Wormhole spacetimes, CTCs and chronology protection in a dc-SQUID array

We present an analog quantum simulator of spacetimes containing traversable wormholes. A suitable spatial dependence in the external bias of a dc-SQUID array mimics the propagation of light in a 1D wormhole background. The impedance of the array places severe limitations on the type of spacetime that we are able to implement. However, we find that wormhole throat radius in the sub-mm range are achievable. We show how to modify this spacetime in order to allow the existence of closed timelike curves. The quantum fluctuations of the phase associated to the finite array impedance might be seen as an analogue of Hawking's chronology protection mechanism.