Towards Quantum Simulation of Black Holes in a dc-SQUID Array

We propose quantum simulations of 1 + 1D radial sections of different black hole spacetimes (Schwarzschild, Reissner–Nordstrøm, Kerr and Kerr–Newman), by means of a dc-SQUID array embedded on an open transmission line. This was achieved by reproducing the spatiotemporal dependence of 1 + 1D sections of the spacetime metric with the propagation speed of the electromagnetic field in the simulator, which can be modulated by an external magnetic flux. We show that the generation of event horizons—and therefore Hawking radiation—in the simulator could be achieved for non-rotating black holes, although we discuss limitations related to fluctuations of the quantum phase. In the case of rotating black holes, it seems that the simulation of ergospheres is beyond reach.

Entangling Superconducting Qubits through an Analogue Wormhole

We propose an experimental setup to test the effect of curved spacetime upon the extraction of entanglement from the quantum field vacuum to a pair of two-level systems. We consider two superconducting qubits coupled to a dc-SQUID array embedded into an open microwave transmission line, where an external bias can emulate a spacetime containing a traversable wormhole. We find that the amount of vacuum entanglement that can be extracted by the qubits depends on the wormhole parameters. At some distances qubits which would be in a separable state in flat spacetime would become entangled due to the analogue wormhole background.

Quantum detection of wormholes

We show how to use quantum metrology to detect a wormhole. A coherent state of the electromagnetic field experiences a phase shift with a slight dependence on the throat radius of a possible distant wormhole. We show that this tiny correction is, in principle, detectable by homodyne measurements after long propagation lengths for a wide range of throat radii and distances to the wormhole, even if the detection takes place very far away from the throat, where the spacetime is very close to a flat geometry. We use realistic parameters from state-of-the-art long-baseline laser interferometry, both Earth-based and space-borne. The scheme is, in principle, robust to optical losses and initial mixedness.

Mapping curved spacetimes into Dirac spinors

We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.