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Monthly Notices of the Royal Astronomical Society

Experimental progress in controlling and manipulating trapped atomic ions has opened the door for a series of proof-of-principle quantum simulations. This article reviews these experiments, together with the methods and tools that have enabled them, and provides an outlook on future directions in the field.

Quantum simulations with trapped ions

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

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Modern Tests of Lorentz Invariance

Quantum simulation makes use of a well controlled quantum system to make predictions on another quantum system under investigation. Here, we report on quantum simulations using trapped ions to investigate quantum relativistic effects and spin systems.

http://absimage.aps.org/image/MAR12/MWS_MAR12-2011-030011.pdf

We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.

Entanglement between the future and the past in the quantum vacuum.

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

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Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

An intriguing property of the massless quantum vacuum state is that it contains entanglement between both spacelike and timelike separated regions of space-time The implications of timelike entanglement and its connection to standard entanglement, however, are unexplored Here we show that timelike entanglement can be extracted from the massless Minkowski vacuum and converted into standard entanglement ``at a given time'' between two inertial, two-state detectors at the same spatial location: one coupled to the field in the past and the other coupled to the field in the future The procedure used here demonstrates a time correlation as a requirement for extraction; eg, if the past detector was active at a quarter to 12:00, then the future detector must wait to become active at precisely a quarter past 12:00 in order to achieve entanglement

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Extraction of timelike entanglement from the quantum vacuum

We propose a new experimental test bed that uses ions in the collective ground state of a static trap to study the analogue of quantum-field effects in cosmological spacetimes, including the Gibbons–Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analogue gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analogue of an expanding universe using trapped ions, and it enlarges the validity of the ion-trap analogy to a wide range of interesting cases.

https://iopscience.iop.org/article/10.1088/1367-2630/12/9/095019/pdf

Simulating quantum effects of cosmological expansion using a static ion trap

Ng and van Dam have argued that quantum theory and general relativity give a lower bound Δl l1/3lP2/3 on the uncertainty of any distance, where l is the distance to be measured and lP is the Planck length. Their idea is roughly that to minimize the position uncertainty of a freely falling measuring device, one must increase its mass, but if its mass becomes too large it will collapse to form a black hole. Here we show that one can go below the Ng–van Dam bound by attaching the measuring device to a massive elastic rod. Relativistic limitations on the rod's rigidity, together with the constraint that its length exceeds its Schwarzschild radius, imply that zero-point fluctuations of the rod give an uncertainty Δl lP.

https://iopscience.iop.org/article/10.1088/0264-9381/19/14/101/pdf

S. Jay Olson

Papers

Entanglement between the future and the past in the quantum vacuum.

Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

Extraction of timelike entanglement from the quantum vacuum

Simulating quantum effects of cosmological expansion using a static ion trap

Uncertainty in measurements of distance