We present experiments on two-photon excitation of ${\rm ^{87}}$Rb atoms to Rydberg states. For this purpose, two continuous-wave (cw)-laser systems for both 780 nm and 480 nm have been set up. These systems are optimized to a small linewidth (well below 1 MHz) to get both an efficient excitation process and good spectroscopic resolution. To test the performance of our laser system, we investigated the Stark splitting of Rydberg states. For n=40 we were able to see the hyperfine levels splitting in the electrical field for different finestructure states. To show the ability of spatially selective excitation to Rydberg states, we excited rubidium atoms in an electrical field gradient and investigated both linewidths and lineshifts. Furthermore we were able to excite the atoms selectively from the two hyperfine ground states to Rydberg states. Finally, we investigated the Autler-Townes splitting of the 5S$_{1/2}$$\to$5P$_{3/2}$ transition via a Rydberg state to determine the Rabi frequency of this excitation step.
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
In this paper, we report on numerical calculations of the spontaneous emission rates and Lamb shifts of a $^{87}\text{Rb}$ atom in a Rydberg-excited state $\left(n\leq30\right)$ located close to a silica optical nanofiber. We investigate how these quantities depend on the fiber's radius, the distance of the atom to the fiber, the direction of the atomic angular momentum polarization as well as the different atomic quantum numbers. We also study the contribution of quadrupolar transitions, which may be substantial for highly polarizable Rydberg states. Our calculations are performed in the macr…
We present the direct measurements of electric-dipole moments for $5P_{3/2}\to nD_{5/2}$ transitions with $20<n<48$ for Rubidium atoms. The measurements were performed in an ultracold sample via observation of the Autler-Townes splitting in a three-level ladder scheme, commonly used for 2-photon excitation of Rydberg states. To the best of our knowledge, this is the first systematic measurement of the electric dipole moments for transitions from low excited states of rubidium to Rydberg states. Due to its simplicity and versatility, this method can be easily extended to other transitions and o…
We apply reservoir engineering to construct a thermal environment with controllable temperature in an ultracold atomic Rydberg system. A Boltzmann distribution of the system's eigenstates is produced by optically driving a small environment of ultracold atoms, which is coupled to a photonic continuum through spontaneous emission. This technique provides a useful tool for quantum simulation of dynamics coupled to a thermal environment. Additionally, we demonstrate that pure eigenstates, such as Bell states, can be prepared in the Rydberg atomic system using this method.
It is clearly important to pursue atomic standards for quantities like electromagnetic fields, time, length and gravity. We have recently shown, using Rydberg states, that Rb atoms in a vapor cell can serve as a practical, compact standard for microwave electric field strength. Here, we demonstrate, for the first time, that Rb atoms excited in a vapor cell can also be used for vector microwave electrometry by using Rydberg atom electromagnetically induced transparency. We describe the measurements necessary to obtain an arbitrary microwave electric field polarization at a resolution of $0.5^\c…
Population dynamics in weakly-excited clouds of ultracold $^{87}$Rb Rydberg atoms were studied by means of trap loss, fluorescence detection, and state dependent stimulated emission. Rydberg atoms were excited to various nl Rydberg states via continuous two-photon excitation from a magneto-optical trap. A stimulated emission probe laser was then used to bring the Rydberg atoms down to the 6P$_{3/2}$ state, allowing state-dependent detection of the Rydberg atoms. Measurements of trap loss and fluorescent emission reveal information about the evolution of the Rydberg populations. In particular, …
Experiments in dense, ultracold gases of rubidium Rydberg atoms show a considerable decrease of the radiative excited state lifetimes compared to dilute gases. This accelerated decay is explained by collective and cooperative effects, leading to superradiance. A novel formalism to calculate effective decay times in a dense Rydberg gas shows that for these atoms the decay into nearby levels increases by up to three orders of magnitude. Excellent agreement between theory and experiment follows from this treatment of Rydberg decay behavior.
We propose a setup of an open quantum system in which the environment can be tuned such that either Markovian or non-Markovian system dynamics can be achieved. The implementation uses ultracold Rydberg atoms, relying on their strong long-range interactions. Our suggestion extends the features available for quantum simulators of molecular systems employing Rydberg aggregates and presents a new test bench for fundamental studies of the classification of system-environment interactions and the resulting system dynamics in open quantum systems.
Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and…
The exquisite properties of Rydberg levels make them particularly appealing for emerging quantum technologies. The lifetime of low-angular-momentum laser-accessible levels is however limited to a few $100\,μ\mathrm{s}$ by optical transitions and microwave blackbody radiation (BBR) induced transfers at room temperature. A considerable improvement would be obtained with the few $10\,\mathrm{ms}$ lifetime of circular Rydberg levels in a cryogenic environment reducing the BBR temperature. We demonstrate the preparation of long-lived circular Rydberg levels of laser-cooled Rubidium atoms in a cryos…
We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser excitation cycle as a function of the laser detuning provides a measure for the Rydberg interaction coefficient. With the lattice spacing precisely known, the proposed scheme only relies on the measurement of the number of Rydberg atoms and thus circumvents the necessity to map the interaction potential by varying the interparticle separation.
Ultracold Rb atoms were used to demonstrate non-degenerate four-wave mixing through a Rydberg state. Continuous 5S-5P-nD two-photon excitation to the Rydberg state was combined with an nD-6P tuned laser in a phase matched geometry. The angular dependence, spatial profile, and dependence on detuning were investigated, showing good agreement with theory. Under optimum conditions 50 percent of the radiation was emitted into the phase-matched direction.
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show…
Experiments on the spectroscopy of the Förster 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 fiel…
We show that ultracold chemical reactions can be manipulated and controlled by using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasi-bound) states exist near the collision threshold. We investigate how, by Rydberg-dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmar…
Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms …
We consider two rubidium atoms, prepared in the same S or P Rydberg states near an optical nanofibre. We determine the van der Waals interaction between them and identify novel features, including the reshaping of the interaction anisotropy and the formation of an interaction potential well near the nanofibre for P states. We attribute these phenomena to the breaking of the rotation symmetry around the interatomic axis due to the presence of the fibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.
Transfer mechanism of orbital angular moment(OAM) of light to trapped ground-state atoms under paraxial approximation is well known. Here we show how optical OAM of a Laguerre-Gaussian(LG) beam under paraxial approximation can be transferred to trapped Rydberg atoms. Optical OAM is shown to be transferable to a Rydberg electronic state in dipole transition. The Gaussian part of the profile of the LG beam, which is generally neglected , is found to have an important effect on the OAM transfer to the Rydberg atoms. Numerical calculations are calculated based on this theory for Rubidium Rydberg a…
We present the coherent excitation of a single Rubidium atom to the Rydberg state (58d3/2) using a two-photon transition. The experimental setup is described in detail, as well as experimental techniques and procedures. The coherence of the excitation is revealed by observing Rabi oscillations between ground and Rydberg states of the atom. We analyze the observed oscillations in detail and compare them to numerical simulations which include imperfections of our experimental system. Strategies for future improvements on the coherent manipulation of a single atom in our settings are given.
We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N=0 and N=2 rotational levels, is engineered which exploits the unique Rydberg electron-molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck-Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.
We propose a new approach to excite ion-pair states of ultracold dimers. The central idea is a two-step process where first long-range Rydberg molecules are formed by photoassociation, which are then driven by stimulated emission towards the ion-pair state, a process bearing features of a photo-induced harpooning reaction. We assess the feasibility of this approach through a detailed experimental and theoretical study on a specific system, p-wave-scattering dominated long-range Rydberg molecules in caesium, and discuss potential applications for the study of strongly correlated plasmas consist…
We investigate static properties of laser-driven, ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and discussed.
We study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in t…
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 $n$p$_{3/2}$ Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs$_2$ 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 interaction…
We have studied the behavior of cold Rydberg atoms embedded in an ultracold plasma. We demonstrate that even deeply bound Rydberg atoms are completely ionized in such an environment, due to electron collisions. Using a fast pulse extraction of the electrons from the plasma we found that the number of excess positive charges, which is directly related to the electron temperature Te, is not strongly affected by the ionization of the Rydberg atoms. Assuming a Michie-King equilibrium distribution, in analogy with globular star cluster dynamics, we estimate Te. Without concluding on heating or cool…
We measure nonlocal third-order spatial correlations in non-degenerate ultracold gases of bosonic ($^{84}$Sr) and spin-polarized fermionic ($^{87}$Sr) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of six (3!) in the case of bosonic $^{84}$Sr due to bunching, and a marked reduction for spin-polarized fermionic $^{87}$Sr due to anti-bunching. The experimental results are compared to theoretical predictions an…
We report on our recent progress on the manipulation of single rubidium atoms trapped in optical tweezers and the generation of entanglement between two atoms, each individually trapped in neighboring tweezers. To create an entangled state of two atoms in their ground states, we make use of the Rydberg blockade mechanism. The degree of entanglement is measured using global rotations of the internal states of both atoms. Such internal state rotations on a single atom are demonstrated with a high fidelity.
