Coupling a single electron to a Bose–Einstein condensate

Rydberg-Atom Manipulation through Strong Interaction with Free Electrons

Optically trapped Rydberg atoms are a suitable platform to explore quantum many-body physics mediated by long-range atom-atom interactions that can be engineered through externally applied light fields. However, this approach is limited to dipole-allowed transitions and a spatial resolution of the order of the optical wavelength. Here, we theoretically investigate the interaction between free electrons and individual Rydberg atoms as an approach to induce nondipolar transitions with subnanometer spatial precision and a substantial degree of control over the final atomic states. We observe unity-order excitation probabilities produced by a single electron for suitably chosen combinations of electron energies and electron-beam distance to the atom. We further discuss free-electron-atom entanglement and atom-atom entanglement in combination with lateral shaping of the electron followed by postselection. Our results support free electrons as powerful tools to manipulate Rydberg atoms in previously inaccessible ways.

Observation of 1/k^{4}-Tails after Expansion of Bose-Einstein Condensates with Impurities

We measure the momentum density in a Bose-Einstein condensate (BEC) with dilute spin impurities after an expansion in the presence of interactions. We observe tails decaying as 1/k^{4} at large momentum k in the condensate and in the impurity cloud. These algebraic tails originate from the impurity-BEC interaction, but their amplitudes greatly exceed those expected from two-body contact interactions at equilibrium in the trap. Furthermore, in the absence of impurities, such algebraic tails are not found in the BEC density measured after the interaction-driven expansion. These results highlight the key role played by impurities when present, a possibility that had not been considered in our previous work [Chang et al., Phys. Rev. Lett. 117, 235303 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.235303]. Our measurements suggest that these unexpected algebraic tails originate from the nontrivial dynamics of the expansion in the presence of impurity-bath interactions.

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.

Exact Quasiparticle Properties of a Heavy Polaron in BCS Fermi Superfluids

We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using the exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson's orthogonality catastrophe that occurs in a noninteracting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum, and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the subgap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a nonmagnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.

Universal Aspects of a Strongly Interacting Impurity in a Dilute Bose Condensate

We study the properties of an impurity immersed in a weakly interacting Bose gas, i.e., of a Bose polaron. In the perturbatively tractable limit of weak impurity-boson interactions many of its properties are known to depend only on the scattering length. Here we demonstrate that for strong (unitary) impurity-boson interactions all quasiparticle properties of a heavy Bose polaron, such as its energy, its residue, its Tan's contact, and the number of bosons trapped nearby the impurity, depend on the impurity-boson potential via a single parameter characterizing its range.

Transport of a Single Cold Ion Immersed in a Bose-Einstein Condensate

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, allow 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. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter.

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.

Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems

We introduce a diagrammatic Monte Carlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

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.

Ionic Impurity in a Bose-Einstein Condensate at Submicrokelvin Temperatures

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 a 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 line shape 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.

Efimov States of Strongly Interacting Photons

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that, in suitably rescaled coordinates, the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the nonequilibrium, many-body regime.

Single-impurity-induced Dicke quantum phase transition in a cavity-Bose-Einstein condensate

We present a new generalized Dicke model, an impurity-doped Dicke model (IDDM), by the use of an impurity-doped cavity-Bose-Einstein condensate (BEC). It is shown that the impurity atom can induce Dicke quantum phase transition (QPT) from the normal phase to superradiant phase at a critic value of the impurity population. It is found that the impurity-induced Dicke QPT can happen in an arbitrary field-atom coupling regime while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens the possibility to realize the control of quantum properties of a macroscopic-quantum system (BEC) by using a microscopic quantum system (a single impurity atom).

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.

Quantum Dynamics of Ultracold Bose Polarons

We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.

Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate

The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ^{39}K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.

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.

Ultracold Long-Range Rydberg Molecules with Complex Multichannel Spectra

A generalized class of ultralong-range Rydberg molecules is predicted which consist of a multichannel Rydberg atom whose outermost electron creates a chemical bond with a distant ground state atom. Such multichannel Rydberg molecules exhibit favorable properties for laser excitation, because states exist where the quantum defect varies strongly with the principal quantum number. The resulting occurrence of near degeneracies with states of high orbital angular momentum promotes the admixture of low l into the high l deeply bound "trilobite" molecule states, thereby circumventing the usual difficulty posed by electric dipole selection rules. Such states also can exhibit multiscale binding possibilities that could present novel options for quantum manipulation.

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.

Giant Cross Section for Molecular Ion Formation in Ultracold Rydberg Gases

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

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.

Exotic topological density waves in cold atomic Rydberg-dressed fermions

Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogues in solid-state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here we study Rydberg-dressed atomic fermions in a three-dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed topological density wave phases. By varying the spatial range of the non-local interaction, we find various chiral density waves with spontaneous time-reversal symmetry breaking, whose quasiparticles form three-dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Our results suggest gapless fermionic states could exhibit far richer topology than previously expected.

Rydberg atomic gases have proven a fertile playground for exploring exotic phases of condensed matter systems. Here, Li and Das Sarma study Rydberg-dressed atomic fermions in a 3D optical lattice and find a series of mixed topological density wave phases having no analogue in conventional materials.

