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Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of Rb-87 in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.

This tutorial provides a hands-on entry point about laser locking for atomic vapor research and related research such as laser cooling. We furthermore introduce common materials and methods for the fabrication of vapor cells as a tool for this research. Its aim is not to be exhaustive, but rather to provide an overview about the possible techniques that are actively employed in labs today. Some critical parameters of locked laser system for use with thermal atomic vapors are introduced and discussed. To exemplify this, we describe a versatile locking system that caters for many of the needs we found during our research with thermal atomic vapors. We also emphasize the compromises we took during our decision-making process., Comment: 58 pages, 14 figures

The onset of collision dynamics between an ion and a Rydberg atom is studied in a regime characterized by a multitude of collision channels. These channels arise from coupling between a non-polar Rydberg state and numerous highly polar Stark states. The interaction potentials formed by the polar Stark states show a substantial difference in spatial gradient compared to the non-polar state leading to a separation of collisional timescales, which is observed in situ. For collision energies in the range of $k_\textrm{B}\cdot\mu$K to $k_\textrm{B}\cdot$K, the dynamics exhibit a counter-intuitive dependence on temperature, resulting in faster collision dynamics for cold - initially "slow" - systems. Dipole selection rules enable us to prepare the collision pair on the non-polar potential in a highly controlled manner, which determines occupation of the collision channels. The experimental observations are supported by semi-classical simulations, which model the pair state evolution and provide evidence for tunable non-adiabatic dynamics.

We report on the current development of a single photon source based on a long-range interacting room temperature rubidium vapor. We discuss the history of the project, the production of vapor cells, and the observation of Rabi-oscillations in the four-wave-mixing excitation scheme., Comment: 8 pages, 6 figures

We report on the collisional shift and line broadening of Rydberg states in nitric oxide (NO) with increasing density of a background gas at room temperature. As a background gas we either use NO itself or nitrogen (N$_{2}$). The precision spectroscopy is performed by a sub-Doppler three-photon excitation scheme with a subsequent readout of the Rydberg states realized by the amplification of a current generated by free charges due to collisions. The shift shows a dependence on the rotational quantum state of the ionic core and no dependence on the principle quantum number of the orbiting Rydberg electron. The experiment was performed in the context of developing a trace-gas sensor for breath-gas analysis in a medical application.

An ensemble of Rydberg atoms can be excited with lasers such that it evolves into an entangled state with just one collective excitation within the Rydberg blockade radius. The decay of this state leads to the emission of a single, antibunched photon. For a hot vapor of Rubidium atoms in a micro cell we numerically study the feasibility of such a single-photon source under different experimental conditions like the atomic density distribution and the choice of electronic states addressed by the lasers. For the excitation process with three rectangular lasers pulses, we simulate the coherent dynamics of the system in a truncated Hilbert space. We investigate the radiative behavior of the moving Rydberg atoms and optimize the laser pulse sequence accordingly. We find that the collective decay of the single-excitation leads to a fast and directed photon emission and further, that a pulse sequence similar to a spin echo increases the directionality of the photon. Finally, we analyze the residual double-excitations and find that they do not exhibit these collective decay properties and play only a minor deleterious role., Comment: 10 pages, 6 figures, 1 table. Removed 6P state calculations for brevity. Added new results for 5P state calculations. Updated color in figures

Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few mV/cm, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenching the electric field. A high resolution ion microscope allows us to detect the molecule's orientation and its temporal vibrational dynamics in real space. Our study opens the door to the control of molecular dynamics in Rydberg molecules., Comment: 7 pages, 4 figures

Preparation of an atomic ensemble in a particular Zeeman state is a critical step of many protocols for implementing quantum sensors and quantum memories. These devices can also benefit from optical fibre integration. In this work we describe experimental results supported by a theoretical model of single-beam optical pumping of $^{87}$Rb atoms within a hollow-core photonic crystal fibre. The observed 50% population increase in the pumped F=2, m$_F$=2 Zeeman substate along with the depopulation of remaining Zeeman substates enabled us to achieve a 3 times improvement in the relative population of the m$_F$=2 substate within the F=2 manifold, with 60% of the F=2 population residing in the m$_F$=2 dark sublevel. Based on our theoretical model, we also propose methods to further improve the pumping efficiency in alkali-filled hollow-core fibres.