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 …
We theoretically investigate the quantum statistical properties of light transmitted through an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. In our setup, atoms are located in a cavity and non-resonantly driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of the weak signal field and a strong control beam. To characterize the transmitted light we compute the second-order correlation function $g^{\left(2\right)}\left(τ\right)$. The simulations we obtained on the specif…
We present a combined experimental and theoretical study of the effects of Rydberg interactions on Autler-Townes spectra of ultracold gases of atomic strontium. Realizing two-photon Rydberg excitation via a long-lived triplet state allows us to probe the thus far unexplored regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atom-loss spectra. The experiment is analyzed within a one-body density matrix approach, accounting for interaction-induced level shifts and de…
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-ord…
We show that the excitation of long-range Rydberg molecules in a three-dimensional optical lattice can be used as a position- and time-sensitive probe of the site occupancy in the system. To this end, we detect the ions which are continuously generated by the decay of the formed Rydberg molecules. While a superfluid gas shows molecule formation for all parameters, a Mott insulator with $n=1$ filling reveals a strong suppression of the number of formed molecules. In the limit of weak probing, the technique can be used to probe the superfluid to Mott-insulator transition in real-time. Our method…
We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schrëdinger equation.
We present evidence for Rydberg-Rydberg interaction in a gas of rubidium atoms above room temperature. Rabi oscillations on the nanosecond timescale to different Rydberg states are investigated in a vapor cell experiment. Analyzing the atomic time evolution and comparing to a dephasing model we find a scaling with the Rydberg quantum number n that is consistent with van der Waals interaction. Our results show that the interaction strength can be larger than the kinetic energy scale (Doppler width) which is the requirement for realization of thermal quantum devices in the GHz regime.
Assembled arrays of individual atoms with Rydberg-mediated interactions provide a powerful platform for the simulation of many-body spin Hamiltonians as well as the implementation of universal gate-based quantum information processing. We demonstrate the first realization of Rydberg excitations and controlled interactions in microlens-generated multisite trap arrays of reconfigurable geometry. We utilize atom-by-atom assembly for the deterministic preparation of pre-defined 2D structures of rubidium Rydberg atoms with exactly known mutual separations and selectable interaction strength. By ada…
We investigate electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral fea…
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ 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 $50S_{1/2}$ states in the blockade regime. For…
We experimentally realize Rydberg excitations in Bose-Einstein condensates of rubidium atoms loaded into quasi one-dimensional traps and in optical lattices. Our results for condensates expanded to different sizes in the one-dimensional trap agree well with the intuitive picture of a chain of Rydberg excitations. We also find that the Rydberg excitations in the optical lattice do not destroy the phase coherence of the condensate, and our results in that system agree with the picture of localized collective Rydberg excitations including nearest-neighbour blockade.
We present a versatile laser system which provides more than 1.5W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial Titanium-Sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we…
We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the pr…
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 …
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, who…
We present a very sensitive and scalable method to measure the population of highly excited Rydberg states in a thermal vapor cell of rubidium atoms. We detect the Rydberg ionization current in a 5 mm electrically contacted cell. The measured current is found to be in excellent agreement with a theory for the Rydberg population based on a master equation for the three level problem including an ionization channel and the full Doppler distributions at the corresponding temperatures. The signal-to-noise ratio of the current detection is substantially better than purely optical techniques.
We present quantum mechanical calculations of Auger decay rates for two Rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis of the two-electron state space. We consider large sets of two-atom states with randomly chosen quantum numbers and find that the charge overlap between the two Rydberg electrons allows one to characterise the magnitude of the Auger decay rates. If the electron clouds overlap by more than one percent, the Auger decay rates increase approximately exp…
We report on a significant discrepancy between recently published highly accurate variational calculations and precise measurements of the spectrum of Rydberg states in $^{87}$Rb on the energy scale of fine splitting. Introducing a modified effective single-electron potential we determine the spectrum of the outermost bound electron from a standard WKB approach. Overall very good agreement with precise spectroscopic data is obtained.
We report the experimental observation of strong two-color optical nonlinearity in an ultracold gas of $^{85}\mathrm{Rb}$-$^{87}\mathrm{Rb}$ atom mixture. By simultaneously coupling two probe transitions of $^{85}$Rb and $^{87}$Rb atoms to Rydberg states in electromagnetically induced transparency (EIT) configurations, we observe significant suppression of the transparency resonance for one probe field when the second probe field is detuned at $\sim1~\mathrm{GHz}$ and hitting the EIT resonance of the other isotope. Such a cross-absorption modulation to the beam propagation dynamics can be desc…
