We propose a thermodynamic refrigeration cycle which uses Indefinite Causal Orders to achieve non-classical cooling. The cycle cools a cold reservoir while consuming purity in a control qubit. We first show that the application to an input state of two identical thermalizing channels of temperature T in an indefinite causal order can result in an output state with a temperature not equal to T . We investigate the properties of the refrigeration cycle and show that thermodynamically, the result is compatible with unitary quantum mechanics in the circuit model but could not be achieved classically. We believe that this cycle could be implemented experimentally using tabletop photonics. Our result suggests the development of a new class of thermodynamic resource theories in which operations are allowed to be performed in an Indefinite Causal Order.
Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants 1,2 . Optical waveguides provide a well-controlled platform to investigate effects that relate to different topological phases of matter, providing insight into phenomena such as topological insulators and superconductors by direct simulation of the states that are protected by the topology of the system. Here, we observe a mode associated with a topological defect 3 in the bulk of a 2D photonic material by introducing a vortex distortion to an hexagonal lattice and analogous to graphene 4,5 . These observations are made possible by advances in our experimental methods. We were able to manufacture uniform large twodimensional photonic crystal structures, containing thousands of identical waveguides arranged in two dimensions 21 , and we developed a new method to excite multiples of these waveguides with a well-defined light field. This allows us to probe the detailed spatial features of topological defect modes for the first time. The observed modes lie mid-gap at zero energy and are closely related to Majorana bound states in superconducting vortices 3,6 . This is the first experimental demonstration of a mode that is a solution to the Dirac equation in the presence of a vortex, as proposed by Jackiw and Rossi 7,8 .
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