Session H3: Rydberg Atoms and Ultracold Plasmas

Ponderomotive spectroscopy: Driving Rydberg transitions using harmonics and magic wavelengths of an intensity-modulated optical lattice

We describe recent developments in a novel spectroscopic method that couples Rydberg states using an intensity-modulated optical lattice. The method is fundamentally different from traditional microwave spectroscopy: it engages the $\mathbf{A} \cdot \mathbf{A}$ (ponderomotive) term rather than the $\mathbf{A} \cdot \mathbf{p}$ term of the atom-field interaction Hamiltonian, allowing us to drive microwave transitions between Rydberg states with optical spatial resolution, free from electric dipole selection rules.\footnote{KR Moore, SE Anderson, G Raithel, Nat Comm, 6:6090 (2015)} Experimentally, cold Rb Rydberg atoms are confined in a 1064nm optical lattice.\footnote{SE Anderson, KC Younge, G Raithel, PRL 107:263001 (2011)} Transitions are driven by modulating the lattice intensity using a tunable electro-optic fiber modulator. Recently we have driven dipole-forbidden transitions in third and fifth order, at frequencies up to 94 GHz, using temporal harmonics in the intensity-modulated lattice. We also demonstrate, for two separate transitions, the novel use of a magic wavelength condition in ponderomotive spectroscopy. We discuss experimental results and propose applications of this method to a precision measurement of the Rydberg constant using circular-state Rydberg atoms.   

Homodyne Microwave Electric Field Measurements Using Cesium Rydberg Atoms in Vapor Cells

Probe laser noise is one of the main factors limiting the sensitivity of microwave electric field measurements that use Rydberg atoms in vapor cells. We apply a homodyne detection technique using a Mach-Zehnder interferometer to achieve a new sensitivity limit for the measurement of microwave electric fields, $\sim 3-5 \mu V cm^{-1} \sqrt{Hz}^{-1}$. The new sensitivity is almost one order of magnitude better than the previous results presented in Ref. [Nat. Phys. 8, 819 (2012)]. We also report on the homogeneous dephasing effects caused by transit time broadening, collision broadening, and the lifetime of Rydberg atoms which we can now directly observe. We show that these dephasing effects are the fundamental limiting factors that determine the shot noise limit.   

Trap losses induced by Rydberg dressing of cold atomic gases

The near-resonant dressing of ultracold strontium gases and BECs contained in an optical dipole trap (ODT) with the $n=30\;^3S_1$ Rydberg state is investigated as a function of the effective two-photon Rabi frequency, detuning, and dressing time. The measurements demonstrate that, even when well detuned from resonance, such dressing can lead to a rapid decrease in the ground-state atom population in the ODT. This decrease is attributed to Rydberg atom excitation which can lead to direct escape from the trap and/or population of very-long-lived metastable states. The large Rydberg atom production rates are explained using a reaction model in which the initial excitation of a Rydberg atom triggers the excitation of neighboring atoms leading to rapid avalanche-like growth in the Rydberg population.   

Two-photon bound states in Rydberg gases

We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency. Here the photons form strongly interacting massive particles, termed Rydberg polaritons. Recent experiments have realized strong interactions between Rydberg polaritons and shown photon blockade [1] as well as pronounced bunching [2] under off-resonant coupling conditions. We derive an effective Hamiltonian for Rydberg polaritons in one spatial dimension for off-resonant coupling. We show that in addition to repulsive polaritons bound pair-states of photons exist. For strong interactions, quantified in terms of optical depth per blockade distance, these states are deeply bound and cannot be prepared under typical experimental conditions. For small optical depth per blockade bound pair-states can, however, be excited near the threshold of the scattering continuum. Using numerical wave-function simulations we analyze the dynamics of the formation of bound states in a pulsed experiment and analyze their properties and time-evolution inside the medium. Furthermore we discuss the interaction between Rydberg polaritons and bound pairs and the pair-pair interaction.\\[4pt] [1] Peyronel et al. Nature 488, 57 (2012)\\[0pt] [2] Firstenberg et al. Nature 502, 71 (2013)   

Lineshapes of Dipole-Dipole Resonances in a Cold Rydberg Gas

We have examined the lineshapes associated with Stark tuned, dipole-dipole resonances involving Rydberg atoms in a cold gas. Rb atoms in a MOT are laser excited from the 5$p$ level to 32$p_{3/2}$ in the presence of a weak electric field. A fast rising electric field pulse Stark tunes the total energy of two 32$p$ atom pairs so it is (nearly) degenerate with that of the 32$s_{1/2}$+33$s_{1/2}$ states. Because of the dipole-dipole coupling, atom pairs separated by a distance $R$, develop 32$s_{1/2}$+33$s_{1/2}$ character. The maximum probability for finding atoms in $s$-states depends on the detuning from degeneracy and on the dipole-dipole coupling. We obtain the ``resonance'' lineshape by measuring, via state-selective field ionization, the $s$-state population as a function of the tuning field. The resonance width decreases with density due to $R^{-3}$ dependence of the dipole-dipole coupling. In principle, the lineshape provides information about the distribution of Rydberg atom spacings in the sample. For equally spaced atoms, the lineshape should be Lorentzian while for a random nearest neighbor distribution it appears as a cusp. At low densities nearly Gaussian lineshapes are observed with widths that are too large to be the result of inhomogeneous electric or magnetic fields.   

