  Two superconductors coupled by a weak link support an equilibrium Josephson
electrical current which depends on the phase difference $\varphi$ between the
superconducting condensates [1]. Yet, when a temperature gradient is imposed
across the junction, the Josephson effect manifests itself through a coherent
component of the heat current that flows oppositely to the thermal gradient for
$ \varphi <\pi/2$ [2-4]. The direction of both the Josephson charge and heat
currents can be inverted by adding a $\pi$ shift to $\varphi$. In the static
electrical case, this effect was obtained in a few systems, e.g. via a
ferromagnetic coupling [5,6] or a non-equilibrium distribution in the weak link
[7]. These structures opened new possibilities for superconducting quantum
logic [6,8] and ultralow power superconducting computers [9]. Here, we report
the first experimental realization of a thermal Josephson junction whose phase
bias can be controlled from $0$ to $\pi$. This is obtained thanks to a
superconducting quantum interferometer that allows to fully control the
direction of the coherent energy transfer through the junction [10]. This
possibility, joined to the completely superconducting nature of our system,
provides temperature modulations with unprecedented amplitude of $\sim$ 100 mK
and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this
quantum structure represents a fundamental step towards the realization of
caloritronic logic components, such as thermal transistors, switches and memory
devices [10,11]. These elements, combined with heat interferometers [3,4,12]
and diodes [13,14], would complete the thermal conversion of the most important
phase-coherent electronic devices and benefit cryogenic microcircuits requiring
energy management, such as quantum computing architectures and radiation
sensors.
