High-Resolution Continuous-Wave Laser Spectroscopy of Long-Lived Rydberg States in NO.

High-resolution continuous-wave (cw) laser spectroscopy of nitric oxide (NO) molecules has been performed to study and characterize the energy-level structure of and effects of electric fields on the high Rydberg states. The experiments were carried out with molecules flowing through a room temperature gas cell. Rydberg-state photoexcitation was implemented using the resonance enhanced (nl)X+ Σ+1←H Σ+2←A Σ+2←XΠ3/22 three-color three-photon excitation scheme. Excited molecules were detected by high-sensitivity optogalvanic methods. Detailed measurements were made of Rydberg states with principal quantum numbers n = 22 and 32 in the series converging to the lowest rotational and vibrational state of the NO+ cation. The experimental data were compared with the results of numerical calculations which provided insight into the orbital angular momentum character of the intermediate H 2Σ+ state, improved determinations of the nf and ng quantum defects, a bound on the magnitude of the nh quantum defect, and information on the decay rates of the nf and ng Rydberg states. These measurements represent a step-change in laser spectroscopic studies of high Rydberg states in small atmospheric molecules. They open opportunities for more detailed studies of slow decay processes of Rydberg NO molecules confined in electrostatic traps, the synthesis of ultralong range Rydberg bimolecules, and the development of optical methods for trace gas detection.

Observation of Vibrational Dynamics of Orientated Rydberg-Atom-Ion Molecules.

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 millivolts per centimeter, 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.

Dipolar physics: a review of experiments with magnetic quantum gases.

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Transient Density-Induced Dipolar Interactions in a Thin Vapor Cell.

We exploit the effect of light-induced atomic desorption to produce high atomic densities (n≫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 ≈ 1 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.

Observation of a molecular bond between ions and Rydberg atoms.

Atoms with a highly excited electron, called Rydberg atoms, can form unusual types of molecular bonds1-4. The bonds differ from the well-known ionic and covalent bonds5,6 not only by their binding mechanisms, but also by their bond lengths ranging up to several micrometres. Here we observe a new type of molecular ion based on the interaction between the ionic charge and a flipping-induced dipole of a Rydberg atom with a bond length of several micrometres. We measure the vibrational spectrum and spatially resolve the bond length and the angular alignment of the molecule using a high-resolution ion microscope7. As a consequence of the large bond length, the molecular dynamics is extremely slow. These results pave the way for future studies of spatio-temporal effects in molecular dynamics (for example, beyond Born-Oppenheimer physics).

Topological Quantum Critical Points in the Extended Bose-Hubbard Model.

The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results show that the topological critical points separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. The long-range order persists also at the topological critical points and explains the presence of localized edge states protected by a finite charge gap. Finally, we introduce a superresolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids.

Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.

Integrating two-photon nonlinear spectroscopy of rubidium atoms with silicon photonics.

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 ≈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 the 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.

Highly customized 1010†nm, ns-pulsed Yb-doped fiber amplifier as a key tool for on-demand single-photon generation.

The development of highly customized technical devices is a decisive feature of technically complex setups, as frequently observed in quantum experiments. This paper describes the development and realization of an Yb-doped all-fiber amplifier system designed for such a special application, more specifically, an on-demand single-photon source based on four-wave mixing with rubidium Rydberg atoms. The laser is capable of generating bandwidth-limited configurable nanosecond pulses up to peak powers of >100 W and with pulse repetition frequencies (PRF) between 50 Hz and 1 MHz at selectable wavelengths (1008-1024 nm). Especially the amplification of the 1010 nm reference seed at the lower edge of the amplification range for Yb-based fibers is challenging and tends to produce amplified spontaneous emission (ASE) at higher wavelengths. To achieve high ASE suppression, particularly at low pulse repetition frequencies, two acousto-optical modulators (AOM) are utilized both for pulse picking and for temporal filtering. The synchronization between pulse repetition frequency and AOM driver signal allows pulse amplitude fluctuations to be kept below 1%, while ASE is suppressed by at least 85 dB (PRF = 1 MHz) and 65 dB (PRF = 1 kHz).

The low-energy Goldstone mode in a trapped dipolar supersolid.

A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid1,2. Since the first prediction3 in the 1950s, experimental efforts to realize this state have focused mainly on helium, in which supersolidity remains unobserved4. Recently, supersolidity has also been studied in ultracold quantum gases, and some of its defining properties have been induced in spin-orbit-coupled Bose-Einstein condensates (BECs)5,6 and BECs coupled to two crossed optical cavities7,8. However, no propagating phonon modes have been observed in either system. Recently, two of the three hallmark properties of a supersolid-periodic density modulation and simultaneous global phase coherence-have been observed in arrays of dipolar quantum droplets9-11, where the crystallization happens in a self-organized manner owing to intrinsic interactions. Here we directly observe the low-energy Goldstone mode, revealing the phase rigidity of the system and thus proving that these droplet arrays are truly supersolid. The dynamics of this mode is reminiscent of the effect of second sound in other superfluid systems12,13 and features an out-of-phase oscillation of the crystal array and the superfluid density. This mode exists only as a result of the phase rigidity of the experimentally realized state, and therefore confirms the superfluidity of the supersolid.

