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.