We explore the photonic (bright) side of dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated to the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory. PACS numbers: 74.50+r, 73.23Hk, 85.25Cp Dynamical Coulomb blockade (DCB) of tunneling is a quantum phenomenon in which tunneling of charge through a small tunnel junction is modified by its electromagnetic environment [1][2][3][4]. This environment is described as an impedance in series with the tunnel element (see Fig. 1a). The sudden charge transfer associated with tunneling can generate photons in the electromagnetic modes of the environment. In a normal metal tunnel junction, biased at voltage V , the energy eV of a tunneling electron can be dissipated both into quasiparticle excitations in the electrodes and into photons. At low temperature energy conservation forbids tunneling processes emitting photons with total energy higher than eV . This suppression reduces the conductance at low bias voltage [1, 2, 4]. In a Josephson junction, DCB effects are more prominent since at bias voltages smaller than the gap voltage 2∆/e quasiparticle excitations cannot take away energy. Therefore, as shown in Fig. 1a, the entire energy 2eV of tunneling Cooper pairs has to be transformed into photons in the impedance for a dc current to flow through the junction [3,4]. Experiments have confirmed the predictions of DCB theory for the tunneling current, both in the normal [5][6][7] and superconducting case [8,9] but the associated emission of photons into the environment has never been investigated. The aim of this work is precisely to fill this gap by exploring the photonic side of DCB. We do so by embedding a Josephson junction into a well controlled electromagnetic environment provided by a microwave resonator. The resonator in turn leaks photons into an amplifier, allowing to measure the rate and spectrum of photons emitted by the junction.The experimental setup is represented in Fig. 1b. A small SQUID acts as a tunable Josephson junction with Josephson energy E J = E J0 | cos(eΦ/ )| adjustable via the magnetic flux Φ threading its loop. The microwave resonator is made of two quarter-wave transformers and its fundamental mode has frequency ν 0 6.0 GHz and quality factor Q 0 9.4. Higher modes of the resonator appear at ν n (2n + 1)ν 0 (n = 1, 2, . . .) with the same lineshape up to small deviations caused by the junction

Conventional lasers make use of optical cavities to provide feedback to gain media. Conversely, mirrorless lasers can be built by using disordered structures to induce multiple scattering, which increases the effective path length in the gain medium and thus provides the necessary feedback. These so-called random lasers potentially offer a new and simple mean to address applications such as lighting. To date, they are all based on condensed-matter media. Interestingly, light or microwave amplification by stimulated emission occurs also naturally in stellar gases and planetary atmospheres. The possibility of additional scattering-induced feedback (that is, random lasing) has been discussed and could explain unusual properties of some space masers. Here, we report the experimental observation of random lasing in a controlled, cold atomic vapour, taking advantage of Raman gain. By tuning the gain frequency in the vicinity of a scattering resonance, we observe an enhancement of the light emission of the cloud due to random lasing. The unique possibility to both control the experimental parameters and to model the microscopic response of our system provides an ideal test bench for better understanding natural lasing sources, in particular the role of resonant scattering feedback in astrophysical lasers

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P (x) ∝ x −(1+α) , with α ≈ 1. We show that this step size distribution leads to a violation of Ohm', as expected for a Lévy walk of independent steps. Furthermore the spatial profile of the transmitted light develops power law tails [T diff (r) ∝ r −3−α ]. In an experiment using a slab geometry with hot rubidium vapor, we measured the total diffuse transmission T diff and the spatial profile of the transmitted light T diff (r). We obtained the microscopic Lévy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

We consider the Raman process developing in a disordered medium of alkali-metal atoms when the scattered modes are trapped on a closed transition. Our theoretical analysis, based on numerical simulations of the Bethe-Salpeter equation for the light correlation function, which includes all Zeeman states and light polarization, lets us track the stimulated amplification as well as the losses associated with the inverse anti-Stokes scattering channel. We discuss possible conditions when this process could approach the instability point and enter the regime of random lasing.

Atomic physics experiments, based on hot vapors or laser-cooled atomic samples, may be useful to simulate some astrophysical problems, where radiation pressure, radiative transport or light amplification are involved. We discuss several experiments and proposals, dealing with multiplescattering of light in hot and cold atomic vapors, random lasing in cold atoms and light-induced long-range forces, which may be relevant in this context.

In this paper, we use steady-state measurements to obtain evidence of radiation trapping in an optically thick a cloud of cold rubidium atoms. We investigate the fluorescence properties of our sample, pumped on opened transitions. This fluorescence exhibits a non trivial dependence on the optical thickness of the media. A simplified model, based on rate equations self-consistently coupled to a diffusive model of light transport, is used to explain the experimental observations in terms of incoherent radiation trapping on one spectral line. Measurements of the atomic populations and the fluorescence spectrum qualitatively agree with this interpretation.

We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.

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