There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.

/pdf/probing-many-body-dynamics-on-a-51-atom-quantum-simulator-2i0okyhlxf.pdf

Probing many-body dynamics on a 51-atom quantum simulator.

Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom–based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.

http://science.sciencemag.org/content/sci/357/6355/995.full.pdf

Quantum simulations with ultracold atoms in optical lattices

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

Quantum simulation of spin Hamiltonians is currently a very active field of research, using different implementations such as trapped ions, superconducting qubits, or ultracold atoms in optical lattices. All of these approaches have their own assets and limitations. Here, we report on a novel platform for quantum simulation of spin systems, using individual atoms trapped in highly-tunable two-dimensional arrays of optical microtraps, that interact via strong, anisotropic interactions when excited to Rydberg $D$-states. We illustrate the versatility of our system by studying the dynamics of an Ising-like spin-$1/2$ system in a transverse field with up to thirty spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. Our data agree well with numerical simulations of the spin-$1/2$ model except at long times, where we observe deviations that we attribute to the multilevel structure of Rydberg $D$-states.

A highly-tunable quantum simulator of spin systems using two-dimensional arrays of single Rydberg atoms

Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. Here, we report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Our results demonstrate the precise control of Rydberg many-body systems and may enable future studies of phase transitions and quantum correlations in interacting quantum magnets.

https://science.sciencemag.org/content/sci/347/6229/1455.full.pdf

Crystallization in Ising quantum magnets

We propose a versatile Loschmidt echo protocol to detect and quantify multiparticle entanglement. It allows us to extract the quantum Fisher information for arbitrary pure states, and finds direct application in quantum metrology. In particular, the protocol applies to states that are generally difficult to characterize, as non-Gaussian states, and states that are not symmetric under particle exchange. We focus on atomic systems, including trapped ions, polar molecules, and Rydberg atoms, where entanglement is generated dynamically via long-range interaction, and show that the protocol is stable against experimental detection errors.

Loschmidt Echo for quantum metrology

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single-particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions, which lead to extreme nonlinearities in laser-coupled atomic ensembles. As a result, multiple excitation of a micrometer-sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called a "superatom," is a valuable resource for quantum information, providing a collective qubit. Here, we report on the preparation of 2 orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub-shot-noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in situ detection of the Rydberg excitations and observe the characteristic square-root scaling of the optical coupling with the number of atoms. Enabled by the full control over the atomic sample, including the motional degrees of freedom, we infer the overlap of the produced many-body state with a W state from the observed Rabi oscillations and deduce the presence of entanglement. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.

Tommaso Macrì

Papers

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

A highly-tunable quantum simulator of spin systems using two-dimensional arrays of single Rydberg atoms

Crystallization in Ising quantum magnets

Loschmidt Echo for quantum metrology

Microscopic Characterization of Scalable Coherent Rydberg Superatoms