We report on Doppler-free continuous-wave optical UV-spectroscopy resolving the hyperfine structure of the $\mathrm{A}\,^2\Sigma^+ \leftarrow \mathrm{X}\,^2\Pi_{3/2}$ transition in nitric oxide for total angular momenta $J_X=1.5-19.5$ on the $\mathrm{oP_{12ee}}$ branch. The resulting line splittings are compared to calculated splittings and fitted determining new values for the molecular constants $b, c, eQq_0$ and $b_F$ for the $\mathrm{A}\,^2\Sigma^+$ state. The constants are in good agreement with values previously determined by quantum beat spectroscopy., Comment: 8 Pages, 4 figures

We present a new type of compact and all-glass based vapour cell integrating hollow-core photonic crystal fibres. The absence of metals, as in a traditional vacuum chamber and the much more compact geometry allows for fast and homogeneous heating. As a consequence we can fill the fibres on much faster timescales, ranging from minutes to hours. Additionally the all-glass design ensures optical access along the fibre. This allows live monitoring of the diffusion of rubidium atoms inside the hollow-core by measuring the frequency-dependent fluorescence from the atoms. The atomic density is numerically retrieved using a 5-level system of Bloch-equations., Comment: 9 pages, 5 figures

Strong light-induced interactions between atoms are known to cause nonlinearities at a few-photon level which are crucial for applications in quantum information processing. Compared to free space, the scattering and the light-induced dipolar interaction of atoms can be enhanced by a dielectric environment. For this \emph{Purcell effect}, either a cavity or a waveguide can be used. Here, we combine the high densities achievable in thermal atomic vapors with an efficient coupling to a slot waveguide. In contrast to free-space interactions, atoms aligned within the slot exhibit repulsive interactions that are further enhanced by a factor of 8 due to the Purcell effect. The corresponding blueshift of the transition frequency of atoms arranged in the essentially one-dimensional geometry vanishes above the saturation, providing a controllable nonlinearity at the few-photon level. The experimental results are in good agreement with Monte-Carlo simulations that include the dielectric environment, dipolar interactions, and motional effects. The results pave the way towards a robust scalable platform for quantum nonlinear optics and all-optical quantum information processing at room temperature., Comment: 12 pages, 7 figures

We exploit the effect of light-induced atomic desorption to produce high atomic densities ($n\gg k^3$) in a rubidium vapor cell. An intense off-resonant laser is pulsed for roughly one nanosecond on a micrometer-sized sapphire-coated cell, which results in the desorption of atomic clouds from both internal surfaces. We probe the transient atomic density evolution by time-resolved absorption spectroscopy.With a temporal resolution of $\approx1\,\mathrm{ns}$, we measure the broadening and line shift of the atomic resonances. Both broadening and line shift are attributed to dipole-dipole interactions. This fast switching of the atomic density and dipolar interactions could be the basis for future quantum devices based on the excitation blockade., Comment: 13 pages, 4+6 figures

We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm0.1)$ and $(-21.2\pm0.1)$ dB in the two outputs, with a corresponding transmission of 97 and 99 %. This technique avoids the need to use spatial separation of four-wave mixing modes and thus opens the door for the process efficiency to be enhanced in waveguide experiments. As a proof-of-principle we generate light via four-wave mixing in $^{87}$Rb loaded into a hollow-core photonic crystal fiber and interface it with the atomic Faraday dichroic beam splitter., Comment: 8 pages, 7 figures

We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resolved field-dissociation technique to trace the relaxation dynamics of the recombination products. Our observations are in good agreement with numerical simulations based on Langevin capture dynamics and provide complementary means to study stability and reaction dynamics of ionic impurities in ultracold quantum gases., Comment: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2007.00309

We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allows us to study a regime of frequent collisions of the impurity within only tens of microseconds. Comparison of our measurements with stochastic trajectory simulations based on sequential Langevin collisions indicate diffusive transport properties of the impurity and allows us to measure its mobility. Furthermore, working with a free and untrapped ion provides unique means to distinguish single realizations, where the impurity is subject to inelastic molecular-ion formation via three-body recombination. We study the cold chemistry of these events and find evidence for subsequent rovibrational quenching collisions of the produced molecule. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter., Comment: 10 pages, 9 figures

The collective response of an atomic ensemble is shaped by its macroscopic environment. We demonstrate this effect in the near-resonant transmission of light through a thermal rubidium vapor confined in a planar nanocavity. Our model reveals density-dependent line shifts and broadenings beyond continuous electrodynamics models that oscillate with cavity width and have been observed in recent experiments. We predict that the amplitudes of these oscillations can be controlled by coatings that modify the cavity's Finesse., Comment: 12 pages, 5 figures

