Quantum transport and phase transitions in superconducting systems

This dissertation focuses on charge and thermal transport phenomena in mesoscopic superconducting circuits, particularly emphasizing the effects of Coulomb blockade on photonic heat transport at cryogenic temperatures. We investigate tunneling in mesoscopic systems with Coulomb blockade effects, the role of the electromagnetic environment on small Josephson junctions (JJs), and the impact of these factors on the bolometry of microwave photons through superconducting circuits. We propose and test a variant of the Maxwell demon experiment, the gambling demon. Unlike the standard Maxwell demon, the gambling demon decides, based on the acquired information, whether to stop the process following a customary gambling condition. Within this context, we derive and verify second-law-like inequalities accounting for the average work done when gambling is involved. For experimental verification, we use a single electron box connected capacitively to an electrometer, where an electrostatic potential governs the dynamics of electron tunneling into a metallic island. Our findings align closely with theoretical predictions, showing remarkable accuracy within 0.5%. We present results on photon-mediated heat transport through a superconducting circuit. We exploit the Johnson-Nyquist archetype to do that, where two thermal reservoirs are connected via a frequency-dependent transmission line. Here, two different frequency-dependent transmission lines are studied: one is a Cooper pair transistor controlled by an electric field, and the other is a superconducting quantum interference device (SQUID) controlled by a magnetic field. The first experiment with the Cooper pair transistor demonstrates a precise control of the thermal conductance close to its quantum limit with the gate voltage. The second experiment examines the environmental back-action effect on photon-mediated heat transport, revealing that while strong fluctuations produced by the environment affect charge transport through the SQUID as expected, they do not impact heat transport. This indicates that, unlike in the DC charge transport experiment, the Josephson effect survived regardless of the strength of the dissipation, which is a complementary experiment to test the anticipated dissipative phase transition by Schmid and Bulgadaev. In this scenario, we have performed a DC charge transport experiment through a JJ connected to a voltage source via an Ohmic resistor with resistance either greater or smaller than the superconducting resistance quantum RQ~6.5 kΩ to revisit the debated dissipative phase transition in a JJ. Our results support the existence of this transition, evidenced by a distinct dip in electrical conductance at zero voltage bias in the JJ connected to an environmental resistance exceeding RQ. Conversely, in devices where the environmental resistance is less than RQ, a conductance peak appears at zero voltage bias, indicative of the Josephson effect.