Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation.PACS numbers: 3.65. Ta, 42.50.Lc 32.80.Pj, 42.50.Ct, 42.50.Vk, 32.80.Lg Quantum optics, and more recently mesoscopic condensed matter physics, have taken a leading role in realizing individual quantum systems, which can be monitored continuously in quantum limited measurements, and at the same time can be controlled by external fields on time scales fast in comparison with the system evolution. Examples include cold trapped ions and atoms [1], cavity QED [2,3,4,5] and nanomechanical systems [6]. This setting opens the possibility of manipulating individual quantum systems by feedback, a problem which is not only of a fundamental interest in quantum mechanics, but also promises a new route to generating interesting quantum states in the laboratory. First experimental efforts to realize quantum feedback have been reported only recently. While not all of them may qualify as quantum feedback in a strict sense, feedback has been applied to various quantum systems [5,7,8,9,10,11]. On the theory side, this has motivated during the last decade the development of a quantum feedback theory [12,13], where the basic ingredients are the interplay between quantum dynamics and the back-action of the measurement on the system evolution. In this letter we report a first experiment to demonstrate quantum feedback control, i.e. quantum feedback cooling, of a single trapped ion by monitoring the fluorescence of the laser driven ion in front of a mirror. We establish a continuous measurement of the position of the ion which allows us to act back in a feedback loop demonstrating "cold damping" [14,15]. We will show that quantum control theory based on a quantum optical modelling of the system dynamics and continuous measurement theory of photodetection provides a quantitative understanding of the experimental results.We study a single 138 Ba + ion in a miniature Paul trap which is continuously laser-excited and laser-cooled to the Doppler limit on its S 1/2 to P 1/2 transition at 493 nm, as outlined in Fig. 1. The ion is driven by a laser near the atomic resonance, and the scattered light is emitted both into the radiation modes reflected by the mirror, as well as the other (background) modes of the quantized light field [16]. Light scattered into the mirror modes can either reach the photodetector directly, or after reflection from the mirror. From the resulting interference the motion of the ion (its projection onto the ion-mirror axis) is detected as a vibrational sideband in the fluctuation spectrum of the photon counting signal [17]. Of the three sidebands at about (1,1.2,2.3) MHz, corresponding to the three axes of vibration, we observe the one at ν = 1 MHz. It has a width Γ ≈ 400 Hz and is superimposed on the background shot noise...

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Photon correlations are investigated for a single laser-excited ion trapped in front of a mirror. Varying the relative distance between the ion and the mirror, photon correlation statistics can be tuned smoothly from an antibunching minimum to a bunching-like maximum. Our analysis concerns the non-Markovian regime of the ion-mirror interaction and reveals the field establishment in a half-cavity interferometer. 42.50.Lc, 42.50.Ct, 42.50.Vk Experiments with laser-cooled trapped ions have provided important contributions to the understanding of quantum phenomena. A single trapped ion is in fact a model system whose internal and external degrees of freedom can be controlled at the quantum level: non-classical motional states such as Fock states and quadraturesqueezed states have been successfully engineered with a single Be + ion [1]; the internal levels of trapped ions have been coherently manipulated by sequences of laser pulses, and have been entangled with the motional state, leading to the preparation of Schrödinger cat states [2] and to multi-ion entangled states for quantum information processing [3].The internal dynamics of a laser-driven single ion or atom is well characterized by the statistical analysis of the measured stream of fluorescence photons, namely by the second order correlation function G (2) (T ) [4], i.e. the frequency of time intervals of length T between detected photons. For a single atom trapped in free space, this correlation function exhibits sub-Poissonian statistics and violates the Cauchy-Schwarz inequality, i.e. G (2) (0) < G (2) (T ). More precisely, G (2) (T ) exhibits a minimum at T = 0 which indicates the quantum nature of photon emission, or the projective character of photon detection. This is defined as anti-bunching [5,6]. On the contrary, for a large ensemble of atoms the emitted radiation exhibits classical bunching [7] A smooth transition from anti-bunching to bunching has recently been observed in a high-Q resonator when increasing the number of interacting atoms [8].The second order correlation function can be viewed as representing the (average) dynamics of the observed system conditioned on the emission of a photon at time T = 0. While G (2) thereby draws on the photon character of the emitted light, it is the wave character which is responsible for interference phenomena, in particular for QED effects in resonators. In this letter, we examine the interplay of photon detection and wave interference in a simple cavity QED experiment, by measuring the second order photon correlation for a single trapped Ba + ion in a half-cavity interferometer. In this set-up part of the resonance fluorescence of the laser-excited ion is retroreflected by a mirror at a distance L and focussed back onto its source. Earlier experiments with our system revealed back-action of the interferometer on the emitting atom such as modification of its decay rate [9] and energy shifts of the excited state [10]; even mechanical action was observed [11]. Such effects intrinsically pertain to the ...

We report measurements of an intensity-field correlation function of the resonance fluorescence of a single trapped 138Ba+ ion. Detection of a photon prepares the atom in its ground state, and we observe its subsequent evolution under interaction with a laser field of well-defined phase. We record the regression of the resonance fluorescence source field. This provides a direct measurement of the field of the radiating dipole of a single atom and exhibits its strong nonclassical behavior. In the setup, an interference measurement is conditioned on the detection of a fluorescence photon.

Single-molecule (particle) tracking is a powerful method to study dynamic processes in cells at highest possible spatial and temporal resolution. We have developed SMTracker, a graphical user interface for automatic quantifying, visualizing and managing of data. Version 2.0 determines distributions of positional displacements in x- and y- direction using multi-state diffusion models, discriminates between Brownian, sub- or superdiffusive behaviour, and locates slow or fast diffusing populations in a standardized cell. Using SMTracker, we show that the Bacillus subtilis RNA degradosome consists of a highly dynamic complex of RNase Y and binding partners. We found similar changes in molecule dynamics for RNase Y, CshA, PNPase and enolase, but not for phosphofructokinase, RNase J1 and J2, to inhibition of transcription. However, the absence of PfkA or of RNase J2 affected molecule dynamics of RNase Y-mVenus, indicating that these two proteins are indeed part of the degradosome. Molecule counting suggests that RNase Y is present as a dimer in cells, at an average copy number of about 500, of which 46% are present in a slow-diffusive state and thus likely engaged within degradosomes. Thus, RNase Y, CshA, PNPase and enolase likely play central roles, and RNase J1, J2 and PfkA more peripheral roles, in degradosome architecture.