Rydberg States Research Articles

Comment on "Localized and Delocalized States of a Diamine Cation: Resolution of a Controversy".

Since its appearance in [Cheng, X.; Zhang, Y.; Jónsson, E.; Jónsson, H.; Weber, P. M. Nat. Commun. 2016, 7, 11013] and recent re-investigation in [Gałyńska, M.; Ásgeirsson, V.; Jónsson, H.; Bjornsson, R. J. Phys. Chem. Lett., 2021, 12, 1250-1255], the dimethylpiperazine cation (DMP+) has generated considerable discussion and controversy in the scientific literature over the existence of stable, local energy minima in this molecular system. Specifically, prior assumptions that the Rydberg state and radical cation of DMP are similar have led to significant confusion and debate regarding the accuracy of various quantum chemistry methods and the existence of stable configurations of DMP+ itself. The purpose of this Viewpoint is to highlight recent studies that call into question the main findings in the previously mentioned works as well as present new CCSDT (Coupled-Cluster with Single, Double, and Triple excitations) calculations to finally bring closure to this controversy.

Double Resonance of Electromagnetically Induced Transparency of Rydberg Atom in Counter-Propagating Configuration

The double resonance phenomenon of EIT is studied through the ladder three-level Rydberg system. A probe laser with the wavelength λp=852.35 nm is used to coupling the ground state 6S1/2 to the middle state 6P3/2, and a coupling laser with the wavelength λc=509.08 nm is implemented to couple the state 6P3/2 to the Rydberg state 62D5/2. A special optical scheme is designed, in which the co-propagating and counter-propagating configurations are both used. As a result, the double resonance of electromagnetically induced transparency (EIT) with the Rydberg atom is observed. By comparing the distance between the double peaks, it is found that the double resonance phenomenon comes from the Doppler effect, and the distance between the two resonance peaks in the absorption spectrum is related to the detuning of the resonant lasers.

Room temperature single-photon terahertz detection with thermal Rydberg atoms

Single-photon terahertz (THz) detection is one of the most demanding technologies for a variety of fields and could lead to many breakthroughs. Although significant progress has been made in the past two decades, operating it at room temperature still remains a great challenge. Here, we demonstrate, for the first time, a room temperature THz detector at single-photon levels based on nonlinear wave mixing in thermal Rydberg atomic vapor. The low-energy THz photons are coherently upconverted to high-energy optical photons via a nondegenerate Rydberg state involved in a six-wave mixing process, and therefore, single-photon THz detection is achieved by a conventional optical single-photon counting module. The noise equivalent power of such a detector reaches 9.5 × 10−19 W/Hz1/2, which is more than four orders of magnitude lower than the state-of-the-art room temperature THz detectors. The optimum quantum efficiency of the whole-wave mixing process is about 4.3%, with 40.6 dB dynamic range, and the maximum conversion bandwidth is 172 MHz, which is all-optically controllable. The developed fast and continuous-wave single-photon THz detector at room temperature operation has a great potential for portability and chip-scale integration, and could be revolutionary for a wide range of applications in remote sensing, wireless communication, biomedical diagnostics, and quantum optics.

Implementation of time-dependent Hartree–Fock in real space

Abstract Time-dependent Hartree–Fock (TDHF) is one of the fundamental post-Hartree–Fock (HF) methods to describe excited states. In its Tamm-Dancoff form, equivalent to Configuration Interaction Singles, it is still widely used and particularly applicable to big molecules where more accurate methods may be unfeasibly expensive. However, it is rarely implemented in real space, mostly because of the expensive nature of the exact-exchange potential in real space. Compared to widely used Gaussian-type orbitals (GTO) basis sets, real space often offers easier implementation of equations and more systematic convergence of Rydberg states, as well as favorable scaling, effective domain parallelization, flexible boundary conditions, and ability to treat model systems. We implemented TDHF in the Octopus real-space code as a step toward linear-response hybrid time-dependent density-functional theory (TDDFT), other post-HF methods, and ensemble density-functional theory methods involving exact exchange. Calculation of HF’s non-local exact exchange is very expensive in real space. We overcome this limitation with Octopus’ implementation of Adaptively Compressed Exchange, and find the appropriate mixing scheme and starting point to complete the ground-state calculation in a practical amount of time, and thus enable TDHF. We compared our results to those from GTOs on a set of small molecules and confirmed close agreement of results, though with larger deviations than in the case of semi-local TDDFT. We find that convergence of TDHF demands a finer real-space grid than semi-local TDDFT. We also present the subtleties in benchmarking a real-space calculation against GTOs, relating to Rydberg and vacuum states.

