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

Adrián Terrones,Carlos Sabín

doi:10.3390/universe7120499

Adrián Terrones, Carlos Sabín

Open Access

https://doi.org/10.3390/universe7120499

Copy DOI

Abstract

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.

Highlights

Black holes are some of the most unique and fascinating objects in the universe, but a full understanding of them remains elusive, mostly due to their extreme nature and the lack of experimental support to guide and test our theoretical progress
From a theoretical point of view, we have not yet found the way to make general relativity (GR) compatible with quantum field theory (QFT) [1]. This might be related to other paradigmatic problems of GR, such as the existence of closed timelike curves (CTCs), which are allowed by GR and would break the principle of causality by allowing time travel
A Josephson junction is, in turn, a device formed by two superconducting leads coupled by a weak link, made by a thin insulating barrier, which allows one to implement the Josephson effect [23] in the superconducting circuit

Summary

Introduction

Black holes are some of the most unique and fascinating objects in the universe, but a full understanding of them remains elusive, mostly due to their extreme nature and the lack of experimental support to guide and test our theoretical progress. Other examples include the Unruh effect [6] or Hawking’s aforementioned chronology protection conjecture All this progress is very good news from a theoretical point of view, as it seems to let us take a step towards quantum gravity. Some proposals for quantum simulations include traversable wormholes [12,13], and searching for a chronology protection mechanism [14] or other exotic spacetimes, such as warp drives, Gödel spacetimes or extreme Kerr black holes [15]. In a dc-SQUID array embedded in an open transmission line, the effective propagation speed of the electromagnetic field can be spatially and temporally modulated through the inductance of the circuit, which depends on the external magnetic flux passing through it, because c = √1. There could be other ways to achieve a particular spatiotemporal dependence of the speed of propagation, even with superconducting setups [26]

Black Holes

Schwarzschild

Summary and Conclusions