From molecular spectra to a density shift in dense Rydberg gases

Universal terminal for cloud quantum computing

To bring the quantum computing capacities to the personal edge devices, the optimum approach is to have simple non-error-corrected personal devices that offload the computational tasks to scalable quantum computers via edge servers with cryogenic components and fault-tolerant schemes. Hence the network elements deploy different encoding protocols. This article proposes quantum terminals that are compatible with different encoding protocols; paving the way for realizing mobile edge-quantum computing. By accommodating the atomic lattice processor inside a cavity, the entangling mechanism is provided by the Rydberg cavity-QED technology. The auxiliary atom, responsible for photon emission, senses the logical qubit state via the long-range Rydberg interaction. In other words, the state of logical qubit determines the interaction-induced level-shift at the central atom and hence derives the system over distinguished eigenstates, featuring photon emission at the early or late times controlled by quantum interference. Applying an entanglement-swapping gate on two emitted photons would make the far-separated logical qubits entangled regardless of their encoding protocols. The proposed scheme provides a universal photonic interface for clustering the processors and connecting them with the quantum memories and quantum cloud compatible with different encoding formats.

Scalable quantum processors empowered by the Fermi scattering of Rydberg electrons

Quantum computing promises exponential speed-up compared to its classical counterpart. While the neutral atom processors are the pioneering platform in terms of scalability, the dipolar Rydberg gates impose the main bottlenecks on the scaling of these devices. This article presents an alternative scheme for neutral atom quantum processing, based on the Fermi scattering of a Rydberg electron from ground-state atoms in spin-dependent lattice geometries. Instead of relying on Rydberg pair-potentials, the interaction is controlled by engineering the electron cloud of a sole Rydberg atom. The present scheme addresses the scaling obstacles in Rydberg processors by exponentially suppressing the population of short-lived states and by operating in ultra-dense atomic lattices. The restoring forces in molecule type Rydberg-Fermi potential preserve the trapping over a long interaction period. Furthermore, the proposed scheme mitigates different competing infidelity criteria, eliminates unwanted cross-talks, and significantly suppresses the operation depth in running complicated quantum algorithms.

Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers

The preparation of light pulses with well-defined quantum properties requires precise control at the individual photon level. Here, we demonstrate exact and controlled multi-photon subtraction from incoming light pulses. We employ a cascaded system of tightly confined cold atom ensembles with strong, collectively enhanced coupling of photons to Rydberg states. The excitation blockade resulting from interactions between Rydberg atoms limits photon absorption to one per ensemble and rapid dephasing of the collective excitation suppresses stimulated re-emission of the photon. We experimentally demonstrate subtraction with up to three absorbers. Furthermore, we present a thorough theoretical analysis of our scheme where we identify weak Raman decay of the long-lived Rydberg state as the main source of infidelity in the subtracted photon number and investigate the performance of the multi-photon subtractor for increasing absorber numbers in the presence of Raman decay.

Interaction of photons with Rydberg atoms can be used to modify quantum states of light. Here the authors demonstrate a controlled nonlinear quantum behavior of multi-photon subtraction in a cascaded system based on Rydberg superatoms.

Dressed Ion-Pair States of an Ultralong-Range Rydberg Molecule

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than R_{∞}/2.

Rydberg-State-Resolved Resonant Energy Transfer in Cold Electric-Field-Controlled Intrabeam Collisions of NH3 with Rydberg He Atoms

The resonant transfer of energy from the inversion sublevels in NH₃ to He atoms in triplet Rydberg states with principal quantum number n = 38 has been controlled using electric fields below 15 V/cm in intrabeam collisions at translational temperatures of ∼1 K. The experiments were performed in pulsed supersonic beams of NH₃ seeded in He at a ratio of 1:19. The He atoms were prepared in the metastable 1s2s ³S₁ level in a pulsed electric discharge in the trailing part of the beams. The velocity slip between the heavy NH₃ and the lighter metastable He was exploited to perform collision studies at center-of-mass collision speeds of ∼70 m/s. Resonant energy transfer in the atom-molecule collisions was identified by Rydberg-state-selective electric-field ionization. The experimental data have been compared to a theoretical model of the resonant dipole-dipole interactions between the collision partners based on the impact parameter method.