We study an integrated silicon photonic chip, composed of several sub-wavelength ridge waveguides, and immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observe that the waveguide transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. Due to the enhanced electric field in the waveguide cladding, the atomic transition can be saturated at a photon number $\approx$ 80 times less than a free-propagating beam case. The non-linearity of the atom-clad Si-waveguide is about 4 orders of magnitude larger than maximum achievable value in doped Si photonics. The measured spectra corroborate well with a generalized effective susceptibility model that includes the Casimir-Polder potentials, due to the dielectric surface, and the transient interaction between flying atoms and the evanescent waveguide mode. This work paves the way towards a miniaturized, low-power, and integrated hybrid atomic-photonic system compatible with CMOS technologies., Comment: 9 pages, 8 figures, added references for section 1

Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To path the way to a specific target state, we explore quantum optimal control framework based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization is particularly suitable for quantum experiments where data acquisition can be expensive. Using numerical simulations for the superfluid to Mott-insulator transition for bosons in a lattice as well for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control., Comment: 29 pages, 10 figures

The paradigm of cavity QED is a two-level emitter interacting with a high quality factor single mode optical resonator. The hybridization of the emitter and photon wave functions mandates large vacuum Rabi frequencies and long coherence times; features that so far have been successfully realized with trapped cold atoms and ions and localized solid state quantum emitters such as superconducting circuits, quantum dots, and color centers. Thermal atoms on the other hand, provide us with a dense emitter ensemble and in comparison to the cold systems are more compatible with integration, hence enabling large-scale quantum systems. However, their thermal motion and large transit time broadening is a major challenge that has to be circumvented. A promising remedy could benefit from the highly controllable and tunable electromagnetic fields of a nano-photonic cavity with strong local electric-field enhancements. Utilizing this feature, here we calculate the interaction between fast moving, thermal atoms and a nano-beam photonic crystal cavity (PCC) with large quality factor and small mode volume. Through fully quantum mechanical calculations, including Casimir-Polder potential (i.e. the effect of the surface on radiation properties of an atom) we show, when designed properly, the achievable coupling between the flying atom and the cavity photon would be strong enough to lead to Rabi flopping in spite of short interaction times. In addition, the time-resolved detection of different trajectories can be used to identify single and multiple atom counts. This probabilistic approach will find applications in cavity QED studies in dense atomic media and paves the way towards realizing coherent quantum control schemes in large-scale macroscopic systems aimed at out of the lab quantum devices.

The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so far unobserved fine structure of the $^3P_J$ triplet of Rb$^-$ and allow us to extract parameters of the associated $p$-wave scattering resonances which deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion., Comment: 11 pages, 6 figures

We investigate the phenomenon of bistability in a thermal gas of cesium atoms excited to Rydberg states. We present both measurements and a numerical model of the phenomena based on collisions. By directly measuring the plasma frequency, we show that the origin of the bistable behavior lies in the creation of a plasma formed by ionized Rydberg atoms. Recombination of ions and electrons manifests as fluorescence which allows us to characterize the plasma properties and study the transient dynamics of the hysteresis that occurs. We determine scaling parameters for the point of plasma formation, and verify our numerical model by comparing measured and simulated spectra. These measurements yield a detailed microscopic picture of ionization and avalanche processes occurring in thermal Rydberg gases. From this set of measurements, we conclude that plasma formation is a fundamental ingredient in the optical bistability taking place in thermal Rydberg gases and imposes a limit on usable Rydberg densities for many applications., Comment: 13 pages, 10 figures

We study the long-range interaction of a single ion with a highly excited ultracold Rydberg atom and report on the direct observation of ion-induced Rydberg excitation blockade mediated over tens of micrometer distances. Our hybrid ion-atom system is directly produced from an ultracold atomic ensemble via near-threshold photo-ionization of a single Rydberg excitation, employing a two-photon scheme which is specifically suited for generating a very low-energy ion. The ion's motion is precisely controlled by small electric fields, which allows us to analyze the blockade mechanism for a range of principal quantum numbers. Finally, we explore the capability of the ion as a high-sensitivity single-atom-based electric field sensor. The observed ion - Rydberg-atom interaction is of current interest for entanglement generation or studies of ultracold chemistry in hybrid ion-atom systems., Comment: 7 pages, 7 figures

Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with principal quantum number up to $n = 190$ are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed lineshape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics., Comment: 9 pages, 6 figures

We demonstrate the applicability of 2-photon Rydberg excitations of nitric oxide (NO) at room temperature in a gas mixture with helium (He) as an optogalvanic gas sensor. The charges created initially from succeeding collisions of excited NO Rydberg molecules with free electrons are measured as a current on metallic electrodes inside a glass cell and amplified using a custom-designed highbandwidth transimpedance amplifier attached to the cell. We fnd that this gas sensing method is capable of detecting NO concentrations lower than 10 ppm even at atmospheric pressures, currently only limited by the way we prepare the gas dilutions.

We introduce an all-glass, vacuum tight, fiber-integrated and alkali compatible spectroscopy device consisting of two conventional optical fibers spliced to each end of a capillary. This is mainly realized through a decentered splicing method allowing refilling of the capillary and controlling the vapor density inside. We analyze the light guidance of the setup through simulations and measurements of the transmission efficiency at different wavelengths and show that filling it with highly reactive alkali metals is possible, and that the vapor density can be controlled reliably., Comment: 5 pages, 7 figures

We demonstrate a method to produce vacuum tight, metal free, bakeable and alkali compatible feedthroughs for optical fibers. The manufacturing process mainly relies on encasing fibers made of fused silica with glass materials with lower melting points by heating. We analyze the vacuum and optical performance of the devices by various methods including helium leak checking and several spectroscopic schemes, among others electromagnetically induced transparency involving Rydberg states., Comment: 4 Pages, 4 Figures

We report on a novel method for photo-association 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 photo-association techniques. Here, we show that for suitable principal quantum numbers 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 ${\rm{S}}$-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., Comment: 8 pages, 4 figures

We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to experimental data., Comment: 6 pages, 4 figures, 4 tables

We investigate the phenomenon of optical bistability in a driven ensemble of Rydberg atoms. By performing two experiments with thermal vapors of rubidium and cesium, we are able to shed light onto the underlying interaction mechanisms causing such a non-linear behavior. Due to the different properties of these two atomic species, we conclude that the large polarizability of Rydberg states in combination with electric fields of spontaneously ionized Rydberg atoms is the relevant interaction mechanism. In the case of rubidium, we directly measure the electric field in a bistable situation via two-species spectroscopy. In cesium, we make use of the different sign of the polarizability for different l-states and the possibility of applying electric fields. Both these experiments allow us to rule out dipole-dipole interactions, and support our hypothesis of a charge-induced bistability., Comment: 8 pages, 7 figures

We discuss the density shift and broadening of Rydberg spectra measured in cold, dense atom clouds in the context of Rydberg atom spectroscopy done at room temperature, dating back to the experiments of Amaldi and Segr\`e in 1934. We discuss the theory first developed in 1934 by Fermi to model the mean-field density shift and subsequent developments of the theoretical understanding since then. In particular, we present a model whereby the density shift is calculated using a microscopic model in which the configurations of the perturber atoms within the Rydberg orbit are considered. We present spectroscopic measurements of a Rydberg atom, taken in a Bose-Einstein condensate (BEC) and thermal clouds with densities varying from $5\times10^{14}\textrm{cm}^{-3}$ to $9\times10^{12}\textrm{cm}^{-3}$. The density shift measured via the spectrum's center of gravity is compared with the mean-field energy shift expected for the effective atom cloud density determined via a time of flight image. Lastly, we present calculations and data demonstrating the ability of localizing the Rydberg excitation via the density shift within a particular density shell for high principal quantum numbers., Comment: 27 pages, 12 figures, Review Paper

Strongly interacting atom-cavity systems within a network with many nodes constitute a possible realization for a quantum internet which allows for quantum communication and computation on the same platform. To implement such large-scale quantum networks, nanophotonic resonators are promising candidates because they can be scalably fabricated and interconnected with waveguides and optical fibers. By integrating arrays of ring resonators into a vapor cell we show that thermal rubidium atoms above room temperature can be coupled to photonic cavities as building blocks for chip-scale hybrid circuits. Although strong coupling is not yet achieved in this first realization, our approach provides a key step towards miniaturization and scalability of atom-cavity systems., Comment: 5 pages, 4 figures

