Cold Rydberg Atoms Research Articles

Electric-field sensing near the surface microstructure of an atom chip using cold Rydberg atoms

The electric fields near the heterogeneous metal/dielectric surface of an atom chip were measured using cold atoms. The atomic sensitivity to electric fields was enhanced by exciting the atoms to Rydberg states that are 10^8 times more polarizable than the ground state. We attribute the measured fields to charging of the insulators between the atom chip wires. Surprisingly, it is observed that these fields may be dramatically lowered with appropriate voltage biasing, suggesting configurations for the future development of hybrid quantum systems.

Observation of a Resonant Four-Body Interaction in Cold Cesium Rydberg Atoms

Cold Rydberg atoms subject to long-range dipole-dipole interactions represent a particularly interesting system for exploring few-body interactions and probing the transition from 2-body physics to the many-body regime. In this work we report the direct observation of a resonant 4-body Rydberg interaction. We exploit the occurrence of an accidental quasicoincidence of a 2-body and a 4-body resonant Stark-tuned Förster process in cesium to observe a resonant energy transfer requiring the simultaneous interaction of at least four neighboring atoms. These results are relevant for the implementation of quantum gates with Rydberg atoms and for further studies of many-body physics.

Probing Electronic Coherence in a Gas of Dipole-Dipole Coupled Rydberg Atoms

We demonstrate a novel time-domain method to probe electronic coherence in ensembles of cold Rydberg atoms coupled via nearly resonant dipole-dipole interactions. Short laser pulses create coherent superpositions of few-electron eigenstates which evolve under the influence of pulsed electric fields. The pulses steer the dynamics, enhancing the probability for finding atoms in np, rather than initially excited ns states. The enhancement reflects the underlying electronic coherence which persists for >10 μs, 2orders of magnitude longer than previously measured dephasing times in the same system. Simulations suggest that atom motion is responsible for the eventual decoherence.

Effect of photoions on the line shape of the Förster resonance lines and microwave transitions in cold rubidium Rydberg atoms

Experiments on the spectroscopy of the F\"orster resonance Rb(37P)+Rb(37P) -> Rb(37S)+Rb(38S) and microwave transitions nP -> n'S, n'D between Rydberg states of cold Rb atoms in a magneto-optical trap have been performed. Under ordinary conditions, all spectra exhibited a 2-3 MHz line width independently of the interaction time of atoms with each other or with microwave radiation, although the ultimate resonance width should be defined by the inverse interaction time. Analysis of the experimental conditions has shown that the main source of the line broadening was the inhomogeneous electric field of cold photoions appeared at the excitation of initial Rydberg nP states by broadband pulsed laser radiation. Using an additional pulse of the electric field, which rapidly removed the photoions after the laser pulse, lead to a substantial narrowing of the microwave and F\"orster resonances. An analysis of various sources of the line broadening in cold Rydberg atoms has been conducted.

Optimal networks for excitonic energy transport

We investigate coherent and incoherent excitation transfer in a random network with dipole–dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms. For this purpose, we introduce and compare two different measures (the maximum output probability and the average transfer time) for the efficiency of transport from the input to the output site. We especially focus on optimal configurations which maximize the transfer efficiency and the impact of dephasing noise on the transport dynamics. For most configurations of the random network, the transfer efficiency increases when adding noise, giving rise to essentially classical transport. These noise-assisted configurations are, however, systematically less efficient than the optimal configurations. The latter reach their highest efficiency for purely coherent dynamics, i.e. in the absence of noise.

Dislocation-mediated melting of one-dimensional Rydberg crystals

We consider cold Rydberg atoms in a one-dimensional optical lattice in the Mott regime with a single atom per site at zero temperature. An external laser drive with Rabi frequency $\ensuremath{\Omega}$ and laser detuning $\ensuremath{\Delta}$ creates Rydberg excitations whose dynamics is governed by an effective spin-chain model with (quasi) long-range interactions. This system possesses intrinsically a large degree of frustration resulting in a ground-state phase diagram in the $(\ensuremath{\Delta},\ensuremath{\Omega})$ plane with a rich topology. As a function of $\ensuremath{\Delta}$, the Rydberg blockade effect gives rise to a series of crystalline phases commensurate with the optical lattice that form a so-called devil's staircase. The Rabi frequency $\ensuremath{\Omega}$, on the other hand, creates quantum fluctuations that eventually lead to a quantum melting of the crystalline states. Upon increasing $\ensuremath{\Omega}$, we find that generically a commensurate-incommensurate transition to a floating Rydberg crystal that supports gapless phonon excitations occurs first. For even larger $\ensuremath{\Omega}$, dislocations within the floating Rydberg crystal start to proliferate and a second, Kosterlitz-Thouless-Nelson-Halperin-Young dislocation-mediated melting transition finally destroys the crystalline arrangement of Rydberg excitations. This latter melting transition is generic for one-dimensional Rydberg crystals and persists even in the absence of an optical lattice. The floating phase and the concomitant transitions can, in principle, be detected by Bragg scattering of light.