Quantum Rydberg Central Spin Model

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron undergoes spin-changing collisions with surrounding atoms. This system realizes a new type of quantum impurity problems that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupling transformation with a Gaussian ansatz for the bath particles. We find several unexpected features of this model that are not present in traditional impurity problems, including interaction-induced renormalization of the absorption spectrum that eludes simple explanations from molecular bound states, and long-lasting oscillations of the Rydberg-electron spin. We discuss generalizations of our analysis to other systems in atomic physics and quantum chemistry, where an electron excitation of high orbital quantum number interacts with a spinful quantum bath.

Recovering the Homogeneous Absorption of Inhomogeneous Media

The resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened. Recovering the lost absorption cross section is of great importance for various applications of light-matter interactions, particularly in quantum optics, but no recovery mechanism has yet been identified and successfully demonstrated. Here, we formulate the limit set by the inhomogeneity on the absorption, and present a mechanism able to circumvent this limit and fully recover the homogeneous absorption of the ensemble. We experimentally study this mechanism using two different level schemes in atomic vapors and demonstrate up to fivefold enhancement of the absorption above the inhomogeneous limit. Our scheme relies on light shifts induced by auxiliary fields and is thus applicable to various physical systems and inhomogeneity mechanisms.

Effective Three-Body Interactions in Cs(6s)-Cs(nd) Rydberg Trimers

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs(nd_{3/2}) atoms. The anisotropy of the atomic Rydberg state allows for the formation of angular trimers, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers coexist with Rydberg dimers. The existence of such effective three-body interactions is confirmed with the observation of asymmetric line profiles and interpreted by a theoretical approach that includes relativistic spin interactions. Simulations of the observed spectra with and without angular trimer lines lend convincing support to the existence of effective three-body interactions.

Deterministic Free-Space Source of Single Photons Using Rydberg Atoms

We propose an efficient free-space scheme to create single photons in a well-defined spatiotemporal mode. To that end, we first prepare a single source atom in an excited Rydberg state. The source atom interacts with a large ensemble of ground-state atoms via a laser-mediated dipole-dipole exchange interaction. Using an adiabatic passage with a chirped laser pulse, we produce a spatially extended spin wave of a single Rydberg excitation in the ensemble, accompanied by the transition of the source atom to another Rydberg state. The collective atomic excitation can then be converted to a propagating optical photon via a coherent coupling field. In contrast to previous approaches, our single-photon source does not rely on the strong coupling of a single emitter to a resonant cavity, nor does it require the heralding of collective excitation or complete Rydberg blockade of multiple excitations in the atomic ensemble.

Ultracold Rydberg molecules

Ultracold molecules formed from association of a single Rydberg atom with surrounding atoms or molecules and those from double Rydberg excitations are discussed in this review. Ultralong-range Rydberg molecules possess a novel molecular bond resulting from scattering of the Rydberg electron from the perturber atoms or molecules. The strong interactions between Rydberg atoms in ultracold gases may lead to formation of macroscopic Rydberg macrodimers. The exquisite control over the properties of the Rydberg electron means that interesting and unusual few-body and quantum many-body features can be realized in such systems.

Rydberg molecules have been extensively studied both theoretically and experimentally. Here the authors review the recent developments in the study of various types of Rydberg molecules and their potential for future applications in spectroscopy, sensing and quantum information.

