Quantum thermodynamics is emerging both as a topic of fundamental research and as means to understand and potentially improve the performance of quantum devices [1][2][3][4][5][6][7][8][9][10]. A prominent platform for achieving the necessary manipulation of quantum states is superconducting circuit quantum electrodynamics (QED) [11]. In this platform, thermalization of a quantum system [12][13][14][15] can be achieved by interfacing the circuit QED subsystem with a thermal reservoir of appropriate Hilbert dimensionality. Here we study heat transport through an assembly consisting of a superconducting qubit [16] capacitively coupled between two nominally identical coplanar waveguide resonators, each equipped with a heat reservoir in the form of a normal-metal mesoscopic resistor termination. We report the observation of tunable photonic heat transport through the resonator-qubit-resonator assembly, showing that the reservoir-to-reservoir heat flux depends on the interplay between the qubit-resonator and the resonator-reservoir couplings, yielding qualitatively dissimilar results in different coupling regimes. Our quantum heat valve is relevant for the realisation of quantum heat engines [17] and refrigerators, that can be obtained, for example, by exploiting the time-domain dynamics and coherence of driven superconducting qubits [18,19]. This effort would ultimately bridge the gap between the fields of quantum information and thermodynamics of mesoscopic systems. * alberto.ronzani@aalto.fi arXiv:1801.09312v3 [cond-mat.mes-hall]

We investigate hysteresis in the transport properties of superconductor -normal-metal -superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

When a superconductor is placed close to a non-superconducting metal, it can induce superconducting correlations in the metal [1][2][3][4][5][6][7][8][9][10] , known as the 'proximity effect' 11. Such behaviour modifies the density of states (DOS) in the normal metal [12][13][14][15] and opens a minigap 12,13,16 with an amplitude that can be controlled by changing the phase of the superconducting order parameter 12,15 . Here, we exploit such behaviour to realize a new type of interferometer, the superconducting quantum interference proximity transistor (SQUIPT), for which the operation relies on the modulation with the magnetic field of the DOS of a proximized metal embedded in a superconducting loop. Even without optimizing its design, this device shows extremely low flux noise, down to ∼10 −5 Φ 0 HzWb is the flux quantum) and dissipation several orders of magnitude smaller than in conventional superconducting interferometers [17][18][19] . With optimization, the SQUIPT could significantly increase the sensitivity with which small magnetic moments are detected.One typical SQUIPT fabricated with electron-beam lithography is shown in Fig. 1a. It consists of an aluminium (Al) superconducting loop interrupted by a copper (Cu) normal-metal wire in good electric contact with it. Furthermore, two Al electrodes are tunnel-coupled to the normal region to enable the device operation. A detailed view of the sample core (see Fig. 1b) shows the Cu region of length L 1.5 µm and width 240 nm coupled to the tunnel probes and the superconducting loop. The SQUIPTs were implemented into two different designs (see Fig. 1c), namely, the A-type configuration, where the loop extends into an extra third lead, and the B-type configuration, which contains only two tunnel probes. The ring geometry enables us to change the phase difference across the normal-metal/superconductor boundaries through the application of an external magnetic field, which gives rise to a total flux Φ through the loop area. This modifies the DOS in the normal metal, and hence the transport through the tunnel junctions.Insight into the interferometric nature of the SQUIPT can be gained by first analysing the theoretical prediction of its behaviour. Figure 2a shows the simplest implementation of the device in the A-type configuration, that is, that with just one junction tunnelcoupled to the normal metal. For simplicity, we suppose the tunnel probe (with resistance R T ) to be placed in the middle of the wire, and to feed a constant electric current I through the circuit while the voltage drop V is recorded as a function of Φ. In the limit that the kinetic inductance of the superconducting loop is negligible, the magnetic flux fixes a phase difference φ = 2πΦ/Φ 0 across the normal metal, where Φ 0 = πh/e is the flux quantum,h is the reduced Planck's constant and e is the electron charge. Figure 2b shows the low-temperature quasiparticle current-voltage (I -V ) characteristic of the SQUIPT calculated at a few selected values of Φ. The calculations were carried out f...

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%.

We demonstrate evidence of coherent magnetic flux tunneling through superconducting nanowires patterned in a thin highly disordered NbN film. The phenomenon is revealed as a superposition of flux states in a fully metallic superconducting loop with the nanowire acting as an effective tunnel barrier for the magnetic flux, and reproducibly observed in different wires. The flux superposition achieved in the fully metallic NbN rings proves the universality of the phenomenon previously reported for InO x . We perform microwave spectroscopy and study the tunneling amplitude as a function of the wire width, compare the experimental results with theories, and estimate the parameters for existing theoretical models.

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 use a hysteretic Josephson junction as an on-chip detector of the third moment of shot noise of a tunnel junction. The detectable bandwidth is determined by the plasma frequency of the detector, which is about 50 GHz in the present experiment. The third moment of shot noise results in a measurable change of the switching rate when reversing polarity of the current through the noise source. We analyze the observed asymmetry assuming adiabatic response of the detector.

We present tunnel spectroscopy experiments on the proximity effect in lateral superconductor-normal-metalsuperconductor Josephson junctions. Our weak link is embedded into a superconducting ring allowing phase biasing of the Josephson junction by an external magnetic field. We explore the temperature and phase dependence of both the induced minigap and the modification of the density of states in the normal metal. Our results agree with a model based on the quasiclassical theory in the diffusive limit. The device presents an advanced version of the superconducting quantum interference proximity transistor, now reaching flux sensitivities of 3 nA/ 0 , where 0 is the flux quantum.