High-lying Rydberg States Research Articles

Probing new physics using Rydberg states of atomic hydrogen

We consider the role of high-lying Rydberg states of simple atomic systems such as $^1$H in setting constraints on physics beyond the Standard Model. We obtain highly accurate bound states energies for a hydrogen atom in the presence of an additional force carrier (the energy levels of the Hellmann potential). These results show that varying the size and shape of the Rydberg state by varying the quantum numbers provides a way to probe the range of new forces. By combining these results with the current state-of-the-art QED corrections, we determine a robust global constraint on new physics that includes all current spectroscopic data in hydrogen. Lastly we show that improved measurements that fully exploit modern cooling and trapping methods as well as higher-lying states could lead to a strong, statistically robust global constraint on new physics based on laboratory measurements only.

Electron trapping in strong-field dissociative frustrated ionization of CO molecules

We experimentally investigate the laser-induced dissociative frustrated multiple ionization of CO molecules; in this process one of the released electrons does not escape to the continuum but is eventually trapped into high-lying Rydberg states of the outgoing positively charged nuclear fragments at the ends of the laser pulse, leading to the formation of neutral Rydberg fragments, i.e., ${\mathrm{C}}^{*}$ or ${\mathrm{O}}^{*}$. By measuring the ejected neutral Rydberg and ionic nuclear fragments as well as the freed electrons in coincidence, we trace the probability of electron trapping by different nuclear fragments and find that formation of ${\mathrm{C}}^{*}$ is preferred to ${\mathrm{O}}^{*}$. Furthermore, the electron trapping to one of the outgoing nuclear fragments of the breaking molecule can be steered by using a phase-controlled two-color laser pulse. Our results show that Rydberg fragments are more likely to be produced for CO molecules when they are exposed to a laser field pointing from C to O. This orientation-dependent asymmetric emission of the neutral Rydberg fragments is further confirmed in the multiple ionization of CO molecules by using a single-color elliptically polarized femtosecond laser pulse.

Electronic and vibrational relaxation dynamics of NH3 Rydberg states probed by vacuum-ultraviolet time-resolved photoelectron imaging.

Time-resolved dynamics of high-lying Rydberg states of ammonia (NH3) prepared by using a vacuum ultraviolet (VUV) pump (∼9.3 eV) and an ultraviolet (UV) probe (∼4.7 eV) pulse are reported using photoelectron imaging detection. After photoexcitation, two main features appear in the photoelectron spectrum with vertical binding energies of ∼1.8 eV and ∼3.2 eV and with distinctly different anisotropy parameters β of ∼1.3 and ∼0.7, respectively. This information allows the unambiguous assignment of the respective Rydberg states and disentangles the induced electronic and vibrational dynamics. The combination of velocity-map imaging with femtosecond VUV and UV pulses is shown to offer an attractive approach for studying the dynamics of high-lying Rydberg states of small molecules.

Measurements of single-state and state-ensemble lifetimes of high-lying Rb Rydberg levels

We demonstrate a hybrid method based on field ionization and state-selective de-excitation capable of measuring the lifetimes of high-lying Rydberg states. For nS Rydberg states of Rb atoms with principal quantum number $60\leq n\leq88$, we measure both the individual target state lifetimes and those of the ensemble of Rydberg states populated via black-body radiation-induced transitions. We find good overall agreement with numerical calculations of the expected lifetimes in both cases. However, for the target state lifetimes, we find a local deviation towards shorter lifetimes for states around $n=72$, which we interpret as a signature of a modified black-body spectrum in the finite volume in which our experiments take place.

Exploring nonequilibrium phases of the generalized Dicke model with a trapped Rydberg-ion quantum simulator

Trapped ions are a versatile platform for the investigation of quantum many-body phenomena, in particular for the study of scenarios where long-range interactions are mediated by phonons. Recent experiments have shown that the trapped ion platform can be augmented by exciting high-lying Rydberg states. This introduces controllable state-dependent interactions that are independent from the phonon structure. However, the many-body physics in this newly accessible regime is largely unexplored. We show that this system grants access to generalized Dicke model physics, where dipolar interactions between ions in Rydberg states drastically alter the collective non-equilibrium behavior. We analyze and classify the emerging dynamical phases and identify a host of non-equilibrium signatures such as multi-phase coexistence regions and phonon-lasing regimes. We moreover show how they can be detected and characterized through the fluorescence signal of scattered photons. Our study thus highlights new capabilities of trapped Rydberg ion systems for creating and detecting quantum non-equilibrium phases.