A room-temperature single-photon source based on strongly interacting Rydberg atoms.

Tailored quantum states of light can be created via a transfer of collective quantum states of matter to light modes. Such collective quantum states emerge in interacting many-body systems if thermal fluctuations are overcome by sufficient interaction strengths. Therefore, ultracold temperatures or strong confinement are typically required. We show that the exaggerated interactions between Rydberg atoms allow for collective quantum states even above room temperature. The emerging Rydberg interactions lead both to suppression of multiple Rydberg state excitations and destructive interference due to polariton dephasing. We experimentally implemented a four-wave mixing scheme to demonstrate an on-demand single-photon source. The combination of glass cell technology, identical atoms, and operation around room temperature promises scalability and integrability. This approach has the potential for various applications in quantum information processing and communication.

Anisotropic Superfluid Behavior of a Dipolar Bose-Einstein Condensate.

We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of ^{162}Dy with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. This observation is compatible with an anisotropic critical velocity for the breakdown of dissipationless flow, which, in the spirit of the Landau criterion, can directly be connected to the anisotropy of the underlying dipolar excitation spectrum. In addition, the heating rate above this critical velocity reflects the same anisotropy. Our observations are in excellent agreement with simulations based on the Gross-Pitaevskii equation and highlight the effect of dipolar interactions on macroscopic transport properties, rendering dissipation anisotropic.

Scissors Mode of Dipolar Quantum Droplets of Dysprosium Atoms.

We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic field. By modulating the orientation of this magnetic field, we introduce a new spectroscopic technique for studying dipolar quantum droplets. This provides a precise probe for interactions in the system, allowing us to extract a background scattering length for ^{164}Dy of 69(4)a_{0}. Our results establish an analogy between quantum droplets and atomic nuclei, where the existence of the scissors mode is also only due to internal interactions. They further open the possibility to explore physics beyond the available theoretical models for strongly dipolar quantum gases.

Self-bound droplets of a dilute magnetic quantum liquid.

Self-bound many-body systems are formed through a balance of attractive and repulsive forces and occur in many physical scenarios. Liquid droplets are an example of a self-bound system, formed by a balance of the mutual attractive and repulsive forces that derive from different components of the inter-particle potential. It has been suggested that self-bound ensembles of ultracold atoms should exist for atom number densities that are 108 times lower than in a helium droplet, which is formed from a dense quantum liquid. However, such ensembles have been elusive up to now because they require forces other than the usual zero-range contact interaction, which is either attractive or repulsive but never both. On the basis of the recent finding that an unstable bosonic dipolar gas can be stabilized by a repulsive many-body term, it was predicted that three-dimensional self-bound quantum droplets of magnetic atoms should exist. Here we report the observation of such droplets in a trap-free levitation field. We find that this dilute magnetic quantum liquid requires a minimum, critical number of atoms, below which the liquid evaporates into an expanding gas as a result of the quantum pressure of the individual constituents. Consequently, around this critical atom number we observe an interaction-driven phase transition between a gas and a self-bound liquid in the quantum degenerate regime with ultracold atoms. These droplets are the dilute counterpart of strongly correlated self-bound systems such as atomic nuclei and helium droplets.

Observation of Quantum Droplets in a Strongly Dipolar Bose Gas.

Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here, we report on the observation of stable quantum droplets containing ∼800 atoms that are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations mechanically stabilize them against the mean-field collapse. We observe in addition the interference of several droplets indicating that this stable many-body state is phase coherent.

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.

Pulsed Rydberg four-wave mixing with motion-induced dephasing in a thermal vapor.

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 timescales. Combined with a 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 (Huber et al. in Phys Rev A 90: 053806, 2014) 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.

Observing the Rosensweig instability of a quantum ferrofluid.

Ferrofluids exhibit unusual hydrodynamic effects owing to the magnetic nature of their constituents. As magnetization increases, a classical ferrofluid undergoes a Rosensweig instability and creates self-organized, ordered surface structures or droplet crystals. Quantum ferrofluids such as Bose-Einstein condensates with strong dipolar interactions also display superfluidity. The field of dipolar quantum gases is motivated by the search for new phases of matter that break continuous symmetries. The simultaneous breaking of continuous symmetries such as the phase invariance in a superfluid state and the translational symmetry in a crystal provides the basis for these new states of matter. However, interaction-induced crystallization in a superfluid has not yet been observed. Here we use in situ imaging to directly observe the spontaneous transition from an unstructured superfluid to an ordered arrangement of droplets in an atomic dysprosium Bose-Einstein condensate. By using a Feshbach resonance to control the interparticle interactions, we induce a finite-wavelength instability and observe discrete droplets in a triangular structure, the number of which grows as the number of atoms increases. We find that these structured states are surprisingly long-lived and observe hysteretic behaviour, which is typical for a crystallization process and in close analogy to the Rosensweig instability. Our system exhibits both superfluidity and, as we show here, spontaneous translational symmetry breaking. Although our observations do not probe superfluidity in the structured states, if the droplets establish a common phase via weak links, then our system is a very good candidate for a supersolid ground state.