Rydberg Molecules for Ion-Atom Scattering in the Ultracold Regime

We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. The key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wave function, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initio calculations of the interaction potential. We demonstrate that, in the predicted bounds, the scattering length can be experimentally determined from the velocity of the scattered wave packet in the case of ^{6}Li^{+}-^{6}Li and from the molecular ion fraction in the case of ^{7}Li^{+}-^{7}Li. The proposed method to utilize Rydberg molecules for ultracold ion-atom scattering, here particularized for the lithium ion-atom system, is readily applicable to other ion-atom systems as well.

Photon Subtraction by Many-Body Decoherence

We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

Polyatomic Trilobite Rydberg Molecules in a Dense Random Gas

Trilobites are exotic giant dimers with enormous dipole moments. They consist of a Rydberg atom and a distant ground-state atom bound together by short-range electron-neutral attraction. We show that highly polar, polyatomic trilobite states unexpectedly persist and thrive in a dense ultracold gas of randomly positioned atoms. This is caused by perturbation-induced quantum scarring and the localization of electron density on randomly occurring atom clusters. At certain densities these states also mix with an s state, overcoming selection rules that hinder the photoassociation of ordinary trilobites.

Induced Cavities for Photonic Quantum Gates

Effective cavities can be optically induced in atomic media and employed to strengthen optical nonlinearities. Here we study the integration of induced cavities with a photonic quantum gate based on Rydberg blockade. Accounting for loss in the atomic medium, we calculate the corresponding finesse and gate infidelity. Our analysis shows that the conventional limits imposed by the blockade optical depth are mitigated by the induced cavity in long media, thus establishing the total optical depth of the medium as a complementary resource.

Quantum Zeno Suppression of Intramolecular Forces

We show that Born-Oppenheimer surfaces can intrinsically decohere, implying loss of coherence among constituent electronic basis states. We consider the example of interatomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultracold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoherence, a Zeno-like effect causes a complete cessation of interatomic forces. We finally show how short decohering pulses can controllably redistribute population between the different molecular energy surfaces.

Single-Photon Absorber Based on Strongly Interacting Rydberg Atoms

We report on the realization of a free-space single-photon absorber, which deterministically absorbs exactly one photon from an input pulse. Our scheme is based on the saturation of an optically thick medium by a single photon due to Rydberg blockade. By converting one absorbed input photon into a stationary Rydberg excitation, decoupled from the light field through fast engineered dephasing, we blockade the full atomic cloud and change our optical medium from opaque to transparent. We show that this results in the subtraction of one photon from the input pulse over a wide range of input photon numbers. We investigate the change of the pulse shape and temporal photon statistics of the transmitted light pulses for different input photon numbers and compare the results to simulations. Based on the experimental results, we discuss the applicability of our single-photon absorber for number resolved photon detection schemes or quantum gate operations.

Theory of Ultralong-Range Rydberg Molecule Formation Incorporating Spin-Dependent Relativistic Effects: Cs(6s)-Cs(np) as Case Study

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules that form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the Cs perturber atoms by including the full set of spin-resolved ^1,3 S_J and ^1,3 P_J scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet (S=1) spin states through Rydberg electron spin-orbit and ground state electron hyperfine interactions. Excellent agreement with observed data in Saßmannshausen et al. [Phys. Rev. Lett. 2015, 113, 133201] in line positions and profiles is obtained. We also determine the spin-dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules for which all of the relativistic contributions are accounted.

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.

Studying long-range interactions in the controlled environment of trapped ultracold gases can help our understanding of fundamental many-body physics. Here the authors excite a gas of Rydberg atoms with a ps laser pulse, demonstrating behaviour consistent with many-body correlations beyond mean-field.

Rydberg Molecule-Induced Remote Spin Flips

We have performed high resolution photoassociation spectroscopy of rubidium ultralong-range Rydberg molecules in the vicinity of the 25P state. Because of the hyperfine interaction in the ground state perturber atom, the emerging mixed singlet-triplet potentials contain contributions from both hyperfine states. We show that this can be used to induce remote spin flips in the perturber atom upon excitation of a Rydberg molecule. Furthermore, when the spin-orbit splitting of the Rydberg state is comparable to the hyperfine splitting in the ground state, the orbital angular momentum of the Rydberg electron is entangled with the nuclear spin of the perturber atom. Our results open new possibilities for the implementation of spin-dependent interactions for ultracold atoms in bulk systems and in optical lattices.

Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances

Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Förster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a fidelity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Förster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates.

Single photon level of light control is possible by using the effective interaction between single photons and Rydberg atoms. Here the authors utilized such interaction of Stark-tuned Forster resonances to boost the gain of a Rydberg single-photon transistor and perform high precision spectroscopy.

Dark High Density Dipolar Liquid of Excitons

The possible phases and the nanoscale particle correlations of two-dimensional interacting dipolar particles is a long-sought problem in many-body physics. Here we observe a spontaneous condensation of trapped two-dimensional dipolar excitons with internal spin degrees of freedom from an interacting gas into a high density, closely packed liquid state made mostly of dark dipoles. Another phase transition, into a bright, highly repulsive plasma, is observed at even higher excitation powers. The dark liquid state is formed below a critical temperature Tc ≈ 4.8 K, and it is manifested by a clear spontaneous spatial condensation to a smaller and denser cloud, suggesting an attractive part to the interaction which goes beyond the purely repulsive dipole-dipole forces. Contributions from quantum mechanical fluctuations are expected to be significant in this strongly correlated, long living dark liquid. This is a new example of a two-dimensional atomic-like interacting dipolar liquid, but where the coupling of light to its internal spin degrees of freedom plays a crucial role in the dynamical formation and the nature of resulting condensed dark ground state.

Mesoscopic Rydberg Impurity in an Atomic Quantum Gas

Giant impurity excitations are powerful probes for exploring new regimes of far out of equilibrium dynamics in few- and many-body quantum systems, and in situ observations of correlations. Motivated by recent experimental progress in spectroscopic studies of Rydberg excitations in ultracold atoms, we develop a new theoretical approach for describing multiscale dynamics of Rydberg excitations in quantum Bose gases. We find that the crossover from few- to many-body dynamics manifests in a dramatic change in spectral profile from resolved molecular lines to broad Gaussian distributions representing a superpolaronic state in which many atoms bind to the Rydberg impurity. We discuss signatures of this crossover in the temperature and density dependence of the spectra.

Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas

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 Segrè in 1934, but a line shape that 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 e^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14}  cm^{-3}, and therefore an interparticle spacing of 1300 a_{0} 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, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

Many-body decoherence dynamics and optimized operation of a single-photon switch

We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimized switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments (Nat. Commun. 7 12480) and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.

Phase-Imprinting of Bose-Einstein Condensates with Rydberg Impurities

We show how the phase profile of Bose-Einstein condensates can be engineered through its interaction with localized Rydberg excitations. The interaction is made controllable and long range by off-resonantly coupling the condensate to another Rydberg state with laser light. Our technique allows the mapping of entanglement generated in systems of few strongly interacting Rydberg atoms onto much larger atom clouds in hybrid setups. As an example we discuss the creation of a spatial mesoscopic superposition state from a bright soliton. Additionally, the phase imprinted onto the condensate using the Rydberg excitations is a diagnostic tool for the latter. For example, a condensate time-of-flight image would permit reconstructing the pattern of an embedded Rydberg crystal.

Microwaves Probe Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas

We show that microwave spectroscopy of a dense Rydberg gas trapped on a superconducting atom chip in the dipole blockade regime reveals directly the dipole-dipole many-body interaction energy spectrum. We use this method to investigate the expansion of the Rydberg cloud under the effect of repulsive van der Waals forces and the breakdown of the frozen gas approximation. This study opens a promising route for quantum simulation of many-body systems and quantum information transport in chains of strongly interacting Rydberg atoms.

Experimental characterization of singlet scattering channels in long-range Rydberg molecules

We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.