Image-Charge Detection of the Rydberg States of Surface Electrons on Liquid Helium.

We propose and experimentally demonstrate a new spectroscopic method, image-charge detection, for the Rydberg states of surface electrons on liquid helium. The excitation of the Rydberg states of the electrons induces an image current in the circuit to which the electrons are capacitively coupled. In contrast to the conventional microwave absorption measurement, this method makes it possible to resolve the transitions to high-lying Rydberg states of the surface electrons. We also show that this method can potentially be used to detect quantum states of a single electron, which would pave a way to utilize the quantum states of the surface electrons on liquid helium for quantum computing.

Probing Stark-induced nonlinear phase variation with opto-optical modulation

We extend the recently developed technique of opto-optical modulation (OOM) to probe state-resolved ac-Stark-induced phase variations of a coherently excited ensemble of helium atoms. In a joint experimental and theoretical study, we find that the spatial redirection of the resonant emission from the OOM process is different for the low-lying 1s2p state as compared with the higher-lying Rydberg states, and that this redirection can be controlled through the spatial characteristics of the infrared (IR) probe beam. In particular, we observe that the intensity dependence of the IR-induced Stark phase on the 1s2p emission is nonlinear, and that the phase accumulation changes sign for moderate intensities. Our results suggest that OOM, combined with precise experimental shaping of the probe beam, could be used to measure the Stark-induced phase shifts of excited states.

Microwave-to-optical conversion via four-wave mixing in a cold ytterbium ensemble

Interfacing superconducting qubits with optical photons requires noise-free microwave-to-optical transducers, a technology currently not realized at the single-photon level. We propose to use four-wave-mixing in an ensemble of cold ytterbium (Yb) atoms prepared in the metastable 'clock' state. The parametric process uses two high-lying Rydberg states for bidirectional conversion between a 10 GHz microwave photon and an optical photon in the telecommunication E-band. To avoid noise photons due to spontaneous emission, we consider continuous operation far detuned from the intermediate states. We use an input-output formalism to predict conversion efficiencies of $\approx50\%$ with bandwidths of $\approx100$ kHz.

Predissociation dynamics of D2 + hv→ D(1s1/2) + D(2p1/2,3/2, 2s1/2) revealed by the spin-orbit state resolved fragment branching ratios and angular distributions.

For molecular photodissociations, the spin-orbit state resolved fragment branching ratios and angular distributions provide deep insight into the dynamics. For the first excited state of the H(2p1/2,3/2) atom, a branching ratio measurement is a challenge because of small energy spacing between them. For the D(2p1/2,3/2) fragments from the predissociation of D2 + 14.76 eV → D(1s) + D(2s, 2p1/2,3/2) in the 2pπC1Πu (υ = 19) state, we made such measurements by pumping the D(2s, 2p1/2,3/2) fragments to high-lying Rydberg states that are subsequently ionized by a delayed-pulse electric field. In the 2pπC1Πu (υ = 19) state, the D2 molecule dissociates via both shape and Feshbach resonances correlating to the channels D(1s) + D(2p3/2) and D(1s) + D(2p1/2), respectively. The measured spin-orbit branching ratios, 2p3/2/(2p1/2 + 2p3/2), correspond to the diabatic limit, 2/3, which indicates strong spin-orbit state mixings near the dissociation limits. The spin-orbit state resolved fragment angular distributions also support the diabatic dissociation mechanism and illustrate simultaneous shape and Feshbach resonances for the R(0) transition.

Roton-induced trapping in strongly correlated Rydberg gases

Atoms excited into high-lying Rydberg states and under strong dipole-dipole interactions exhibit phenomena associated with highly correlated and complex systems. We perform first principles numerical simulations on the dynamics of such systems. The emergence of a roton minimum in the excitation spectrum, as expected in strongly correlated gases and accurately described by Feynman's theory of liquid helium, is shown to significantly inhibit particle transport, with a strong suppression of the diffusion coefficient, due to the emerging spatial order. We also demonstrate how the ability to temporally tune the interaction strength among Rydberg atoms can be used in order to overcome the effects of disorder induced heating, allowing the study of unprecedented highly coupled regimes.