Continuous broadband Rydberg receiver using AC Stark shifts and Floquet states

We demonstrate the continuous broadband microwave receivers based on AC Stark shifts and Floquet states of Rydberg levels in a cesium atomic vapor cell. The resonant transition frequency of two adjacent Rydberg states 78 S1/2 and 78 P1/2 is tuned based on AC Stark effect of 70 MHz radio frequency (RF) field that is applied outside the vapor cell. The use of the j=1/2 Rydberg states ensures that only a single mj sublevel is involved. The generated Rydberg Floquet states act to enhance the sensitivity of the AC-Stark-tuned states when the frequency is matched and further extend the bandwidths. We achieve microwave field measurements with over 1.172 GHz continuous frequency tuning and a sensitivity ranging from 280.2 nVcm−1Hz−1/2 to 14.6 μ Vcm−1Hz−1/2. The achieving of continuous frequency and high sensitivity microwave detection will promote the application of Rydberg receivers in the radar technique and wireless communication.

Rydberg electromagnetically induced transparency based laser lock to Zeeman sublevels with 0.6GHz scanning range.

We propose a technique for frequency locking a laser to the Zeeman sublevel transitions between the 5P3/2 intermediate and 32D5/2 Rydberg states in 87Rb. This method allows for continuous frequency tuning over 0.6GHz by varying an applied external magnetic field. In the presence of the applied field, the electromagnetically induced transparency (EIT) spectrum of an atomic vapor splits via the Zeeman effect according to the strength of the magnetic field and the polarization of the pump and probe lasers. We show that the 480nm pump laser, responsible for transitions between the Zeeman sublevels of the intermediate state and the Rydberg state, can be locked to the Zeeman-split EIT peaks. The short-term frequency stability of the laser lock is 0.15MHz, and the long-term stability is within 0.5MHz. The linewidth of the laser lock is ∼0.8 and ∼1.8MHz in the presence and absence of the external magnetic field, respectively. In addition, we show that in the absence of an applied magnetic field and adequate shielding, the frequency shift of the lock point has a peak-to-peak variation of 1.6MHz depending on the polarization of the pump field, while when locked to Zeeman sublevels, this variation is reduced to 0.6MHz. The proposed technique is useful for research involving Rydberg atoms, where large continuous tuning of the laser frequency with stable locking is required.

Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to∼40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

Double, triple, and quadruple magic wavelengths for cesium ground, excited, and Rydberg states

Double, triple, and quadruple magic wavelengths for cesium ground, excited, and Rydberg states

Observation of reversible conformational interconversion accompanied by 3p internal conversions in Rydberg-excited N,N-dimethylethylamine

Conformational dynamics has been well observed in the 3s Rydberg state of amines, whereas its observation in higher-energy, non-equilibrium 3p Rydberg states is very rare, especially for a reversible conformational transition that could compete with other non-adiabatic transitions. Herein, we report the observation of a reversible conformational interconversion phenomenon in the 3p Rydberg excited-state dynamics of N,N-dimethylethylamine (DMEA). Upon electronic excitation, a forward and backward interconversion between the initially prepared 3p_l and 3p_h conformers accompanied by 3p internal conversions occurs, resulting in a 3p_l/3p_h equilibrium ratio of 61 %/39 % within ∼1.5 ps. The ensuing parallel internal conversions from the 3p_l to 3s_l and 3p_h to 3s_h deposit about 1.80 eV of vibrational energy into the 3s state, enabling a fast conformational interconversion between the 3s_h and 3s_l conformers to proceed within ∼2.0 ps. The final 3s_l/3s_h equilibrium ratio was determined to be 76 %/24 %. This work presents a real-time observation of the entire conformational interconversion process initiating from the higher-energy 3p states and finally reaching an equilibrium on the lower-energy 3s state.

