S. Haroche

Superradiance: An essay on the theory of collective spontaneous emission

Abstract This essay presents a theoretical description of the superradiance phenomenon, in which both the quantal and the classical aspects are discussed. Starting from the simple two-level atom-small sample Dicke model, we successively introduce various complications inherent to a realistic superradiance experiment: effects of Van der Waals interaction between the atoms, propagation and diffraction of the electromagnetic field in the sample and finally the effects related to atomic level degeneracy or near degeneracy. We recall how to calculate the field radiated by a superradiant system in a single experiment and how to determine, for a series of identically prepared superradiant samples, the large shot to shot fluctuations of the emitted light properties. The presentation tries to unify various points of view and formalisms developed in previous works and to introduce simply and progressively the basic physical concepts relevant to the superradiance phenomenon.

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.

Very High-Q Whispering-Gallery Mode Resonances Observed on Fused Silica Microspheres

We have studied by phase modulation spectroscopy the whispering-gallery modes (Mie resonances) of 60 to 200 μm diameter microspheres obtained by fusing with a CO2 laser the end of a high-transmission silica fibre. An evanescent wave at 780 nm was produced by total internal reflection of a phase-modulated semiconductor diode laser beam in a glass prism. It was coupled into the Mie mode of the microsphere positioned at a fixed distance from the prism face. The spectrum was obtained by measuring the phase-to-amplitude conversion of the laser beam modulation as its carrier frequency was scanned. Record Q-factors ≥ 2 109 were observed, corresponding to photon storage times longer than 1 μs. Applications of these resonances to fundamental and applied projects are discussed.

Quantum jumps of light recording the birth and death of a photon in a cavity

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.

Reconstruction of non-classical cavity field states with snapshots of their decoherence

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.

Splitting of high-Q Mie modes induced by light backscattering in silica microspheres

We have observed that very high-Q Mie resonances in silica microspheres are split into doublets. This splitting is attributed to internal backscattering that couples the two degenerate whispering-gallery modes propagating in opposite directions along the sphere equator. We have studied this doublet structure by high-resolution spectroscopy. Time-decay measurements have also been performed and show a beat note corresponding to the coupling rate between the clockwise and counterclockwise modes. A simple model of coupled oscillators describes our data well, and the backscattering efficiency that we measure is consistent with what is observed in optical fibers.

Real-time quantum feedback prepares and stabilizes photon number states

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.

Seeing a single photon without destroying it

Light detection is usually a destructive process, in that detectors annihilate photons and convert them into electrical signals, making it impossible to see a single photon twice. But this limitation is not fundamental—quantum non-demolition strategies permit repeated measurements of physically observable quantities, yielding identical results. For example, quantum non-demolition measurements of light intensity have been demonstrated, suggesting possibilities for detecting weak forces and gravitational waves. But such experiments, based on nonlinear optics, are sensitive only to macroscopic photon fluxes. The non-destructive measurement of a single photon requires an extremely strong matter–radiation coupling; this can be realized in cavity quantum electrodynamics, where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interferometry to measure the phase shift in an atomic wavefunction, caused by a cycle of photon absorption and emission. Our method amounts to a restricted quantum non-demolition measurement which can be applied only to states containing one or zero photons. It may lead to quantum logic gates based on cavity quantum electrodynamics, and multi-atom entanglement.

Progressive field-state collapse and quantum non-demolition photon counting.

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.

Strain-tunable high-Q optical microsphere resonator

Abstract We demonstrate the tuning of high- Q optical whispering-gallery modes in a fused silica microsphere by applying mechanical strain. The measured total tunability is over 0.3 nm in the near-infrared band, with the undercoupled quality-factor being Q >1×10 8 . The tunability of mode frequencies in this high- Q solid-state microcavity expands its applicability in quantum optics and photonics.