Molecular physics. Production of trilobite Rydberg molecule dimers with kilo-Debye permanent electric dipole moments

Permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions, and realization of strongly correlated many-body quantum systems. However, large molecular permanent electric dipole moments are challenging to realize experimentally. We report the observation of ultralong-range Rydberg molecules with bond lengths of ~100 nanometers and kilo-Debye permanent electric dipole moments that form when an ultracold ground-state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit. The electronic character of this hybrid class of "trilobite" molecules is dominated by degenerate Rydberg manifolds, making them difficult to produce by conventional photoassociation. We used detailed coupled-channel calculations to reproduce their properties quantitatively. Our findings may lead to progress in ultracold chemistry and strongly correlated many-body physics.

Giant Rydberg excitons in the copper oxide Cu2O

A highly excited atom having an electron that has moved into a level with large principal quantum number is a hydrogen-like object, termed a Rydberg atom. The giant size of Rydberg atoms leads to huge interaction effects. Monitoring these interactions has provided insights into atomic and molecular physics on the single-quantum level. Excitons--the fundamental optical excitations in semiconductors, consisting of an electron and a positively charged hole--are the condensed-matter analogues of hydrogen. Highly excited excitons with extensions similar to those of Rydberg atoms are of interest because they can be placed and moved in a crystal with high precision using microscopic energy potential landscapes. The interaction of such Rydberg excitons may allow the formation of ordered exciton phases or the sensing of elementary excitations in their surroundings on a quantum level. Here we demonstrate the existence of Rydberg excitons in the copper oxide Cu2O, with principal quantum numbers as large as n = 25. These states have giant wavefunction extensions (that is, the average distance between the electron and the hole) of more than two micrometres, compared to about a nanometre for the ground state. The strong dipole-dipole interaction between such excitons is indicated by a blockade effect in which the presence of one exciton prevents the excitation of another in its vicinity.

Single-photon transistor mediated by interstate Rydberg interactions

We report on the realization of an all-optical transistor by mapping gate and source photons into strongly interacting Rydberg excitations with different principal quantum numbers in an ultracold atomic ensemble. We obtain a record switch contrast of 40% for a coherent gate input with mean photon number one and demonstrate attenuation of source transmission by over ten photons with a single gate photon. We use our optical transistor to demonstrate the nondestructive detection of a single Rydberg atom with a fidelity of 0.72(4).

From molecular spectra to a density shift in dense Rydberg gases

In Rydberg atoms, at least one electron is excited to a state with a high principal quantum number. In an ultracold environment, this low-energy electron can scatter off a ground state atom allowing for the formation of a Rydberg molecule consisting of one Rydberg atom and several ground state atoms. Here we investigate those Rydberg molecules created by photoassociation for the spherically symmetric S-states. A step by step increase of the principal quantum number up to n=111 enables us to go beyond the previously observed dimer and trimer states up to a molecule, where four ground state atoms are bound by one Rydberg atom. The increase of bound atoms and the decreasing binding potential per atom with principal quantum number results finally in an overlap of spectral lines. The associated density-dependent line broadening sets a fundamental limit, for example, for the optical thickness per blockade volume in Rydberg quantum optics experiments.

Ultracold Rydberg atoms — atoms with highly excited electrons — can form molecules with ground state atoms. By tuning the principal quantum number of the Rydberg state, Gaj et al. study the transition from resolvable molecular lines to the mean shift regime, where indistinguishable lines form a band.

Alignment of D-state Rydberg molecules

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 a Fermi pseudopotential approach including s- and p-wave scattering terms, reproduces the measured binding energies. The calculated molecular wave functions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or antialignment with respect to the magnetic field axis.

Single-photon switch based on Rydberg blockade

All-optical switching is a technique in which a gate light pulse changes the transmission of a target light pulse without the detour via electronic signal processing. We take this to the quantum regime, where the incoming gate light pulse contains only one photon on average. The gate pulse is stored as a Rydberg excitation in an ultracold atomic gas using electromagnetically induced transparency. Rydberg blockade suppresses the transmission of the subsequent target pulse. Finally, the stored gate photon can be retrieved. A retrieved photon heralds successful storage. The corresponding postselected subensemble shows an extinction of 0.05. The single-photon switch offers many interesting perspectives ranging from quantum communication to quantum information processing.

Defect-induced supersolidity with soft-core bosons

More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev-Lifshitz-Chester scenario.

Ultrafast quantum random access memory utilizing single Rydberg atoms in a Bose-Einstein condensate

We propose a long-lived and rapidly accessible quantum memory unit, for which the operational Hilbert space is spanned by states involving the two macroscopically occupied hyperfine levels of a miscible binary atomic Bose-Einstein condensate and the Rydberg state of a single atom. It is shown that an arbitrary qubit state, initially prepared using a flux qubit, can be rapidly transferred to and from the trapped atomic ensemble in approximately 10 ns and with a large fidelity of 97%, via an effective two-photon process using an external laser for the transition to the Rydberg level. The achievable ultrafast transfer of quantum information therefore enables a large number of storage and retrieval cycles from the highly controllable quantum optics setup of a dilute ultracold gas, even within the typically very short flux qubit lifetimes of the order of microseconds.