Driving Alkali Rydberg Transitions with a Phase-Modulated Optical Lattice.

We develop and demonstrate a spectroscopic method for Rydberg-Rydberg transitions using a phase-controlled and -modulated, standing-wave laser field focused on a cloud of cold ^{85}Rb Rydberg atoms. The method is based on the ponderomotive (A^{2}) interaction of the Rydberg electron, which has less-restrictive selection rules than electric-dipole couplings, allowing us to probe both nS_{1/2}→nP_{1/2} and nS_{1/2}→(n+1)S_{1/2} transitions in first order. Without increase in laser power, third- and fourth-order subharmonic drives are employed to access Rydberg transitions in the 40 to 70 GHz frequency range using widely available optical phase modulators in the Ku band (12 to 18 GHz). Measurements agree well with simulations based on the model we develop. The spectra have prominent Doppler-free components with linewidths ≲200 kHz. The method paves the way for optical Doppler-free high-precision spectroscopy of Rydberg-Rydberg transitions and for spatially selective qubit manipulation with µm-scale resolution in Rydberg-based simulators and quantum computers, provided that magic states are chosen and that the atoms are sufficiently cold.

DC electric fields in electrode-free glass vapor cell by photoillumination.

We demonstrate laser induced DC electric fields in an all-glass vapor cell without bulk or thin film electrodes. The spatial field distribution is mapped by Rydberg electromagnetically induced transparency (EIT) spectroscopy. The fields are generated by a photoelectric effect and allow DC electric field tuning of up to 0.8 V/cm within the Rydberg EIT probe region. We explain the measured with a boundary-value electrostatic model. This work may inspire new approaches for DC electric field control in designing miniaturized atomic vapor cell devices. Limitations and other charge effects are also discussed.

Photoassociation of Trilobite Rydberg Molecules via Resonant Spin-Orbit Coupling.

We report on a novel method for the photoassociation of strongly polar trilobite Rydberg molecules. This exotic ultralong-range dimer, consisting of a ground-state atom bound to the Rydberg electron via electron-neutral scattering, inherits its polar character from the admixture of high-angular-momentum electronic orbitals. The absence of low-L character hinders standard photoassociation techniques. Here, we show that for suitable principal quantum numbers the resonant coupling of the orbital motion with the nuclear spin of the perturber, mediated by electron-neutral scattering, hybridizes the trilobite molecular potential with the more conventional S-type molecular state. This provides a general path to associate trilobite molecules with large electric dipole moments, as demonstrated via high-resolution spectroscopy. We find a dipole moment of 135(45) D for the trilobite state. Our results are compared to theoretical predictions based on a Fermi model.

Control of Spatial Correlations between Rydberg Excitations using Rotary Echo.

We manipulate correlations between Rydberg excitations in cold atom samples using a rotary-echo technique in which the phase of the excitation pulse is flipped at a selected time during the pulse. The correlations are due to interactions between the Rydberg atoms. We measure the resulting change in the spatial pair correlation function of the excitations via direct position-sensitive atom imaging. For zero detuning of the lasers from the interaction-free Rydberg-excitation resonance, the pair-correlation value at the most likely nearest-neighbor Rydberg-atom distance is substantially enhanced when the phase is flipped at the middle of the excitation pulse. In this case, the rotary echo eliminates most uncorrelated (unpaired) atoms, leaving an abundance of correlated atom pairs at the end of the sequence. In off-resonant cases, a complementary behavior is observed. We further characterize the effect of the rotary-echo excitation sequence on the excitation-number statistics.

Atom-Pair Kinetics with Strong Electric-Dipole Interactions.

Rydberg-atom ensembles are switched from a weakly to a strongly interacting regime via adiabatic transformation of the atoms from an approximately nonpolar into a highly dipolar quantum state. The resultant electric dipole-dipole forces are probed using a device akin to a field ion microscope. Ion imaging and pair-correlation analysis reveal the kinetics of the interacting atoms. Dumbbell-shaped pair-correlation images demonstrate the anisotropy of the binary dipolar force. The dipolar C_{3} coefficient, derived from the time dependence of the images, agrees with the value calculated from the permanent electric-dipole moment of the atoms. The results indicate many-body dynamics akin to disorder-induced heating in strongly coupled particle systems.

