Optomechanical systems couple light stored inside an optical cavity to the motion of a mechanical mode. Recent experiments have demonstrated setups, such as photonic crystal structures, that in principle allow one to confine several optical and vibrational modes on a single chip. Here we start to investigate the collective nonlinear dynamics in arrays of coupled optomechanical cells. We show that such "optomechanical arrays" can display synchronization, and that they can be described by an effective Kuramoto-type model

We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that those systems can exhibit an instability towards a regime where the cantilever settles into self-sustained oscillations. In this paper, we briefly review the classical theory of the optomechanical instability, and then discuss the features arising in the quantum regime. We solve numerically a full quantum master equation for the coupled system, and use it to analyze the photon number, the cantilever's mechanical energy, the phonon probability distribution and the mechanical Wigner density, as a function of experimentally accessible control parameters. We observe and discuss the quantum-to-classical transition as a function of a suitable dimensionless quantum parameter.

We study electron transport through a closed Aharonov-Bohm interferometer containing two noninteracting single-level quantum dots. The quantum-dot levels are coupled to each other indirectly via the leads. We find that this coupling yields signatures of an effective flux-dependent level attraction in the linear conductance. Furthermore, we predict a suppression of transport when both levels are close to the Fermi level of the leads. The width of this anomaly is also flux dependent. We identify different regimes in which constructive interference of transmission through identical dots yields a signal that is 1, 2, or 4 times as large as the conductance through a single dot.

Motivated by recent experiments on superconducting circuits consisting of a dc-voltage biased Josephson junction in series with a resonator, quantum properties of these devices far from equilibrium are studied. This includes a crossover from a domain of incoherent to a domain of coherent Cooper pair tunneling, where the circuit realizes a driven nonlinear oscillator. Equivalently, weak photon-charge coupling turns into strong correlations captured by a single degree of freedom. Radiated photons offer a new tool to monitor charge flow and current noise gives access to nonlinear dynamics, which allows to analyze quantum-classical boundaries.

We study the influence of Coulomb interaction on the thermoelectric transport coefficients for a metallic single-electron transistor. By performing a perturbation expansion up to second order in the tunnel-barrier conductance, we include sequential and cotunneling processes as well as quantum fluctuations that renormalize the charging energy and the tunnel conductance. We find that Coulomb interaction leads to a strong violation of the Wiedemann-Franz law: the Lorenz ratio becomes gate-voltage dependent for sequential tunneling, and is increased by a factor 9/5 in the cotunneling regime. Finally, we suggest a measurement scheme for an experimental realization.

We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures. The flow of heat at the microscopic level is a fundamentally important issue, in particular if it can be converted into free energy via thermoelectric effects [1]. The ability of most conductors to sustain heat flow is linked to the electrical conductance σ via the Wiedemann-Franz law: κ/σ = L 0 T , where κ is the heat conductance,3e 2 the Lorenz number and T the temperature. While the understanding of quantum charge transport in nano-electronic devices has reached a great level of maturity, heat transport experiments are lagging far behind [2], for two essential reasons: (i) unlike charge, heat is not conserved and (ii) there is no simple thermal equivalent to the ammeter. Heat transport can nevertheless give insight to phenomena that charge transport is blind to [3,4] and, remarkably, a series of experiments has demonstrated the very universality of the quantization of heat conductance, regardless of the carriers statistics [3][4][5][6][7][8][9][10][11].As device dimensions are reduced, electron interactions gain capital importance, leading to Coulomb blockade in mesoscopic devices in which a small island is connected by tunnel junctions. A metallic island connected to a source and a drain through tunnel junctions exceeding the Klitzing resistance R K = h/e 2 and under the influence of a gate electric field constitutes a Single-Electron Transistor (SET) [12]. The charging energy of the island by a single electron writes E C = e 2 /2C where C is the total capacitance of the island. It defines the temperature and bias thresholds below which single-electron physics appears. In the regime where charge transport is governed by unscreened Coulomb interactions, the question of the associated heat flow has been addressed by several theoretical studies [13][14][15][16][17][18][19][20]. The Wiedemann-Franz law is expected to hold in an SET only at the charge degener- acy points in the limit of small transparency, where the effective transport channel is free from interactions, and is violated otherwise. In this Letter, we report on the measurements of both the heat and charge conduction through a metallic SET, with both quantities displaying a marked gate modulation. A strong deviation from the Wiedemann-Franz law is observed when the transport through the SET is arXiv:1704.02622v1 [cond-mat.mes-hall]

We show experimentally that a dc biased Josephson junction in series with a high-enoughimpedance microwave resonator emits antibunched photons. Our resonator is made of a simple micro-fabricated spiral coil that resonates at 4.4 GHz and reaches a 1.97 kΩ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of 6 10 7 photons per second. Results are found in quantitative agreement with our theoretical predictions. This simple scheme could offer an efficient and bright single-photon source in the microwave domain.PACS numbers: 74.50+r, 73.23Hk, 85.25Cp Single photon sources constitute a fundamental resource for many quantum information technologies, notably secure quantum state transfer using flying photons. In the microwave domain, although photon propagation is more prone to losses and thermal photons present except at extremely low temperature, applications can nevertheless be considered [1,2]. Single microwave photons were first demonstrated in [3] using the standard design of single-photon emitters: an anharmonic atom-like quantum system excited from its ground state relaxes by emitting a single photon on a well-defined transition before it can be excited again. The first and second order correlation functions of such a source [4] demonstrate a rather low photon flux limited by the excitation cycle duration, but an excellent antibunching of the emitted photons. We follow a different approach, where the tunnelling of discrete charge carriers through a quantum coherent conductor creates photons in its embedding circuit. The resulting quantum electrodynamics of this type of circuits [5][6][7][8][9][10][11] has been shown to provide e.g. masers [12][13][14][15], simple sources of non-classical radiation [16][17][18], or near quantum-limited amplifiers [19]. When the quantum conductor is a Josephson junc-tion, dc biased at voltage V in series with a linear microwave resonator, exactly one photon is created in the resonator each time a Cooper pair tunnels through the junction, provided that the Josephson frequency 2eV /h matches the resonator's frequency [20].We demonstrate here that in the strong coupling regime between the junction and the resonator, the presence of a single photon in the resonator inhibits the further tunneling of Cooper pairs, leading to the antibunching of the photons leaking out of the resonator [21,22]. Complete antibunching is expected when the characteristic impedance of the resonator reaches Z c = 2R Q /π, with R Q = h/(2e) 2 6.45 kΩ the superconducting resistance quantum. This regime, for which the analogue of the fine structure constant of the problem is of order 1, has recently attracted attention [23,24], as it allows the investigation of many-body physics with photons [25,26] or ultra-strong coupling physics [27], offering new strategies for the generation of non classical radiation [28].The simple circuit used in...

We study thermal conductance and thermopower of a metallic single-electron transistor beyond the limit of weak tunnel coupling. Employing both a systematic second-order perturbation expansion and a nonperturbative approximation scheme, we find, in addition to sequential and cotunneling contributions, terms that are associated with the renormalization of system parameters due to quantum fluctuations. The latter can be identified by their logarithmic temperature dependence that is typical for many-channel Kondo correlations. In particular, the temperature dependence of thermopower, which provides a direct measure of the average energy of transported particles, reflects the logarithmic reduction of the Coulomb-blockade gap due to quantum fluctuations.