Ultracold Rydberg Gases Research Articles

Microwave photo-association of fine-structure-induced Rydberg (n+2)D5/2nFJ macro-dimer molecules of cesium

Long-range (n+2)D5/2nFJ Rydberg macro-dimers are observed in an ultracold cesium Rydberg gas for 39≤n≤48. Strong dipolar flip (〈D5/2F5/2|V̂dd|F5/2D5/2〉, 〈D5/2F7/2|V̂dd|F7/2D5/2〉) and cross (〈D5/2F7/2|V̂dd|F5/2D5/2〉) couplings lead to bound, fine-structure-mixed (n+2)D5/2nFJ macro-dimers at energies between the FJ fine-structure levels. The (n+2)D5/2nFJ macro-dimers are measured by microwave photo-association from optically prepared [(n+2)D5/2]2 Rydberg-pair precursor states. Calculated adiabatic potential curves are used to elucidate the underlying physics and to model the macro-dimer spectra, with good overall agreement. Microwave photo-association allows Franck-Condon tuning, which we have studied by varying the detuning of a Rydberg-atom excitation laser. Further, in Stark spectroscopy, we have measured molecular DC electric polarizabilities that are considerably larger than those of the atomic states. The large molecular polarizabilities are unexpected and may be caused by high-ℓ mixing. The observed linewidths of the Stark-shifted molecular lines provide initial evidence for intramolecular induced-dipole-dipole interaction. Published by the American Physical Society 2024

Symmetric Fano Profiles of Two-photon Electronic Transitions Observed in an Ultracold Rydberg Gas

Fano profiles are caused by the interference between the discrete states and continuum. It is a very common phenomenon
 in multi-electron Rydberg states, such as the Rydberg states of group II elements in the periodic table. It often leads to
 autoionization due to the fact that a discrete state couples with an autoionizing state. Unlike the typical asymmetric line
 shape, here we report a symmetric unusual Fano line shape that has been predicted. In addition, this profile is caused
 by molecular states or polymer states instead of multi-electron atomic states. Moreover, it is shown that the fano profile
 caused by the multi-electron polymer states does not necessarily lead to autoionization. We propose that the Fano profile
 studied is caused by the interference between discrete levels and the multipole-multipole coupled continuum, or energy
 band.

Electron temperature relaxation in the clusterized ultracold plasmas

Ultracold plasmas are a promising candidate for the creation of strongly coupled Coulomb systems. Unfortunately, the values of the coupling parameter Γe actually achieved after photoionization of the neutral atoms remain relatively small because of the considerable intrinsic heating of the electrons. A conceivable way to get around this obstacle might be to utilize a spontaneous ionization of the ultracold Rydberg gas, where the initial kinetic energies could be much less. However, the spontaneous avalanche ionization will result in a very inhomogeneous distribution (clusterization) of the ions, which can change the efficiency of the electron relaxation in the vicinity of such clusters substantially. In the present work, this hypothesis is tested by an extensive set of numerical simulations. As a result, it is found that despite a less initial kinetic energy, the subsequent relaxation of the electron velocities in the clusterized plasmas proceeds much more violently than in the case of the statistically uniform ionic distribution. The electron temperature, first, experiences a sharp initial jump (presumably, caused by the “virialization” of energies of the charged particles) and, second, exhibits a gradual subsequent increase (presumably, associated with a multi-particle recombination of the electrons at the ionic clusters). As a possible tool to reduce the anomalous temperature increase, we also considered a two-step plasma formation, involving the blockaded Rydberg states. This leads to a suppression of the clusterization due to a quasi-regular distribution of ions. In such a case, according to the numerical simulations, the subsequent evolution of the electron temperature proceeds more gently, approximately with the same rate as in the statistically uniform ionic distribution.