Within a dense environment ($\rho \approx 10^{14}\,$atoms/cm$^3$) at ultracold temperatures ($T < 1\,\mu{}\text{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ $^{87}$Rb Rydberg states and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at $n\approx 100$ for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities ($\rho\approx4.8\times 10^{14}\,\text{cm}^{-3}$), the lifetime of a Rydberg atom exceeds $10\,\mu\text{s}$ at $n > 140$ compared to $1\,\mu\text{s}$ at $n=90$. In addition, a second observed reaction mechanism, namely Rb$_2^+$ molecule formation, was studied. Both reaction products are equally probable for $n=40$ but the fraction of Rb$_2^+$ created drops to below 10$\,$% for $n\ge90$., Comment: 13 pages, 13 figures

The giant electro-optical response of Rydberg atoms manifests itself in the emergence of sidebands in the Rydberg excitation spectrum if the atom is exposed to a radio-frequency (RF) electric field. Here we report on the study of RF-dressed Rydberg atoms inside hollow-core photonic crystal fibres (HC-PCF), a system that enables the use of low modulation voltages and offers the prospect of miniaturised vapour-based electro-optical devices. Narrow spectroscopic features caused by the RF field are observed for modulation frequencies up to 500 MHz.

We present a pulsed four-wave mixing (FWM) scheme via a Rydberg state to create, store and retrieve collective Rydberg polaritons. The storage medium consists of a gas of thermal Rb atoms confined in a 220 {\mu}m thick cell, which are heated above room temperature. The experimental sequence consists of a pulsed excitation of Rydberg polaritons via the D1 line, a variable delay or storage time, and a final retrieval pulse via the D2 line. The lifetime of the Rydberg polaritons is around 1.2 ns, almost entirely limited by the excitation bandwidth and the corresponding motional dephasing of the atoms. The presented scheme combined with a tightly confined atomic ensemble is a good candidate for a deterministic single-photon source, as soon as strong interactions in terms of a Rydberg blockade are added., Comment: 5 pages, 3 figures

We report on time-resolved pulsed four-wave mixing (FWM) signals in a thermal Rubidium vapor involving a Rydberg state. We observe FWM signals with dephasing times up to 7 ns, strongly dependent on the excitation bandwidth to the Rydberg state. The excitation to the Rydberg state is driven by a pulsed two-photon transition on ns time scales. Combined with a third cw de-excitation laser, a strongly directional and collective emission is generated according to a combination of the phase matching effect and averaging over Doppler classes. In contrast to a previous report [1] using off-resonant FWM, at a resonant FWM scheme we observe additional revivals of the signal shortly after the incident pulse has ended. We infer that this is a revival of motion-induced constructive interference between the coherent emissions of the thermal atoms. The resonant FWM scheme reveals a richer temporal structure of the signals, compared to similar, but off-resonant excitation schemes. A simple explanation lies in the selectivity of Doppler classes. Our numerical simulations based on a four-level model including a whole Doppler ensemble can qualitatively describe the data., Comment: 6 pages, 4 figures

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segre in 1934, but a line shape which changes with the principal quantum number n. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet p-wave shape resonance in the Rydberg electron-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5x10^14 cm^-3, and therefore an inter-particle spacing of 1300 a0 within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion - neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, point-like particles, with binding energies associated with their ion-neutral separation, and good agreement is found., Comment: 5 pages, 4 figures

We present high-resolution spectroscopy of Rb$_\text{2}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. \cite{Anderson2014b}. Our experimental data enables the determination of the effective zero-energy singlet $s$-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$-wave contribution and all orders in the relative momentum $k$, and compare the obtained molecular binding energies to the experimental data.

In recent years several trading platforms appeared which provide a backtest engine to calculate historic performance of self designed trading strategies on underlying candle data. The construction of a correct working backtest engine is, however, a subtle task as shown by Maier-Paape and Platen (cf. arXiv:1412.5558 [q-fin.TR]). Several platforms are struggling on the correctness. In this work, we discuss the problem how the correctness of backtest engines can be verified. We provide models for candles and for intra-period prices which will be applied to conduct a proof of correctness for a given backtest engine if the here provided tests on specific model candles are successful. Furthermore, we hint to algorithmic considerations in order to allow for a fast implementation of these tests necessary for the proof of correctness., Comment: 15 pages, 6 figures; Keywords: backtest evaluation, historical simulation, trading system, candle chart, imperfect data, price model, correctness test, backtest correctness

