Quantum simulation of Rindler transformations

We show how to implement a Rindler transformation of coordinates with an embedded quantum simulator. A suitable mapping allows to realise the unphysical operation in the simulated dynamics by implementing a quantum gate on an enlarged quantum system. This enhances the versatility of embedded quantum simulators by extending the possible in-situ changes of reference frames to the non-inertial realm.Comment: 8 pages, 1 figure. v2: minor changes, published versio

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.Comment: 5 pages, 4 figures. v2: minor changes, published versio

Quantum simulation of traversable wormhole spacetimes 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.Comment: 5 pages, 4 figures. v2: title changed. Minor changes. Published versio

On relativistic particle creation in Bose-Einstein condensates

We show that particle creation of Bogoliubov modes in a Bose-Einstein condensate due to the accelerated motion of the trap is a genuinely relativistic effect. To this end we show that Bogoliubov modes can be described by a time rescaling of the Minkowski metric. A consequence of this is that Rindler transformations are perceived by the phonons as generalised Rindler transformations where the speed of light is replaced by the speed of sound, enhancing particle creation at small velocities. Since the non-relativistic limit of a Rindler transformation is just a Galilean transformation entailing no length contraction or time dilation, we show that the effect vanishes in the non-relativistic limit.Comment: This work provides further theoretical support to the results in Sci. Rep. 4, 4996 (2014), http://www.nature.com/srep/2014/140521/srep04996/full/srep04996.htm

Quantum estimation via parametric amplification in circuit QED arrays

We propose a scheme for quantum estimation by means of parametric amplification in circuit Quantum Electrodynamics. The modulation of a SQUID interrupting a superconducting waveguide transforms an initial thermal two-mode squeezed state in such a way that the new state is sensitive to the features of the parametric amplifier. We find the optimal initial parameters which maximize the Quantum Fisher Information. In order to achieve a large number of independent measurements we propose to use an array of non-interacting resonators. We show that the combination of both large QFI and large number of measurements enables -in principle- the use of this setup for Quantum Metrology applications.Comment: 6 pages, 7 figures v2:cosmetic changes, published versio

The quantum Rabi model in a superfluid Bose-Einstein condensate

We propose a quantum simulation of the quantum Rabi model in an atomic quantum dot, which is a single atom in a tight optical trap coupled to the quasiparticle modes of a superfluid Bose-Einstein condensate. This widely tunable setup allows to simulate the ultrastrong coupling regime of light-matter interaction in a system which enjoys an amenable characteristic timescale, paving the way for an experimental analysis of the transition between the Jaynes-Cummings and the quantum Rabi dynamics using cold-atom systems. Our scheme can be naturally extended to simulate multi-qubit quantum Rabi models. In particular, we discuss the appearance of effective two-qubit interactions due to phononic exchange, among other features.Comment: Improved version and references adde

Dirac equation in exotic spacetimes

We find solutions of the Dirac equation in curved spacetime. In particular, we consider 1+1 dimensional sections of several exotic metrics: the Alcubierre metric, which describes a scenario that allows faster-than-light (FTL) velocity; the G\"odel metric, that describes a universe containing closed timelike curves (CTC); and the Kerr metric, which corresponds to the spacetime of a rotating black hole. Moreover, we also show that the techniques that we use in these cases can be extended to nonstatic metrics.Comment: 7 pages, 3 figure

Closed timelike curves and chronology protection in quantum and classical simulators

In principe, General Relativity seems to allow the existence of closed timelike curves (CTC). However, when quantum effects are considered, it is likely that their existence is prevented by some kind of chronological protection mechanism, as Hawking conjectured. Confirming or refuting the conjecture would require a full quantum theory of gravity. Meanwhile, the use of simulations could shed some light on this issue. We propose simulations of CTCs in a quantum system as well as in a classical one. In the quantum simulation, some restrictions appear that are not present in the classical setup, which could be interpreted as an analogue of a chronology protection mechanism.Comment: 6 pages, 4 figures. v2: published versio

Parameter estimation of wormholes beyond the Heisenberg limit

We propose to exploit the quantum properties of nonlinear media to estimate the parameters of massless wormholes. The spacetime curvature produces a change in length with respect to Minkowski spacetime that can be estimated in principle with an interferometer. We use quantum metrology techniques to show that the sensitivity is improved with nonlinear media and propose a nonlinear Mach-Zehnder interferometer to estimate the parameters of massless wormholes that scales beyond the Heisenberg limit