Observation of blackbody radiation enhanced superradiance in ultracold Rydberg gases

An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from 300 K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance of ultracold Rydberg atoms embedded in a bath of room-temperature photons. The temporal evolution of the Rydberg |nD⟩ to |(n + 1)P⟩ superradiant decay of Cs atoms (n the principal quantum number) is measured directly in free space. Theoretical simulations confirm the BBR enhanced superradiance in large Rydberg ensembles. We demonstrate that the van der Waals interactions between Rydberg atoms change the superradiant dynamics and modify the scaling of the superradiance. In the presence of static electric fields, we find that the superradiance becomes slow, potentially due to many-body interaction induced dephasing. Our study provides insights into many-body dynamics of interacting atoms coupled to thermal BBR, and might open a route to the design of blackbody thermometry at microwave frequencies via collective, dissipative photon-atom interactions.

Modeling Rydberg gases using random sequential adsorption on random graphs

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects, and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a Random Sequential Adsorption (RSA) process on a Random Geometric Graph (RGG), and a RSA process on a Decomposed Random Intersection Graph (DRIG). The latter model is new, and refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the former two models, it lends itself for a rigorous mathematical analysis; and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time-evolution of number of Rydberg atoms, and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdos-Renyi Random Graph (ERRG). Finally, we also come up with a new heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long time scales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short time scales the statistics are affected most by quantum mechanical effects.

Anisotropic interactions in electric field polarized ultracold Rydberg gases

We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective C3 dipole–dipole and C6 van der Waals coefficients. We compare the C3 and C6 with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole–dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in states in the blockade regime. For internuclear distances close to the blockade radius, Rbl ≈ 4–6 μm, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of C3 and C6 which were used to analyze the original experiment. We find that the calculated C6 coefficient is within 8% of the experimental value while the C3 coefficient is within 20% of the experimental value.

Ultrafast Coherent Control of Condensed Matter with Attosecond Precision.

Coherent control is a technique to manipulate wave functions of matter with light. Coherent control of isolated atoms and molecules in the gas phase is well-understood and developed since the 1990s, whereas its application to condensed matter is more difficult because its coherence lifetime is shorter. We have recently applied this technique to condensed matter samples, one of which is solid para-hydrogen ( p-H2). Intramolecular vibrational excitation of solid p-H2 gives an excited vibrational wave function called a "vibron", which is delocalized over many hydrogen molecules in a manner similar to a Frenkel exciton. It has a long coherence lifetime, so we have chosen solid p-H2 as our first target in the condensed phase. We shine a time-delayed pair of femtosecond laser pulses on p-H2 to generate vibrons. Their interference results in modulation of the amplitude of their superposition. Scanning the interpulse delay on the attosecond time scale gives a high interferometric contrast, which demonstrates the possibility of using solid p-H2 as a carrier of information encoded in the vibrons. In the second example, we have controlled the terahertz collective phonon motion, called a "coherent phonon", of a single crystal of bismuth. We employ an intensity-modulated laser pulse, whose temporal envelope is modulated with terahertz frequency by overlap of two positively chirped laser pulses with their adjustable time delay. This modulated laser pulse is shined on the bismuth crystal to excite its two orthogonal phonon modes. Their relative amplitudes are controlled by tuning the delay between the two chirped pulses on the attosecond time scale. Two-dimensional atomic motion in the crystal is thus controlled arbitrarily. The method is based on the simple, robust, and universal concept that in any physical system, two-dimensional particle motion is decomposed into two orthogonal one-dimensional motions, and thus, it is applicable to a variety of condensed matter systems. In the third example, the double-pulse interferometry used for solid p-H2 has been applied to many-body electronic wave functions of an ensemble of ultracold rubidium Rydberg atoms, hereafter called a "strongly correlated ultracold Rydberg gas". This has allowed the observation and control of many-body electron dynamics of more than 40 Rydberg atoms interacting with each other. This new combination of ultrafast coherent control and ultracold atoms offers a versatile platform to precisely observe and manipulate nonequilibrium dynamics of quantum many-body systems on the ultrashort time scale. These three examples are digested in this Account.

Multicritical behavior in dissipative Ising models.

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady-state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

Emergent equilibrium in many-body optical bistability.

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion-organized around the experimentally relevant limit of weak interactions-the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.

