart are created in a correlated state by a radiative process (spontaneous emission cascade in an atom or down-conversion in a nonlinear medium). Entangled protons have also been studied in an early experiment [5]. All these studies have dealt with very simple elementary particle systems, in which the entanglement mechanism is imposed by spontaneous processes.Entangling more complex systems in a controlled way is a challenging goal, which has been discussed in many recent proposals. The generation of EPR pairs of massive atoms instead of massless photons has been considered [8][9][10][11]. Ideas to generalize entanglement to larger numbers of particles have also been analyzed [8,10,12].The "manipulation" of entanglement is another important aspect of the new EPR experiment proposals. The idea is to apply a set of well-controlled interactions to the particles of the system in order to bring them into a "tailored" entangled state. In this context, the physics of entanglement meets the theory of quantum information processing. Teleportation of quantum states could in principle be achieved [13] as well as quantum cryptography [14]. Simple quantum computation steps could also be carried out. Particles can then be viewed as carriers of quantum bits of information and the realization of "engineered" entanglement is closely related to the building of gates acting on these bits [15].We describe here an experiment in which we have entangled two initially independent a...

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.