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

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Quantum information with Rydberg atoms

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Experiments with ultracold quantum gases provide a platform for creating many-body systems that can be well controlled and whose parameters can be tuned over a wide range. These properties put these systems in an ideal position for simulating problems that are out of reach for classical computers. This review surveys key advances in this field and discusses the possibilities offered by this approach to quantum simulation.

/pdf/quantum-simulations-with-ultracold-quantum-gases-46hfprb333.pdf

Quantum simulations with ultracold quantum gases

Atoms can be used as highly sensitive magnetic-field sensors. By exploiting the effects of electric fields on the optical transitions of excited Rydberg states, it is now demonstrated that it is also possible to probe very weak microwave electric fields with atoms.

Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances

In a Rydberg atom, at least one electron is excited into an orbital with a very high principal quantum number that extends the atom's electronic envelope far beyond the nucleus. Based on ideas introduced by Enrico Fermi in 1934, a recent piece of theoretical work predicted that the scattering of such an electron from a second atom in the ground-state could give rise to attractive interactions. This would yield giant molecules with internuclear separations reaching several thousand Bohr radii. The spectroscopic characterization of such ultra-long-range 'Rydberg molecules' is now reported. The molecules, ultracold rubidium dimers, have spectra in good agreement with model predictions. This achievement raises the exciting prospect of realizing other exotic molecular species such as the so-called trilobite molecules in the near future. A Rydberg atom has one electron excited into an orbital with a very high principal quantum number. The scattering of such an electron from a second atom in the ground state gives rise to long-range bonding, yielding giant molecules with internuclear separations reaching several thousand Bohr radii. Using s-state rubidium Rydberg atoms with quantum numbers between 34 and 40, Bendkowsky and colleagues have now spectroscopically characterized such 'Rydberg molecules', and measured their lifetimes and polarizabilities. Rydberg atoms have an electron in a state with a very high principal quantum number, and as a result can exhibit unusually long-range interactions. One example is the bonding of two such atoms by multipole forces to form Rydberg–Rydberg molecules with very large internuclear distances1,2,3. Notably, bonding interactions can also arise from the low-energy scattering of a Rydberg electron with negative scattering length from a ground-state atom4,5. In this case, the scattering-induced attractive interaction binds the ground-state atom to the Rydberg atom at a well-localized position within the Rydberg electron wavefunction and thereby yields giant molecules that can have internuclear separations of several thousand Bohr radii6,7,8. Here we report the spectroscopic characterization of such exotic molecular states formed by rubidium Rydberg atoms that are in the spherically symmetric s state and have principal quantum numbers, n, between 34 and 40. We find that the spectra of the vibrational ground state and of the first excited state of the Rydberg molecule, the rubidium dimer Rb(5s)–Rb(ns), agree well with simple model predictions. The data allow us to extract the s-wave scattering length for scattering between the Rydberg electron and the ground-state atom, Rb(5s), in the low-energy regime (kinetic energy, <100 meV), and to determine the lifetimes and the polarizabilities of the Rydberg molecules. Given our successful characterization of s-wave bound Rydberg states, we anticipate that p-wave bound states9, trimer states10 and bound states involving a Rydberg electron with large angular momentum—so-called trilobite molecules5—will also be realized and directly probed in the near future.

Observation of ultralong-range Rydberg molecules

We report on strong van der Waals blockade in two-photon Rydberg excitation of ultracold magnetically trapped 87Rb atoms. The excitation dynamics was investigated for a large range of densities and laser intensities and shows a full saturation and a strong suppression with respect to single-atom behavior. The observed scaling of the initial increase with density and laser intensity provides evidence for coherent collective excitation. This coherent collective behavior, that was observed for up to several thousand atoms per blockade volume, is generic for all mesoscopic systems which are able to carry only one single quantum of excitation.

https://arxiv.org/pdf/quant-ph/0701120.pdf

Evidence for coherent collective Rydberg excitation in the strong blockade regime.

We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, high-lying Rydberg states. The major part is dedicated to highly excited S-states of rubidium, which feature an isotropic van der Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping. (Some figures may appear in colour only in the online journal)

https://iopscience.iop.org/article/10.1088/0953-4075/45/11/113001/pdf

An experimental and theoretical guide to strongly interacting Rydberg gases

We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent.

/pdf/quantum-critical-behavior-in-strongly-interacting-rydberg-2gzkd2zaj6.pdf

Robert Löw

Papers

Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances

Observation of ultralong-range Rydberg molecules

Evidence for coherent collective Rydberg excitation in the strong blockade regime.

An experimental and theoretical guide to strongly interacting Rydberg gases

Quantum critical behavior in strongly interacting Rydberg gases.