Autler-Townes splitting of ultracold cesium Rydberg atoms

Autler-Townes (A-T) splitting, known as an AC Stark effect, shows a change of an absorption/emission spectral line of a probe beam when an oscillating field is tuned in resonance with the atomic or molecular transition. The A-T splitting is observed in different three-level atoms and widely investigated in a vapor cell and in a magneto-optical trap (MOT). The A-T splitting plays an important role in the atom-based microwave electric-field measurements where a cascade three-level system involving Rydberg state is adopted. In this work, an A-T splitting is observed in an ultracold cesium Rydberg gas, which is cooled down to about 100 pK and center density is about 1010 cm-3 in a conventional MOT by using the laser cooling technology. We present the A-T spectrum in a ladder three-level atomic system involving a 34D5/2 Rydberg state. The cesium ground state (6S1/2), excited state (6P3/2) and Rydberg state (34D5/2) constitute a Rydberg three-level system. A coupling laser, locked to the Rydberg transition by using a Rydberg electromagnetically induced transparency signal that is obtained from a cesium room-temperature vapor cell, couples 6P3/2 (F'=5) 34D5/2 Rydberg transition. A weak probe laser, stabilized to a ground-state transition by using a polarization spectroscopy, is swept, covering the transition 6S1/2 (F=4) 6P3/2 (F'=5) with a double-passed acousto-optic modulator. The probe and coupling lasers are counter-propagated through the MOT center. The power of probe light is 200 pW, corresponding Rabi frequency p=21.05 MHz. During the experiment, 50 s after turning off the trapping laser, both the coupling and probe beams are switched on and last 100 s. The A-T spectrum as a function of the probe detuning is detected with a single-photon counter module detector. We use Gaussian multiple peak fitting to obtain the positions of the A-T peaks and the A-T splitting. The measured A-T splitting is proportional to the Rabi frequency of the coupling light. We numerically solve the density matrix equations to obtain the A-T spectrum, and the calculations reproduce A-T spectra well. The measured A-T splitting shows good agreement with the theoretical calculation for Rabi frequency of the coupling light c29 MHz. The A-T splitting is less than the calculation for the case of c29 MHz, the deviation is mainly attributed to the increased dephasing rate induced by the strong interaction between Rydberg atoms, whose number increases with the coupling laser Rabi frequency. In this work, the adopted method for the cascade three-level system involving Rydberg state is also suitable for -and V-type cases.

Long-range Rydberg molecules, Rydberg macrodimers and Rydberg aggregates in an ultracold Cs gas

We present an overview of our recent investigations of long-range interactions in an ultracold Cs Rydberg gas. These interactions are studied by high-resolution photoassociation spectroscopy, using excitation close to one-photon transitions into np3/2 Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs2 molecules. We observe two types of molecular resonances. The first type originates from the correlated excitation of two atoms into Rydberg-atom-pair states interacting at long range via multipole-multipole interactions. The second type results from the interaction of one atom excited to a Rydberg state with one atom in the electronic ground state. Which type of resonances is observed in the experiments depends on the laser intensity and frequency and on the pulse sequences used to prepare the Rydberg states. We obtain insights into both types of molecular resonances by modelling the interaction potentials, using a multipole expansion of the long-range interaction for the first type of resonances and a Fermi-contact pseudo-potential for the second type of resonances. We analyse the relation of these long-range molecular resonances to molecular Rydberg states and ion-pair states, and discuss their decay channels into atomic and molecular ions. In experiments carried out with a two-colour two-photon excitation scheme, we observe a large enhancement of Rydberg-excitation probability, which we interpret as a saturable autocatalytic antiblockade phenomenon.

Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas.

Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.

Thermodynamic of mixtures of ultracold Rydberg gases with different levels of excitation

The physical model of the particle system describing the thermodynamics of mixtures of ultracold Rydberg gases with different levels of excitation are proposed. In our model system of particles is a mixture of atoms in S-state and atoms in the P-state. To calculate the thermodynamic of the mixture Rydberg gases the method of Monte-Carlo was used. Computational results of the spatial correlations of dipoles depending on the coupling parameter are presented. At some value of the nonideality parameter the dipole chains are formed.

