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 present an experimental demonstration of converting a microwave field to an optical field via frequency mixing in a cloud of cold $^{87}\mathrm{Rb}$ atoms, where the microwave field strongly couples to an electric dipole transition between Rydberg states. We show that the conversion allows the phase information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme and experimental geometry, we achieve a photon-conversion efficiency of $\ensuremath{\sim}0.3%$ at low microwave intensities and a broad conversion bandwidth of more than 4 MHz. Theoretical simulations agree well with the experimental data, and they indicate that near-unit efficiency is possible in future experiments.

Coherent Microwave-to-Optical Conversion via Six-Wave Mixing in Rydberg Atoms.

We propose a new scalable platform for quantum computing (QC) -- an array of optically trapped symmetric-top molecules (STMs) of the alkaline earth monomethoxide (MOCH$_3$) family. Individual STMs form qubits, and the system is readily scalable to 100 to 1000 qubits.STM qubits have desirable features for quantum computing compared to atoms and diatomic molecules. The additional rotational degree of freedom about the symmetric top axis gives rise to closely-spaced opposite parity $K$-doublets that allow full alignment at low electric fields, and the hyperfine structure naturally provides magnetically insensitive states with switchable electric dipole moments. These features lead to much reduced requirements for electric field control, provide minimal sensitivity to environmental perturbations, and allow for 2-qubit interactions that can be switched on at will. We examine in detail the internal structure of STMs relevant to our proposed platform, taking into account the full effective molecular Hamiltonian including hyperfine interactions, and identify useable STM qubit states. We then examine the effects of the electric dipolar interaction in STMs, which not only guide the designing of high-fidelity gates, but also elucidate the nature of dipolar spin-exchange in STMs. Under realistic experimental parameters, we estimate that the proposed QC platform could yield gate errors at the $10^{-3}$ level, approaching that required for fault-tolerant quantum computing.

https://iopscience.iop.org/article/10.1088/1367-2630/ab428d/pdf

A scalable quantum computing platform using symmetric-Top molecules

This thesis describes the first demonstration of a cooperative optical non-linearity based on Rydberg excitation. Whereas in conventional non-linear optics the non-linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole-dipole interactions between light-induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole-dipole interactions are extremely large and long range, enabling an enormous enhancement of the non-linear effect. Consequently, cooperative non-linear optics using Rydberg excitations opens a new era for quantum optics enabling large single photon non-linearity to be accessible in free space for the first time. The thesis describes the theoretical underpinnings of the non- linear effect, the pioneering experimental results and implications for experiments in the single photon regime.

Cooperative Optical Non-Linearity in a Blockaded Rydberg Ensemble

We study the nonequilibrium many-body dynamics of a cold gas of ground-state alkali-metal atoms weakly admixed by Rydberg states with laser light. On a time scale shorter than the lifetime of the dressed states, effective dipole-dipole or van der Waals interactions between atoms can lead to the formation of strongly correlated phases, such as atomic crystals. Using a semiclassical approach, we study the long-time dynamics where decoherence and dissipative processes due to spontaneous emission and blackbody radiation dominate, leading to heating and melting of atomic crystals as well as particle losses. These effects can be substantially mitigated by performing active laser cooling in the presence of atomic dressing.

Driven-dissipative dynamics of a strongly interacting Rydberg gas

We have measured the radiative lifetimes of ns, np and nd Rydberg states of rubidium in the range 28 < n < 45. To enable long-lived states to be measured, our experiment uses slow-moving Rb atoms in a magneto-optical trap (MOT). Two experimental techniques have been adopted to reduce random and systematic errors. First, a narrow-bandwidth pulsed laser is used to excite the target Rydberg state, resulting in minimal shot-to-shot variation in the initial state population. Second, we monitor the target state population as a function of time delay from the laser pulse using a short-duration, millimetre-wave pulse that is resonant with a one- or two-photon transition. We then selectively field ionize the monitor state, and detect the resulting electrons with a micro-channel plate. This signal is an accurate mirror of the target state population, and is uncontaminated by contributions from other states which are populated by black body radiation. Our results are generally consistent with other recent experimental results obtained using a less sensitive method, and are also in excellent agreement with theory.

Radiative lifetime measurements of rubidium Rydberg states

We have measured the radiative lifetimes of ns, np and nd Rydberg states of rubidium in the range 28 ? n ? 45. To enable long-lived states to be measured, our experiment uses slow-moving (~100 ?K) 85Rb atoms in a magneto-optical trap (MOT). Two experimental techniques have been adopted to reduce random and systematic errors. First, a narrow-bandwidth pulsed laser is used to excite the target n? Rydberg state, resulting in minimal shot-to-shot variation in the initial state population. Second, we monitor the target state population as a function of time delay from the laser pulse using a short-duration, millimetre-wave pulse that is resonant with a one- or two-photon transition to a higher energy 'monitor state', n'?'. We then selectively field ionize the monitor state, and detect the resulting electrons with a micro-channel plate. This signal is an accurate mirror of the n? target state population, and is uncontaminated by contributions from other states which are populated by black body radiation. Our results are generally consistent with other recent experimental results obtained using a method which is more prone to systematic error, and are also in excellent agreement with theory.

http://iopscience.iop.org/article/10.1088/0953-4075/43/1/015002/pdf

Drew B. Branden

Papers

Radiative lifetime measurements of rubidium Rydberg states

Radiative lifetime measurements of rubidium Rydberg states