Resonant Raman Auger spectroscopy on transient core-excited Ne ions

Abstract Short-lived core-ionized neon atoms were investigated by measuring under resonant Raman conditions the Auger decay following the excitation of a second core electron into a Rydberg state. Making use of intense and narrow bandwidth x-ray free-electron laser pulses, the photoexcitation spectrum of the femtosecond-lived Ne+1s02s22p6np series was characterized. Energy position and lifetimes of the lower-lying Rydberg states were determined and the final state configurations following the decay of the Ne+1s02s22p63p double-core hole resonance were partially resolved.

N-changing population of Rydberg states by low-energy electron-Rydberg collisions.

Inelastic n-changing collisions play an important role in the evolution of Rydberg atoms into ultracold plasmas. However, for the initially intermediate n (n ∼ 40) Rydberg states, these collisions can hardly be observed due to the low electron temperature in ultracold plasmas. In this work, we designed an experimental scheme to facilitate collisions between free electrons at 1.5eV and intermediate n Rydberg atoms. Using the field ionization technique, we measured the state distributions resulting from the evolution of initially cold rubidium atoms in the 45P3/2 Rydberg state. The experimentally obtained probability of inelastic collisions excitation agrees well with the Monte Carlo simulation results. In addition, our experimental results indicate that the n-changing population induced by hot electrons is significant for lower nP Rydberg states. Our work plays a significant role in calculating the rates of electron-ion three-body recombination in ultracold plasmas.

Publisher Correction: Rydberg states of alkali atoms in atomic vapour as SI-traceable field probes and communications receivers

Publisher Correction: Rydberg states of alkali atoms in atomic vapour as SI-traceable field probes and communications receivers

Error-robust hybrid atom-photon entangling gate via Gaussian soft control

Hybrid atom-photon gates play an important role for the realization of a quantum interface capable of mapping atomic states to photons for communication across quantum networks. Here, we propose a feasible theoretical scheme for implementing a hybrid atom-photon controlled-Z gate between an atom and a microwave photon in a superconducting coplanar waveguide resonator based on the Gaussian soft control technique. The gate protocol employs a classical auxiliary field that induces an atomic transition between one state of the atomic qubit and Rydberg states for obtaining strong coupling of the atom and microwave resonator. By tailoring the amplitude of this field with Gaussian temporal modulation, the gate performances are improved in various aspects. Numerical simulations demonstrate that the controlled-Z gate based on Gaussian soft control is resilient to the variation of the atom-photon coupling strength and deviation in the gate time, and it is less sensitive to the Rydberg level shifts caused by stray electric fields.

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 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.

Rydberg-State Double-Well Potentials of Van der Waals Molecules

Recent progress in studies of Rydberg double-well electronic energy states of MeNg (Me = 12-group atom, Ng = noble gas atom) van der Waals (vdW) molecules is presented and analysed. The presentation covers approaches in experimental studies as well as ab initio-calculations of potential energy curves (PECs). The analysis is shown in a broader context of Rydberg states of hetero- and homo-diatomic molecules with PECs possessing complex ‘exotic’ structure. Laser induced fluorescence (LIF) excitation spectra and dispersed emission spectra employed in the spectroscopical characterization of Rydberg states are presented on the background of the diverse spectroscopic methods for their investigations such as laser vaporization–optical resonance (LV-OR), pump-and-probe methods, and polarization labelling spectroscopy. Important and current state-of-the-art applications of Rydberg states with irregular potentials in photoassociation (PA), vibrational and rotational cooling, molecular clocks, frequency standards, and molecular wave-packet interferometry are highlighted.

Quantum State-Dependent Fragmentation Dynamics of D2S Molecules Following Excitation at Wavelengths ∼ 129.1 and ∼ 139.1 nm.