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg–Stark states of principal quantum number n in the range between 25 and 35, have been deflected by , decelerated and loaded into off-axis electric traps at initial densities of atoms cm−3 and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as and corresponding closely to the natural lifetimes of the initially prepared Rydberg–Stark states. The decay rate was found to continually decrease over time and to reach an almost n-independent rate of more than (1 ms)−1 after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared Rydberg–Stark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg–Stark states of higher values. While searching for such a mechanism, we discovered that resonant dipole–dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole–dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative processes that the observed decay of the population of Rydberg atoms in the trap could be satisfactorily reproduced for all n values studied experimentally.

Possible existence of van der Waals macrodimers

ABSTRACTFew-body interactions offer the opportunity to study the isolated atom to few-body coupled molecules, and to condensed matter transitions. Atoms in molecules and in condensed matters are coupled by different orders of multipole–multipole interactions, which all stem from different orders of approximations from coulomb interactions between multiple charges. The lowest order multipole–multipole interaction is the dipole–dipole interaction, which is proportional to the size of the dipole. In this article, we use Rydberg atoms, which have more than 1000 times greater electric dipoles than the ground state atoms, to study the van der Waals interaction between few bodies. In addition to the large dipoles, the kinetic energy of the atoms is significantly reduced by reducing the temperature, which makes these interactions stable and observable. Here, we report on the 2D and 3D few-body interaction potentials and possible ways of creating semistable molecules in such an ultracold Rydberg gas with a temperature of ≈100 nK. Although we use Rydberg atoms in this article, this calculation can be applied to other states too. The results reported here are useful for studying repulsive van der Waals interactions and creating ultracold molecules.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n{p}_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22--36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n{p}_{3/2}+n{p}_{3/2}$ dissociation asymptotes, but also to $n{s}_{1/2}+(n+1){s}_{1/2}, n{s}_{1/2}+{n}^{\ensuremath{'}}{f}_{j}$, and $(n\ensuremath{-}4){f}_{j}+(n\ensuremath{-}3){f}_{j}\phantom{\rule{4pt}{0ex}}(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole and higher-order long-range-interaction terms between the Rydberg atoms on the basis of (i) their spectral positions, (ii) their response to static and pulsed electric fields, and (iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom-pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 15 $\ensuremath{\mu}\mathrm{s}$ following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation-blockade effects.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n$p$_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22-36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n$p$_{3/2}+n$p$_{3/2}$ dissociation asymptotes, but also to $n$s$_{1/2}+(n+1)$s$_{1/2}$, $n$s$_{1/2}+n'$f$_{j}$, and $(n-4)$f$_{j}+(n-3)$f$_{j}$ $(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole, and higher-order long-range-interaction terms between the Rydberg atoms on the basis of i) their spectral positions, ii) their response to static and pulsed electric fields, and iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom--pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 10 $\mu$s following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation blockade effects.

Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases.

Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.

Giant Cross Section for Molecular Ion Formation in Ultracold Rydberg Gases.

We have studied the associative ionization of a Rydberg atom and a ground-state atom in an ultracold Rydberg gas. The measured scattering cross section is 3 orders of magnitude larger than the geometrical size of the produced molecule. This giant enhancement of the reaction kinetics is due to an efficient directed mass transport which is accelerated by the Rydberg electron. We also find that the total inelastic scattering cross section is given by the geometrical size of the Rydberg electron's wave function.

Variational analysis of driven-dissipative Rydberg gases

We study the nonequilibrium steady state arising from the interplay between coherent and dissipative dynamics in strongly interacting Rydberg gases using a recently introduced variational method [H. Weimer, Phys. Rev. Lett. 114, 040402 (2015)]. We give a detailed discussion of the properties of this approach and we provide a comparison with methods related to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. We find that the variational approach offers some intrinsic advantages and we also show that it is able to explain the experimental results obtained in an ultracold Rydberg gas on a quantitative level.