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

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

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist

Quantum sensing

It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

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

Atom-based measurements of length, time, gravity, inertial forces and electromagnetic fields are receiving increasing attention. Atoms possess properties that suggest clear advantages as self calibrating platforms for measurements of these quantities. In this review, we describe work on a new method for measuring radio frequency (RF) electric fields based on quantum interference using either Cs or Rb atoms contained in a dielectric vapor cell. Using a bright resonance prepared within an electromagnetically induced transparency window it is possible to achieve high sensitivities, <1 μV cm−1 Hz−1/2, and detect small RF electric fields μV cm−1 with a modest setup. Some of the limitations of the sensitivity are addressed in the review. The method can be used to image RF electric fields and can be adapted to measure the vector electric field amplitude. Extensions of Rydberg atom-based electrometry for frequencies up to the terahertz regime are described.

https://iopscience.iop.org/article/10.1088/0953-4075/48/20/202001/pdf

Atom based RF electric field sensing

It is clearly important to pursue atomic standards for quantities like electromagnetic fields, time, length, and gravity. We have recently shown using Rydberg states that Rb atoms in a vapor cell can serve as a practical, compact standard for microwave electric field strength. Here we demonstrate for the first time that Rb atoms excited in a vapor cell can also be used for vector microwave electrometry by using Rydberg-atom electromagnetically induced transparency. We describe the measurements necessary to obtain an arbitrary microwave electric field polarization at a resolution of 0.5°. We compare the experiments to theory and find them to be in excellent agreement.

Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell.

The coherent control of mesoscopic ensembles of atoms and Rydberg atom blockade are the basis for proposed quantum devices such as integrable gates and single-photon sources. To date, experimental progress has been limited to complex experimental set-ups that use ultracold atoms. Here, we show that coherence times of ∼100 ns are achievable with coherent Rydberg atom spectroscopy in micrometre-sized thermal vapour cells. We investigate states with principle quantum numbers between 30 and 50. Our results demonstrate that microcells with a size on the order of the blockade radius (∼2 µm), at temperatures of 100–300 °C, are robust and promising candidates for investigating low-dimensional strongly interacting Rydberg gases, constructing quantum gates and building single-photon sources. Rydberg blockade — the suppression of excitation of more than one Rydberg atom within a blockade volume — has so far been realized using ultracold atoms. Now, scientists show that coherence times of >100 ns are achievable with coherent Rydberg atomic spectroscopy in micrometre-sized thermal vapour cells, making them good candidates for investigating low-dimensional strongly interacting Rydberg gases, constructing quantum gates and building single-photon sources.

Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells

Tailored quantum states of light can be created via a transfer of collective quantum states of matter to light modes. Such collective quantum states emerge in interacting many-body systems if thermal fluctuations are overcome by sufficient interaction strengths. Therefore, ultracold temperatures or strong confinement are typically required. We show that the exaggerated interactions between Rydberg atoms allow for collective quantum states even above room temperature. The emerging Rydberg interactions lead both to suppression of multiple Rydberg state excitations and destructive interference due to polariton dephasing. We experimentally implemented a four-wave mixing scheme to demonstrate an on-demand single-photon source. The combination of glass cell technology, identical atoms, and operation around room temperature promises scalability and integrability. This approach has the potential for various applications in quantum information processing and communication.

https://science.sciencemag.org/content/sci/362/6413/446.full.pdf

Harald Kübler

Papers

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

Atom based RF electric field sensing

Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell.

Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells

A room-temperature single-photon source based on strongly interacting Rydberg atoms