The first high-resolution translational spectroscopy studies of D atom photoproducts following excitation to the Rydberg states of D2S are reported. Excitation at wavelengths λ ∼ 139.1 nm reveals an unusual 'inverse' isotope effect; the 1B1(3da1←2b1) Rydberg state of D2S predissociates much faster than its counterpart in H2S. This is attributed to accidental near resonance with a vibrationally excited level of a lower-lying, more heavily predissociated Rydberg state of D2S that boosts the probability of nonadiabatic coupling to the dissociation continuum with 1A″ symmetry. Excitation at λ ∼ 129.1 nm populates the 1B1(4da1←2b1) Rydberg state, which predissociates more slowly and allows the study of ways in which the branching into different quantum states of the SD products varies with the choice of parent excited (JKaKc) level. All excited parent levels yield both ground (X) and electronically excited (A) state SD fragments. The former are distributed over a wide range of rovibrational (v″, N″) levels, while the population of levels with low v' and high N' is favored in the latter. These trends reflect the topographies of the dissociative 1A″ (1A') potential energy surfaces that correlate with the respective dissociation limits. Rotational motion about the b-inertial axis in the excited state molecule increases the relative yield of SD(A) products, consistent with dissociation by rotationally (Coriolis-) induced coupling from the photoexcited Rydberg level to the 1A' continuum. Molecules excited to the rotationless (JKaKc = 000) level also yield some SD(A) products, however, confirming the operation of a rival fragmentation pathway wherein photoexcited molecules decay by initial vibronic coupling to the 1A″ continuum, with subsequent nonadiabatic coupling between the 1A″ and 1A' continua enabling access to the D + SD(A) limit.

Investigation on the vibrational relaxation and ultrafast electronic dynamics of S1 state in 2,4-difluoroanisole.

Intramolecular vibrational energy redistribution (IVR) has a profound impact on dynamic processes. We have studied two types of IVR processes, restricted and dissipative, and ultrafast dynamics of the S1 state of 2,4-difluoroanisole using time-resolved photoelectron spectroscopy and time-of-flight mass spectroscopy. The restricted IVR occurs in the intermediate regime of 219cm-1 vibrational level, and the dissipative IVR occurs in the statistical regime of 1200cm-1. The lifetimes of IVR processes are measured to be 90 and 11ps, respectively, depending on the internal energies of the S1 state and differ by a factor of eight. Similar subsequent dynamics were observed at two vibrational levels in the S1 state. The population undergoes IVR following the initial excitation and subsequently leaks into a triplet state, accompanied by intersystem crossing within ∼400ps followed by a slower nonradiative relaxation of the triplet state on the nanosecond time scale. Furthermore, the values of 3s and 3px Rydberg states of 2,4-difluoroanisole were experimentally determined to be 5.02 and 6.28eV.

Quadrupole Coupling of Circular Rydberg Qubits to Inner Shell Excitations.

Divalent atoms provide excellent means for advancing control in Rydberg atom-based quantum simulation and computing due to the second optically active valence electron available. Particularly promising in this context are circular Rydberg atoms, for which long-lived ionic core excitations can be exploited without suffering from detrimental autoionization. Here, we report the implementation of electric quadrupole coupling between the metastable 4D_{3/2} level and a very high-n (n=79) circular Rydberg qubit, realized in doubly excited ^{88}Sr atoms prepared from an optical tweezer array. We measure the kHz-scale differential level shift on the circular Rydberg qubit via beat-node Ramsey interferometry comprising spin echo. Observing this coupling requires coherent interrogation of the Rydberg states for more than 100 μs, which is assisted by tweezer trapping and circular state lifetime enhancement in a black-body radiation suppressing capacitor. Further, we find no noticeable loss of qubit coherence under continuous photon scattering on the ion core, paving the way for laser cooling and imaging of Rydberg atoms. Our results demonstrate access to weak electron-electron interactions in Rydberg atoms and expand the quantum simulation toolbox for optical control of highly excited circular state qubits via ionic core manipulation.

Slowing Down a Coherent Superposition of Circular Rydberg States of Strontium.

Rydberg alkaline earth atoms are promising tools for quantum simulation and metrology. When one of the two valence electrons is promoted to long-lived circular states, the second valence electron can be optically manipulated without significant autoionization. We harness this feature to demonstrate laser slowing of a thermal atomic beam of circular strontium atoms. By driving the main ion core 422nm wavelength resonance, we observe a velocity reduction of 50 m/s without significant autoionization. We also show that a superposition of circular states undergoes very weak decoherence during the cooling process, up to the scattering of more than 1000 photons. This robustness opens new perspectives for quantum simulations over long timescales with circular atoms, while simultaneously cooling their motional state. It makes it possible to mitigate the harmful effects of unavoidable heating due to spin-motion coupling during a quantum simulation.

Rydberg states of alkali atoms in atomic vapour as SI-traceable field probes and communications receivers

Rydberg states of alkali atoms in atomic vapour as SI-traceable field probes and communications receivers