Probe of Rydberg-Atom Transitions via an Amplitude-Modulated Optical Standing Wave with a Ponderomotive Interaction.

In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited peak at the line center. Applicability to precision measurement is discussed.

Photoassociation of long-range nD Rydberg molecules.

We observe long-range homonuclear diatomic nD Rydberg molecules photoassociated out of an ultracold gas of Rb87 atoms for 34≤n≤40. The measured ground-state binding energies of Rb87(nD+5S1/2) molecular states are larger than those of their Rb87(nS+5S1/2) counterparts, which shows the dependence of the molecular bond on the angular momentum of the Rydberg atom. We exhibit the transition of Rb87(nD+5S1/2) molecules from a molecular-binding-dominant regime at low n to a fine-structure-dominant regime at high n [akin to Hund's cases (a) and (c), respectively]. In the analysis, the fine structure of the nD Rydberg atom and the hyperfine structure of the 5S1/2 atom are included.

Bragg scattering and Brownian motion dynamics in optically induced crystals of submicron particles.

A set of four confocal laser beams of 1064-nm wavelength is used to prepare optically induced crystals of submicron particles in aqueous solution. Thousands of polystyrene spheres of about 200 nm in diameter are trapped in three dimensions. Bragg scattering patterns obtained with a probe beam of 532-nm wavelength are in agreement with the calculated lattice structure and its polarization dependence. The decay and rise of the Bragg scattering intensity upon switching the lattice off and on reveal the Brownian motion dynamics of the particles in the periodic optical trapping potential. Experimental results agree well with results from trajectory simulations based on the Langevin equation. The results exhibit the interplay between Brownian motion and deterministic forces in an inhomogeneous (near-)periodic optical trapping potential.

Dependence of Rydberg-atom optical lattices on the angular wave function.

We investigate the dependence of optical-lattice trapping potentials for Rydberg atoms on the angular portion of the atomic wave function. While ground-state atoms are pointlike in relation to an optical-lattice field, Rydberg-atom wave functions extend over a substantial fraction of the lattice period, which leads to a dependence of the lattice trapping potential on the angular portion of the spatial wave function. The angular dependence of the potential is measured using various (j, m(j)) levels of 85Rb Rydberg nD states (50≤n≤65) prepared in a one-dimensional optical lattice (wavelength 1064 nm) and a transverse dc electric field. The measured optical-lattice depths are found to be in agreement with theoretical results.

Imaging spatial correlations of Rydberg excitations in cold atom clouds.

We use direct spatial imaging of cold 85Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function. The results are in qualitative agreement with theoretical predictions [F. Robicheaux and J. V. Hernández, Phys. Rev. A 72, 063403 (2005)]. We determine the blockade radius for states 44D(5/2), 60D(5/2), and 70D(5/2) and investigate the dependence of the correlation behavior on excitation conditions and detection delay. Experimental data hint at the existence of long-range order.

Three-dimensional arrays of submicron particles generated by a four-beam optical lattice.

Using an optical lattice formed by four laser beams, we obtain three-dimensional light-induced crystals of 490-nm-diameter polystyrene spheres in solution. The setup yields face-centered orthorhombic optical crystals of a packing density of about 40%. An alignment procedure is developed in which the crystals are first prepared near a sample wall, and then in the bulk of the sample. A series of tests is performed that demonstrate particle trapping in all three dimensions. For one case, the trapping force is measured, and good agreement with a simple theoretical model is found. Possible applications are discussed.

Trapping Rydberg atoms in an optical lattice.

Rubidium Rydberg atoms are laser excited and subsequently trapped in a one-dimensional optical lattice (wavelength 1064 nm). Efficient trapping is achieved by a lattice inversion immediately after laser excitation using an electro-optic technique. The trapping efficiency is probed via analysis of the trap-induced shift of the two-photon microwave transition 50S→51S. The inversion technique allows us to reach a trapping efficiency of 90%. The dependence of the efficiency on the timing of the lattice inversion and on the trap laser power is studied. The dwell time of 50D(5/2) Rydberg atoms in the lattice is analyzed using lattice-induced photoionization.