Spectroscopic signatures of dressed Rydberg-Rydberg interactions in Sr

Ultracold Rydberg-dressed atoms exhibit strong, long-range interactions that can potentially create exotic phases of matter and entangled states that are useful in quantum computation and metrology. Rydberg-dressed atoms are obtained by off-resonantly admixing a Rydberg state $\vert R\rangle$ into a long-lived electronic state, often the ground state. As a tool to observe dressed Rydberg interactions, we theoretically consider a spectroscopic method that relies on strontium's unique long-lived ($\approx 23\mu$s) electronic excited state ${}^3$P${}_1$. Specifically, we consider an effective two level system: the electronic ground state $|G\rangle$ and the Rydberg dressed state $\vert D\rangle=\vert{}^3$P${}_1\rangle+\epsilon \vert R\rangle$ with $\epsilon\ll 1$. Using spin language to describe this two level system, our proposed Ramsey scheme rotates the spins by angle $\theta$, allows the atoms to interact for a time $t$, and then measures the final spin vector. Our calculation is exact and includes experimental complications, such as dissipation and pulse timing errors. Excitingly, the dependence of the spin vector on time and $\theta$ can be used to experimentally measure the strength and power law dependence of the dressed Rydberg atom interaction.   

Self-Diffusion and Non-Markovian Dynamics in Strongly Coupled Ultracold Neutral Plasmas

Collisional processes in weakly coupled plasmas are well-described by the Landau-Spitzer formalism. Classical plasma theory breaks down, however, in strongly coupled systems because of the non-perturbative nature of particle interactions, and improving our understanding of this regime is an important fundamental challenge. We present experimental measurements of the self-diffusion constant and observation of non-Markovian equilibration for strongly coupled ions in an ultracold neutral plasma (UCNP) created by photoionizing strontium atoms in a magneto-optical trap. Our diagnostic uses optical pumping to create ``spin-tagged'' subpopulations of ions having skewed velocity distributions that then relax back to equilibrium. A Green-Kubo relation is used to extract the self-diffusion constant from the equilibration curves. With improved time resolution (down to 30 ns), we have explored the early time dynamics of these skewed ion distributions within 100 ns after the optical pumping, where molecular dynamics simulations predict non-Markovian deviations from the exponential velocity damping expected for weakly coupled systems. At longer times, we observe oscillations of the average velocity during the relaxation, which indicate coupling of single-particle motion to collective modes.   

Kinetic Energy Oscillations during Disorder Induced Heating in an Ultracold Plasma

Ultracold neutral plasmas of strontium are generated by photoionizing laser-cooled atoms at temperature $T_{MOT}\approx10$\,mK and density $n\approx10^{16}$m$^{-3}$ in a magneto-optical trap (MOT). After photoionization, the ions heat to $\sim1$\,K by a mechanism known as Disorder Induced Heating (DIH). During DIH kinetic energy oscillations (KEO) occur at a frequency $\sim2\omega_{pi}$, where $\omega_{pi}$ is the plasma frequency, indicating coupling to collective modes of the plasma. Electron screening also comes into play by changing the interaction from a Coulomb to a Yukawa interaction. Although DIH has been previously studied, improved measurements combined with molecular dynamics (MD) simulations allow us to probe new aspects. We demonstrate a measurement of the damping of the KEO due to electron screening which agrees with the MD simulations. We show that the MD simulations can be used to fit experimental DIH curves for plasma density $n$, resulting in very accurate density measurements. Finally, we discuss how ion temperature measurements are affected by the non-thermal distribution of the ions during the early stages of DIH.   

Heating and cooling of an ultra-cold neutral plasma by Rydberg atoms

We have experimentally demonstrated a mechanism for controlling the expansion rate of an ultra-cold neutral plasma (UNP) so that it is different from the value determined by the photo-ionizing laser frequency. We achieved this by adding Rydberg atoms to the UNP 10 - 20 ns after its creation. Specifically, we added $nd_{5/2}$ state atoms with $n = 24 - 60$ to UNPs with initial electron temperatures, $T_{e,0}$, in the range 10 - 250 K. The evidence is both indirect, from the change in the electron evaporation rate from the UNP, and direct, from the change in the asymptotic plasma expansion velocity, $v_0$, measured using the time-of-flight spectrum of Rb$^+$ ions. In addition, the results strongly support the existence of a ``bottleneck'' in the state distribution of Rydberg atoms formed by three body recombination (TBR) where the binding energy of the bottleneck state is $E_b \approx 2.3 \times k_B T_{e,0}$. Finally, we show that the amount of heating or cooling is linear in the number density of Rydberg atoms added to the UNP for small Rydberg densities, but saturates at higher densities to a value that is determined solely by the Rydberg binding energy. These results are in good general agreement with Monte-Carlo calculations.   

Electron Ion Collision Rates in Ultracold Plasmas

By using applying a short electric field pulse to an ultracold plasma, it is possible to induce a collective oscillation of the electrons. This oscillation will damp after the application of the electric field pulse. We have found that under certain achievable experimental conditions, this damping can be dominated by the electron-ion collision rate. We have measured this damping rate experimentally under these conditions and thus can compare it to theoretical predictions. We will present our measurement technique and results. In addition, we will discuss extensions of this technique to measurements of electron temperature, to investigating strong-coupling physics in the electron component of an ultracold plasma, and to measuring the electron-ion collision rate when the electrons are highly magnetized.