Dipole-dipole broadening of Rbns−npmicrowave transitions

The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$, a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

Electromagnetically induced transparency in a five-levelΛsystem dominated by two-photon resonant transitions

We study the steady optical response of a five-level atomic system in the parametric region where resonant two-photon transitions are much stronger than far-detuned single-photon transitions. We find that the concurrent absorption of two weak probe fields can be well suppressed in a narrow spectral region to attain electromagnetically induced transparency (EIT) via quantum destructive interference between different two-photon transition pathways. To gain a deeper insight into relevant physics, we adiabatically reduce this five-level system with trivial single-photon transitions into a three-level system with vanishing single-photon transitions by deriving an effective Hamiltonian. The two systems have almost the same two-photon absorption spectra exhibiting typical EIT features but are a little different in fine details. This means that most characteristics of two-photon quantum destructive interference are reserved after the adiabatic elimination approximation. In addition, we verify by numerical calculations that the two-photon EIT spectra are insensitive to the dipole-dipole interaction of cold Rydberg atoms when the uppermost level has a high principle quantum number.

Stark-tuned Förster resonance and dipole blockade for two to five cold Rydberg atoms: Monte Carlo simulations for various spatial configurations

Results of numerical Monte Carlo simulations for the Stark-tuned F\"orster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a F\"orster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the F\"orster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.

Direct evidence of three-body interactions in a coldRb85Rydberg gas

Cold Rydberg atoms trapped in a magneto-optical trap (MOT) are not isolated and they interact through dipole-dipole and multipole-multipole interactions. First-order dipole-dipole interactions and van der Waals interactions between two atoms have been intensively studied. However, the facts that the first-order dipole-dipole interactions and van der Waals interactions show the same size of broadening [A. Reinhard, K. C. Younge, T. C. Liebisch, B. Knuffman, P. R. Berman, and G. Raithel, Phys. Rev. Lett. 100, 233201 (2008)] and there are transitions between two dimer states [S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Cote, E. E. Eyler, and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003); K. R. Overstreet, Arne Schwettmann, Jonathan Tallant, and James P. Shaffer, Phys. Rev. A 76, 011403(R) (2007)] cannot be explained by the two-atom picture. The purpose of this article is to show the few-body nature of a dense cold Rydberg gas by studying the molecular-state microwave spectra. Specifically, three-body energy levels have been calculated. Moreover, the transition from three-body energy levels to two-body coupled molecular energy levels and to isolated atomic energy levels as a function of the internuclear spacing ismore » studied. Finally, single-body, two-body, and three-body interaction regions are estimated according to the experimental data. The results reported here provides useful information for plasma formation, further cooling, and superfluid formation.« less

Manipulation of quantum state transfer in cold Rydberg atom collisions

We investigate the role of the dc Stark effect in multilevel pairwise interactions between cold Rydberg atoms. We have observed the decay of nD+nD quasi-molecules by detecting the products in the (n+2)P state after pulsed excitation for 29⩽n⩽41. The decay rate can be manipulated with a dc electric field and requires a consideration of the multilevel nature of the process to explain the observations. The time dependence of the (n+2)P signal is found to support a time-dependent picture of the dynamics.

Erratum: Thermal Casimir-Polder shifts in Rydberg atoms near metallic surfaces [Phys. Rev. A82, 010901(R) (2010)