State-dependent energy shifts of Rydberg atoms in a ponderomotive optical lattice.

We demonstrate the state dependence of the ponderomotive energy shift of Rydberg atoms in an optical lattice using microwave spectroscopy. Unique to Rydberg atoms, this dependence results from a state-dependent aspect ratio between Rydberg-atom size and lattice period. A semiclassical simulation reproduces all features observed in the microwave spectra and indicates the presence of trapped Rydberg atoms.

Ion imaging in a high-gradient magnetic guide.

We study a photoionization method to detect and image a narrow beam of cold atoms traveling along a high-gradient two-wire magnetic guide that is continuously on. Ions are accelerated in a compact acceleration region, directed through a drift region several centimeters in length, and detected using a position-sensitive ion detector. The potentials of several electrodes can be varied to adjust the imaging properties. Using ion trajectory simulations as well as experiments, we study the passage of the ions through the detection system, the magnification of the detection system, and the time-of-flight characteristics.

Double-resonance spectroscopy of interacting Rydberg-atom systems.

The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.

Rydberg-Rydberg collisions: resonant enhancement of state mixing and penning ionization.

In rubidium Rydberg states, the collision nD_(5/2)+nD_(5/2)-->(n-2)F_(7/2)+(n+2)P_(3/2) is nearly resonant in the vicinity of n=43. As a result, over a short range of n centered around n approximately 43 the Rydberg-Rydberg interaction potential is quite large and turns from repulsive to attractive [Phys. Rev. A 75, 032712 (2007)10.1103/PhysRevA.75.032712]. We use state-selective field ionization to investigate the effect of this resonance on instantaneous excitation of mixed two-particle states, state-mixing collisions, and Penning ionization. We find that these processes depend on the magnitude and sign of the two-particle interaction potential, and thus on n near the resonance. The large magnitude of the observed state mixing provides evidence for many-body effects.

Trapping and evolution dynamics of ultracold two-component plasmas.

We demonstrate the trapping of a strongly magnetized, quasineutral ultracold plasma in a nested Penning trap with a background field of 2.9 T. Electrons remain trapped in this system for several milliseconds. Early in the evolution, the dynamics are driven by a breathing-mode oscillation in the ionic charge distribution, which modulates the electron trap depth. Over longer times scales, the electronic component undergoes cooling. Trap loss resulting from E x B drift is characterized.

Magnetic trapping of long-lived cold Rydberg atoms.

We report on the trapping of long-lived strongly magnetized Rydberg atoms. 85Rb atoms are laser cooled and collected in a superconducting magnetic trap with a strong bias field (2.9 T) and laser excited to Rydberg states. Collisions scatter a small fraction of the Rydberg atoms into long-lived high-angular momentum "guiding-center" Rydberg states, which are magnetically trapped. The Rydberg atomic cloud is examined using a time-delayed, position-sensitive probe. We observe magnetic trapping of these Rydberg atoms for times up to 200 ms. Oscillations of the Rydberg-atom cloud in the trap reveal an average magnetic moment of the trapped Rydberg atoms of approximately -8microB. These results provide guidance for other Rydberg-atom trapping schemes and illuminate a possible route for trapping antihydrogen.

Atom counting statistics in ensembles of interacting Rydberg atoms.

We show that the probability distributions for the number of Rydberg excitations in small ensembles of cold atoms, excited using short (100 ns) laser pulses, can be highly sub-Poissonian. The phenomenon occurs if the atom density and the principal quantum number of the excited Rydberg level are sufficiently high. Our observations are attributed to a blockade of the Rydberg atom excitation.

Landau quantization and time dependence in the ionization of cold, strongly magnetized Rydberg atoms.

The electric-field-ionization and autoionization behavior of cold Rydberg atoms of 85Rb in magnetic fields up to 6 T is investigated. Multiple ionization potentials and field-ionization bands reflecting the Landau energy quantization of the quasifree Rydberg electron are observed. The time-resolved and state-selective field-ionization study provides evidence of mixing and spin flips of the Rydberg electron. Spin-orbit coupling combined with mixing gives rise to a Feshbach-type autoionization of metastable positive-energy atoms.