A terahertz-driven non-equilibrium phase transition in a room temperature atomic vapour

There are few demonstrated examples of phase transitions that may be driven directly by terahertz frequency electric fields, and those that are known require field strengths exceeding 1 MV cm−1. Here we report a non-equilibrium phase transition driven by a weak (≪1 V cm−1), continuous-wave terahertz electric field. The system consists of room temperature caesium vapour under continuous optical excitation to a high-lying Rydberg state, which is resonantly coupled to a nearby level by the terahertz electric field. We use a simple model to understand the underlying physical behaviour, and we demonstrate two protocols to exploit the phase transition as a narrowband terahertz detector: the first with a fast (20 μs) non-linear response to nano-Watts of incident radiation, and the second with a linearised response and effective noise equivalent power ≤1 pW Hz−1/2. The work opens the door to a class of terahertz devices controlled with low-field intensities and operating in a room temperature environment.

Rydberg-Dressed Magneto-optical Trap.

We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at <1 μK. Simulations show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable long-range interactions.

Supersolidity of lattice bosons immersed in strongly correlated Rydberg dressed atoms

Recent experiments have illustrated that long range two-body interactions can be induced by laser coupling atoms to highly excited Rydberg states. Stimulated by this achievement, we study supersolidity of lattice bosons in an experimentally relevant situation. In our setup, we consider two-component atoms on a square lattice, where one species is weakly dressed to an electronically high-lying (Rydberg) state, generating a tunable, soft-core shape long-range interaction. Interactions between atoms of the second species and between the two species are characterized by local inter- and intra-species interactions. Using a dynamical mean-field calculation, we find that interspecies onsite interactions can stabilize a pronounced region of supersolid phases. This is characterized by two distinctive types of supersolids, where the bare species forms supersolid phases that are immersed in strongly correlated quantum phases, i.e. a crystalline solid or supersolid of the dressed atoms. We show that the interspecies interaction leads to a roton-like instability in the bare species and therefore is crucially important to the supersolid formation. We provide a detailed calculation of the interaction potential to show how our results can be explored under current experimental conditions.

Wavepacket dynamics of a Rydberg atom monitored by a pair of time-delayed laser pulses

We have investigated the Rydberg state population of an argon atom by an intense laser pulse and its wavepacket dynamics monitored by another successive laser pulse in the tunneling regime. A wavepacket comprising a superposition of close high-lying Rydberg states is irradiated by a multicycle laser pulse, where the sub-wave components in the wavepacket have fixed relative phases. A time-delayed second laser pulse is employed to apply on the excited Rydberg atom. If the time is properly chosen, one of the sub-wave components will be guided towards the ionization area while the rest remains intact. By means of this pump–probe technique, we could control and monitor the Rydberg wavepacket dynamics and reveal some interesting phenomenon such as the survival rate of individual Rydberg states related to the classical orbital period of electron.

Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms

Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density . This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density–density correlations.

Excitation of Rydberg wave packets in the tunneling regime

In the tunneling regime for strong laser field ionization of atoms, experimental studies have shown that a substantial fraction of atoms survive the laser pulse in many Rydberg states. To explain the origin of such trapping of population into Rydberg states, two mechanisms have been proposed: the first involves ac-Stark-shifted multiphoton resonances, and the second, called frustrated tunneling ionization, leads to the recombination of tunneled electrons into Rydberg states. We use a very accurate spectral method based on complex Sturmian functions to solve the time-dependent Schr\odinger equation for hydrogen in a linearly polarized infrared pulse and to calculate the tunneling probability in terms of the atomic ground-state width. We examine the probability of excitation into Rydberg states as a function of the peak intensity for various pulse durations and two wavelengths, 800 and 1800 nm, and we try to explain the results in light of the two aforementioned mechanisms. For long pulses of 800 nm wavelength, the extreme sensitivity of the trapping of population into high-lying Rydberg states to the peak intensity, the well-defined value, and parity of the angular momentum of the populated Rydberg states and the presence of Freeman resonances can be explained using a multiphotonic excitation mechanism. For strong pulses of 1800 nm wavelength, in the so-called adiabatic or quasistatic tunneling regime, the oscillations of the excitation probability as a function of intensity are in phase opposition to the ionization probability, and we observe a migration toward high values of the angular momentum with different distributions in the angular momentum at the maxima and minima of the oscillations. We also present a detailed study of how the excited-state wave packet builds up in time during the interaction of the atom with the pulse.

Localizing high-lying Rydberg wave packets with two-color laser fields

We demonstrate control over the localization of high-lying Rydberg wave packets in argon atoms with phase-locked orthogonally polarized two-color (OTC) laser fields. With a reaction microscope, we measured ionization signals of high-lying Rydberg states induced by a weak dc field and black-body radiation as a function of the relative phase between the two-color fields. We find that the dc-field ionization yields of high-lying Rydberg argon atoms oscillate with the relative two-color phase with a period of $2\pi$ while the photoionization signal by black-body radiation shows a period of $\pi$. These observations are a clear signature of the asymmetric localization of electrons recaptured into high-lying Rydberg states after conclusion of the laser pulse and are supported by a semiclassical simulation of argon-OTC laser interaction. Our findings thus open an effective pathway to control the localization of high-lying Rydberg wave packets.