The present thesis focuses on several topics within three separate but related branches of the overall field of dispersion forces. The three branches are: temperature corrections to the Casimir force between real materials (Part 1), explicit calculation of Casimir energy in wedge geometries (Part 2), and Casimir-Polder forces on particles out of thermal equilibrium (Part 3). Part 1 deals primarily with analysis of a previously purported thermodynamic inconsistency in the Casimir-Lifshitz free energy of the interaction of two plane mirrors – violation of the third law of thermodynamics – when the latter’s dielectric response is described with dissipative models. It is shown analytically and numerically that the Casimir entropy of the interaction between two metallic mirrors described by the Drude model does tend to zero at zero temperature, provided electronic relaxation does not vanish. The leading order terms at low temperature are found. A similar calculation is carried out for the interaction of semiconductors with small but non-zero DC conductivity. In a generalisation, it is shown that a violation of the third law can only occur for permittivities whose low-frequency behaviour is temperature dependent near zero temperature. A calculation using path integral methods shows that the low temperature behaviour of the interaction of fluctuating Foucault currents in two mirrors of Drude metal is identical to that of the full Casimir-Lifshitz free energy, reasserting a previous finding by Intravaia and Henkel that such fluctuating bulk currents are the physical reason for the anomalous entropy behaviour. In a related effort, an analysis of the frequency dependence of the Casimir force by Ford is generalised to imperfectly reflecting mirrors. A paradox is pointed out, in that the effects of a perturbation of the reflecting properties of the mirrors in a finite frequency window can be calculated in two ways giving different results. It is concluded that optimistic conclusions reached by Ford based on one of these methods, which seems to allow radically changing and tailoring the Casimir force with engineered materials, can not be realised. Part 2 presents several explicit calculations of the Casimir energy of different wedge and cylinder geometries. The Casimir energy of a perfectly conducting wedge intercut by a circularly cylindrical arc, either perfectly conducting or (magneto)dielectric, is calculated. The energy is found to include a singular and non-regularisable term due to the corners where the arc meets the wedge, whereas the finite part is an immediate generalisation of the previously known results for a circular cylinder. The energy of a magnetodielectric wedge obeying a criterion of isorefractivity (spatially uniform speed of light) superimposed coaxially on a perfectly conducting cylindrical shell is calculated. This is the first expression for the energy of a wedge which is not perfectly reflecting. Finally, the energy of the perfectly conducting wedge and arc (and, as a special case, cylinder) is extended to the case of non-zero temperatures. After a regularisation procedure making use of the Chowla-Selberg formula an analytical expression for the temperature-dependent energy at all temperatures is derived, and showed to coincide with previously calculated high-temperature asymptotics by Bordag, Nesterenko and Pirozhenko. Part 3 considers numerical and analytical studies of the Casimir-Polder forces acting on particles prepared in a given eigenstate (or superposition of such) in an environment which is otherwise at thermal equilibrium. We first consider cold polar molecules outside a metallic halfspace. It is found that the force in the near-zone (non-retarded regime) is much weaker than what would result from a naive perturbative calculation, and that in the far-zone (retarded regime) the force becomes spatially oscillatory. It is demonstrated how these spatial oscillations may be enhanced in a resonating planar cavity, although for polar molecules the resulting amplitude is still insufficient for observation. A cylindrical cavity, however, can achieve a better enhancement factor. The Casimir-Polder forces on Rydberg atoms near a surface are calculated; because of the very large transition dipole moments of Rydberg transitions, the force is enormous on an atomic scale. We show that the oscillating force on Rydberg atoms can be enhanced into the observable regime by use of a fine-tuned cylindrical cavity. A particle in an eigenstate which is in the non-retarded regime with respect to all its dominant transitions is shown to feel a Casimir-Polder force which is virtually independent of temperature from zero to room temperature and beyond. Both for cold polar molecules and Rydberg atoms, the temperature-independent regime extends to a few and hundreds of micrometers, respectively, and includes the separations generally accessed in experiments

Dipole blockade in a cold Rydberg atomic sample [Invited

We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.

Observation of the Stark-Tuned Förster Resonance between Two Rydberg Atoms

Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Förster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations.

Quantum tunneling and reflection of a molecule with a single bound state

In this article, we present the results of studies on the quantum mechanical tunneling and reflection of a diatomic, homonuclear molecule with a single bound state incident upon a potential barrier. In the first study, we investigate the tunneling of a molecule using a time-dependent formulation. The molecular wave function is modeled as a Gaussian wave packet, and its propagation is calculated numerically using Crank-Nicholson integration. It is found that a molecule may transition between the bound state and an unbound state numerous times during the process of reflection from or transmission past the barrier. It is also found that, in addition to reflecting and transmitting, the molecule may also temporarily straddle the potential barrier in an unbound state. In the second study, we consider the case of a molecule incident in the bound state upon a step potential with energy less than the step. We show that in the limit where the binding energy ${e}_{0}$ approaches zero and the step potential ${V}_{0}$ goes to infinity, the molecule cannot remain in a bound state if the center of mass gets closer to the step than an arbitrarily large distance ${x}_{0}$ which increases as the magnitude of ${e}_{0}$ decreases, as ${V}_{0}$ increases, or both. We also show that, for ${e}_{0}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ and ${V}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, if the molecule is incident in the bound state, it is reflected in the bound state with probability equal to unity, when the center of mass reaches the reflection distance ${x}_{0}$. We verify that the unbound states exhibit the expected physical behavior. We discuss some surprising results. Connections between our results and investigations done in cold atoms, excitons, Cooper pairs, and Rydberg atoms are discussed.