We present a novel spectroscopic method for probing the \insitu~density of quantum gases. We exploit the density-dependent energy shift of highly excited {Rydberg} states, which is of the order $10$\MHz\,/\,1E14\,cm$^{\text{-3}}$ for \rubidium~for triplet s-wave scattering. The energy shift combined with a density gradient can be used to localize Rydberg atoms in density shells with a spatial resolution less than optical wavelengths, as demonstrated by scanning the excitation laser spatially across the density distribution. We use this Rydberg spectroscopy to measure the mean density addressed by the Rydberg excitation lasers, and to monitor the phase transition from a thermal gas to a Bose-Einstein condensate (BEC)., Comment: This paper omitted consideration of the p-wave shape resonance leading to an inaccurate understanding of the spectroscopic line broadening and ultimately the resolution with which low-n Rydberg atoms could be spatially localized. A thorough theoretical analysis of this data set is found now as arXiv:1607.01325, (to appear in JPhysB) and M. Schlagm\"uller et. al PRL 116 053001 (2016)

We investigate an integrated optical chip immersed in atomic vapor providing several waveguide geometries for spectroscopy applications. The narrow-band transmission through a silicon nitride waveguide and interferometer is altered when the guided light is coupled to a vapor of rubidium atoms via the evanescent tail of the waveguide mode. We use grating couplers to couple between the waveguide mode and the radiating wave, which allow for addressing arbitrary coupling positions on the chip surface. The evanescent atom-light interaction can be numerically simulated and shows excellent agreement with our experimental data. This work demonstrates a next step towards miniaturization and integration of alkali atom spectroscopy and provides a platform for further fundamental studies of complex waveguide structures., Comment: 5 pages, 4 figures

The transition from a few-body system to a many-body system can result in new length scales, novel collective phenomena or even in a phase transition. Such a threshold behavior was shown for example in 4He droplets, where 4He turns into a superfluid for a specific number of particles [1]. A particularly interesting question in this context is at which point a few-body theory can be substituted by a mean field model, i. e. where the discrete number of particles can be treated as a continuous quantity. Such a transition from two non-interacting fermionic particles to a Fermi sea was demonstrated recently [2]. In this letter, we study a similar crossover to a many-body regime based on ultralong-range Rydberg molecules [3] forming a model system with binary interactions., Comment: 5 pages, 3 figures

We demonstrate the use of an anodic bonding technique for building a vacuum tight vapor cell for the use of Rydberg spectroscopy of alkali atoms with thin film electrodes on the inside of the cell. The cell is fabricated by simultaneous triple stack glass-to-glass anodic bonding at 300{\deg}C. This glue-free, low temperature sealing technique provides the opportunity to include thin film electric feedthroughs. The pressure broadening is only limited by the vapor pressure of rubidium and the lifetime is at least four months with operating temperatures up to 230{\deg}C.

The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment., Comment: New J. Phys., accepted

We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using the Born-Oppenheimer approximation including s- and p-wave scattering, reproduces the measured binding energies. The calculated molecular wavefunctions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or anti-alignment with respect to the magnetic field axis., Comment: 10 pages and 8 figures including supplementary

The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose-Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure twobody interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas-Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples., Comment: 21 pages, 9 figures

The coupling of electrons to matter is at the heart of our understanding of material properties such as electrical conductivity. One of the most intriguing effects is that electron-phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, the basis for BCS superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate (BEC) and show that it can excite phonons and eventually set the whole condensate into a collective oscillation. We find that the coupling is surprisingly strong as compared to ionic impurities due to the more favorable mass ratio. The electron is held in place by a single charged ionic core forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size comparable to the dimensions of the BEC, namely up to 8 micrometers. In such a state, corresponding to a principal quantum number of n=202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects due to the electron exploring the wings of the BEC. Based on our results we anticipate future experiments on electron wavefunction imaging, investigation of phonon mediated coupling of single electrons, and applications in quantum optics., Comment: 4 pages, 3 figures and supplementary information

We demonstrate the use of electrically contacted vapor cells to switch the transmission of a probe laser. The excitation scheme makes use of electromagnetically induced transparency involving a Rydberg state. The cell fabrication technique involves thinfilm based electric feedthroughs which are well suited for scaling this concept to many addressable pixels like in flat panel displays.

We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, to high lying Rydberg states. The major part is dedicated to highly excited S-states of Rubidium, which feature an isotropic van-der-Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping., Comment: 23 pages, 22 figures, tutorial