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.

(Phys. Rev. Lett., in press) For a quantum system coupled to a heat bath environment the strong friction limit is studied starting from the exact path integral formulation. Generalizing the classical Smoluchowski limit to low temperatures a time evolution equation for the position distribution is derived and the strong role of quantum fluctuations in this limit is revealed.PACS:03.65. Yz,05.30.Ch, Quantum systems coupled to a heat bath environment can be found almost everywhere in physics and chemistry [1]. Transport processes in Josephson junctions [2] or electron transfer reactions in large molecules [3] are typical examples. What one aims to describe here is the effective dynamics of the relevant system degrees of freedom, i.e. the reduced dynamics. While the corresponding classical theory is well established and based on FokkerPlanck equations, the formulation of dissipation in quantum mechanics is more complicated. In general a simple time evolution equation for the reduced density matrix does not exist [1]; a formally exact expression for the reduced dynamics in terms of path integrals is available, but the path integral expression in many cases cannot be evaluated even numerically. In the last years efforts have focused on the weak coupling regime where a description in terms of Master equations is possible [4]. The opposite limit of strong coupling has been left basically untouched [5]. Here we study this limit. For the first time we show that for large friction the exact dynamics of a dissipative quantum system can be cast into a time evolution equation for the position distribution, the so-called quantum Smoluchowski equation derived below in Eq. (13).In classical physics the Smoluchowski limit is wellknown in all areas [6]. For large friction the FokkerPlanck equation in phase space reduces to a time evolution equation in position space, the Smoluchowski equation (SE). There, the basic condition is a time scale separation between relaxation of momentum and position which allows for an adiabatic elimination of the former degree of freedom. Corrections to the Smoluchowski equation turn out to be algebraically small in the friction constant. Applications are countless; recent examples include transport in systems with fluctuating barriers [7] or ratchets [8] as found in tunnel diodes [10] and complex macromolecules [9], and decay in periodically driven metastable potentials [11]. The quantum Smoluchowski equation should be important for the description of similar processes at low temperatures.Quantum dissipation-The standard way to describe dissipation in quantum mechanics is based on system+reservoir-models with a total Hamiltonian H = H S + H R + H I [1]. The reservoir H R (heat bath) consists of a quasi-continuum of harmonic oscillators which are coupled bilinearly with the system H S via the interaction H I . Classically, this model leads back to a generalized Langevin equation for the reduced system. The quantum dynamics for the reduced density matrix follows from ρ(t) = Tr R {exp(−iHt/h)W (0) e...

We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative algorithm, with no need for Markovian or rotating-wave approximations. The application to a harmonic degree of freedom reveals cooperative effects of driving and dissipation that a standard Markovian treatment cannot capture. Remarkably, control can modify the open-system dynamics to the point where the entropy change turns negative, thus achieving cooling of translational motion without any reliance on internal degrees of freedom.

The quantum dynamics of a two-state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that a changeover from coherent to incoherent relaxation does not occur for a broad class of spectral distributions. In nonequilibrium coherences associated with substantial system-reservoir entanglement exist even when strong dissipation forces the thermodynamic state of the system to behave almost classically. This may be of relevance for current experiments with nanoscale devices.

In developing technologies based on superconducting quantum circuits, the need to control and route heating is a significant challenge in the experimental realisation and operation of these devices. One of the more ubiquitous devices in the current quantum computing toolbox is the transmon-type superconducting quantum bit, embedded in a resonator-based architecture. In the study of heat transport in superconducting circuits, a versatile and sensitive thermometer is based on studying the tunnelling characteristics of superconducting probes weakly coupled to a normal-metal island. Here we show that by integrating superconducting quantum bit coupled to two superconducting resonators at different frequencies, each resonator terminated (and thermally populated) by such a mesoscopic thin film metal island, one can experimentally observe magnetic flux-tunable photonic heat rectification between 0 and 10%.

Non‐Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on‐chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non‐zero third cumulant is presented, together with numerical simulations when the noise source is a tunnel junction with Poisson noise. Comparison between experiment and theory is discussed.

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 analyze the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage biased Josephson junction. When the applied voltage leads to a Josephson frequency across the junction which matches the sum of the two mode frequencies, tunneling Cooper pairs excite photons in both modes simultaneously leading to far-from-equilibrium states. These states display highly non-classical features including strong anti-bunching, violation of Cauchy-Schwartz inequalities, and number squeezing. The regimes of low and high photon occupancies allow for analytical results which are supported by a full numerical treatment. The impact of asymmetries between the two modes is explored, revealing a pronounced enhancement of number squeezing when the modes are damped at different rates.Comment: 12 pages, 8 figures, submitted to PR