Direct observation of a photochemical activation energy: a case study of acetone photodissociation

The ability to observe and quantify the conversion of electronic potential energy to vibrational kinetic energy in a molecule after photoexcitation is essential to understand and control the outcome of photoinduced molecular fragmentation. We exploit the high selectivity of photoelectron–photoion coincidence detection to distinguish different relaxation channels and observe the fragmentation behavior of each channel. We demonstrate the concept by investigating the fragmentation of gas-phase acetone molecules initiated by three-photon excitation to high lying Rydberg states between 9.0 and 9.5 eV above the ground state. By applying variations of the photon energy, pulse duration (100–200 fs) and pulse energy, we are able to fully characterize the fragmentation process. Rydberg states between 5s and 8s are populated, which undergo ultrafast internal conversion to lower states. The corresponding non-adiabatic dynamics in the neutral molecule cause the conversion of electronic to vibrational energy, leading to fragmentation. Our scheme allows us to directly measure the activation energy for fragmentation of acetone to an acetyl ion and a methyl radical, which we determine to be (0.79 ± 0.04) eV. Longer laser pulses result in an increased fragment-to-parent ratio, representing a higher probability for relaxation because the relaxation time constants are comparable to the pulse duration. Upon excitation to Rydberg states at 9.5 eV we surprisingly observe reduced fragmentation, although ∼2 eV are coupled into vibrational energy, indicating that different relaxation pathways become active, which results in a change of the redistribution of vibrational energy within the molecule. Fragmentation due to subsequent excitation of the cation is found to play a minor role.

Ultrafast α -CC bond cleavage of acetone upon excitation to 3p and 3d Rydberg states by femtosecond time-resolved photoelectron imaging.

The radiationless electronic relaxation and α -CC bond fission dynamics of jet-cooled acetone in the S1 (nπ*) state and in high-lying 3p and 3d Rydberg states have been investigated by femtosecond time-resolved mass spectrometry and photoelectron imaging. The S1 state was accessed by absorption of a UV pump photon at selected wavelengths between λ = 320 and 250 nm. The observed acetone mass signals and the S1 photoelectron band decayed on sub-picosecond time scales, consistent with a recently proposed ultrafast structural relaxation of the molecules in the S1 state away from the Franck-Condon probe window. No direct signatures could be observed by the experiments for CC dissociation on the S1 potential energy hypersurface in up to 1 ns. The observed acetyl mass signals at all pump wavelengths turned out to be associated with absorption by the molecules of one or more additional pump and/or probe photons. In particular, absorption of a second UV pump photon by the S1 (nπ*) state was found to populate a series of high-lying states belonging to the n = 3 Rydberg manifold. The respective transitions are favored by much larger cross sections compared to the S1 ← S0 transition. The characteristic energies revealed by the photoelectron images allowed for assignments to the 3p and 3dyz states. At two-photon excitation energies higher than 8.1 eV, an ultrafast reaction pathway for breaking the α -CC bond in 50-90 fs via the 3dyz Rydberg state and the elusive ππ* state was observed, explaining the formation of acetyl radicals after femtosecond laser excitation of acetone at these wavelengths.

Exotic quantum clusters and non-equilibrium dynamics of Rydberg excitations in one-dimensional optical lattices

In this mini-review, we report results from M. Mattioli, et al. [Phys. Rev. Lett. 111, 165302 (2013)], M. Dalmonte, et al. [Phys. Rev. B 92, 045106 (2015)] and M. Mattioli, et al. [New J. Phys. 17, 113039 (2015)], where it is shown that Rydberg atoms trapped in one-dimensional optical lattices are a useful tool to investigate the equilibrium phase diagram and the non-equilibrium dynamics of extended Hubbard models and Kinetically Constrained Models, respectively. Atoms weakly-dressed to an high-lying Rydberg state, which interact with a constant potential extended over several lattice sites, can be in an exotic quantum liquid state, the cluster Luttinger liquid phase [42, 43]. Furthermore, we show how a many-body model of interacting three-level atoms in the V-shaped configuration, where one of the level is a Rydberg state, might relax to equilibrium according to the same rules, so-called kinetic constraints, which are known to reproduce the characteristic dynamical arrest and separation of timescales of real glass-forming materials [62].