Observation of Stückelberg oscillations in dipole-dipole interactions

We have observed Stueckelberg oscillations in the dipole-dipole interaction between Rydberg atoms with an externally applied radio-frequency field. The oscillating RF field brings the interaction between cold Rydberg atoms in two separated volumes into resonance. We observe multi-photon transitions when varying the amplitude of the RF-field and the static electric field offset. The angular momentum states we use show a quadratic Stark shift, which leads to a fundamentally different behavior than linearly shifting states. Both cases are studied theoretically using the Floquet approach and are compared. The amplitude of the sidebands, related to the interaction strength, is given by the Bessel function in the linearly shifting case and by the generalized Bessel function in the quadratically shifting case. The oscillatory behavior of both functions corresponds to Stueckelberg oscillations, an interference effect described by the semi-classical Landau-Zener-Stueckelberg model. The measurements prove coherent dipole-dipole interaction during at least 0.6 micro-seconds.

Observation of molecular resonance during the excitation of a cold Rydberg atom pairs

We present experimental results that show a significant yield of nP atoms after excitation of nS Rb Rydberg atoms from a MOT using a pulsed dye laser, where 29 < n < 37. The observed nP population is quadratically dependent on the nS atomic density. Such results are naturally attributed to binary collisions. However, this cannot be the case here, because the interaction between Rb nS atoms is repulsive. In this experiment, the AC Stark effect and multipole interactions work together to create a nonvanishing final population of nP + (n − 1)P pairs.

Electric Field Effects in the Excitation of Cold Rydberg-Atom Pairs

In this work, we study the role of the ac Stark effects on the excitation of nS1/2 cold Rydberg atoms produced in a rubidium magneto-optical trap. We have observed an atomic population in the nP3/2 state after excitation of nS1/2 for 29<or=n<or=37. Such an observation is normally attributed to binary collisions; however, the interaction between Rb nS1/2 atoms is repulsive. To explain our results, the dipole-dipole interaction and ac Stark shifts from the excitation laser must be considered. We find that the Rydberg-atom-pair state asymptotically correlating to nP3/2+(n-1)P3/2 is excited directly.

Millimeter-wave rubidium Rydberg van der Waals spectroscopy

We have observed the diatomic $nsns\ensuremath{\rightarrow}ns(n+1)s\ensuremath{\rightarrow}(n+1)s(n+1)s$ microwave transitions of pairs of cold Rb Rydberg atoms for $36&lt;n&lt;48$. The $ns(n+1)s$ state has by far the largest van der Waals shift due to its near degeneracy with the nearby $n{p}_{3/2}n{p}_{3/2}$ state. In fact, the energy difference and the van der Waals shift change sign at $n=38$ and we observe shifts of both signs. The combined excitation of the $ns(n+1)s$ and $(n+1)s(n+1)s$ states leads to an unusual line shape which can be described by a three-level Floquet model.

Investigation of cold rubidium Rydberg atoms in a magneto-optical trap

This paper reports on the results of experiments with cold rubidium Rydberg atoms in a magneto-optical trap. The specific feature of the experiments is the excitation of Rydberg atoms in a small volume within a cloud of cold atoms and the sorting of measured signals and spectra according to the number of detected Rydberg atoms. The effective lifetime of the 37P Rydberg state and its polarizability in a weak electric field are measured. The results obtained are in good agreement with theoretical calculations. It is demonstrated that the localization of the excitation volume in the vicinity of the zero-magnetic-field point makes it possible to improve the spectral resolution and to obtain narrow microwave resonances in Rydberg atoms without switching off the quadrupole magnetic field of the trap. The dependence of the amplitude of dipole-dipole interaction resonances in Rydberg atoms on the number of atoms is measured. This dependence exhibits a linear behavior and agrees with the theory for a weak dipole-dipole interaction.