Lifetimes Of Rydberg States Research Articles

Doppler sensitivity and resonant tuning of Rydberg atom-based antennas

Radio frequency antennas based on Rydberg atom vapor cells can in principle reach sensitivities beyond those of any conventional wire antenna, especially at lower frequencies where very long wires are needed to accommodate the increasing wavelength. They also have other desirable features such as consisting of nonmetallic, hence lower profile, elements. This paper presents a detailed theoretical investigation of Rydberg antenna sensitivity, elucidating parameter regimes that could cumulatively lead to a sensitivity increase 2–3 orders of magnitude beyond that of currently tested configurations. The key insight is to optimally combine the advantages of two well-studied approaches: (i) three laser ‘2D star configuration’ setups that, when enhanced with increased laser power, to some degree compensate for atom motion-induced Doppler broadening, and (ii) resonant coupling between a pair of near-degenerate Rydberg levels, tuned via a local oscillator to the incident signal of interest. The advantage of the star setup is subtle because it only restores the overall sensitivity to the expected Doppler-limited value, compensating for additional significant off-resonance reductions where differently moving atom sub-populations destructively interfere with each other in the net signal. An additional unique advantage of local oscillator tuning is that it leads to vastly narrower line widths, as low as ∼10 kHz set by the intrinsic Rydberg state lifetimes, rather than the typical ∼10 MHz scale set by the core state lifetimes. Intuitively, with this setup the two Rydberg states may be tuned to act as an independent high-q cavity, a point of view supported by a study of the frequency-dependence of the antenna resonant response. There are a number of practical experimental advances, especially larger ∼1 cm laser beam widths, required to suppress various extrinsic line broadening effects and to fully exploit this ‘Rydberg superheterodyne’ response.

Calculation of the lifetimes for Rydberg states of Li by B-spline approach

Calculation of the lifetimes for Rydberg states of Li by B-spline approach

Long-Lived Circular Rydberg Qubits of Alkaline-Earth Atoms in Optical Tweezers

Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high-n (n=79) circular states of Sr88. We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the Sr+ core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion. Published by the American Physical Society 2024

Transition Probabilities, Oscillator Strengths and Line Strengths Result From Radiative Transitions

Abstract: The single-electron approximation and quantum defect theory have been used to study the spectral properties of radiative transitions in beryllium ions (Be II). A total of 6386 transitions of Be II have been investigated. The lifetime of nS, nP, nD, and nF Rydberg states of Be II (1s2 nl), for n up to 30, have been computed and compared with the available data. Most of the lifetimes are new. Transition probabilities, oscillator strengths, and line strengths of 6386 radiative transitions of Be II are being reported here. A Python program was developed to calculate the radial integral, and the same program was used to compute the corresponding expectation values < r >, ensuring the validity of the results. This extensive study provides a substantial dataset on spectral properties of radiative transitions in Be II, which holds valuable applications in various spectroscopic contexts. Keywords: Rydberg ion (atom), Radiative lifetimes, Oscillator strength, Transition probability, Rydberg energy, Beryllium ion.

Dynamical generation of chiral W and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers

Motivated by the significantly improved scalability of optically trapped neutral-atom systems, extensive efforts have been devoted in recent years to quantum-state engineering in Rydberg-atom ensembles. Here we investigate the problem of engineering generalized (``twisted'') $W$ states, as well as Greenberger-Horne-Zeilinger (GHZ) states, in the strongly interacting regime of a neutral-atom system. We assume that each atom in the envisioned system initially resides in its ground state and is subject to several external laser pulses that are close to being resonant with the same internal atomic transition. In particular, in the special case of a three-atom system (Rydberg-atom trimer) we determine configurations of field alignments and atomic positions that enable the realization of chiral $W$ states---a special type of twisted three-qubit $W$ states of interest for implementing noiseless-subsystem qubit encoding. Using chiral $W$ states as an example we also address the problem of deterministically converting twisted $W$ states into their GHZ counterparts in the same three-atom system, thus significantly generalizing recent works that involve only ordinary $W$ states. We show that starting from twisted---rather than ordinary---$W$ states is equivalent to renormalizing downward the relevant Rabi frequencies. While this leads to somewhat longer state-conversion times, we also demonstrate that those times are at least two orders of magnitude shorter than typical lifetimes of relevant Rydberg states.

All-optical Stückelberg spectroscopy of strongly driven Rydberg states

The AC Stark shift of electronic levels is ubiquitous in the interaction of intense light fields with atoms and molecules. As the light intensity changes on the rising and falling edges of a femtosecond laser pulse, it shifts the Rydberg states in and out of multiphoton resonances with the ground state. The two resonant pathways for transient excitation arising at the leading and the trailing edges of the pulse generate Young's type interference, generally referred to as the St\"uckelberg oscillations. Here we report the observation of the St\"uckelberg oscillations in the intensity of the coherent free-induction decay following resonant multiphoton excitation. Moreover, combining the experimental results with accurate numerical simulations and a simple model, we use the St\"uckelberg oscillations to recover the population dynamics of strongly driven Rydberg states inside the laser pulse by all-optical measurements after the end of the pulse. We demonstrate the potential of this spectroscopy to characterize lifetimes of Rydberg states dressed by laser fields with strengths far exceeding the Coulomb field between the Rydberg electron and the core.

Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms

We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C2Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C2Z gates.

Efficient microwave-to-optical single-photon conversion with a single flying circular Rydberg atom.

We propose a scheme for converting a microwave (mw) single photon in a mw cavity to a flying optical photon. The conversion is realized by using a flying circular Rydberg atom, which plays a role of the "data bus" as an excellent memory to connect the mw and optical cavities. To link the energy levels of atom in optical domain and mw domain, we use fast decircularization method and three-photon Raman transition method. Thank to these low loss processes and the super long lifetime of circular Rydberg states, this scheme can efficiently convert single mw photons into the optical domain. Based on existing experiments and data, the conversion efficiency is simulated as 60%. The theoretical limit of the conversion efficiency is about 87%.

Finite size cavity effect on nS rubidium Rydberg state lifetimes

In this work, we present lifetime measurements of nS states of Rb as a function of the principal quantum number (40 n 70) using a sample of cold atoms held in a magneto-optical trap, which is performed in a finite size metal vacuum chamber. The Rydberg states are excited through a two-photon transition, and detected by pulsed field ionization. Our measurements are larger than the predictions by well established theoretical model (1984 Phys. Rev. A 30 2881 and 2009 Phys. Rev. A 79 052504). We have implemented a theoretical model, which considers the vacuum chamber as a lossy Fabry–Perot cavity with a discrete spectrum, and compared with experimental results. Such comparison indicates that the blackbody radiation contribution on Rydberg state lifetime can be decreased by using a small size metal cavity, without the need of cryogenic environment. This effect may have application in experiments where longer Rydberg lifetimes are required.

Three-Dimensional Trapping of Individual Rydberg Atoms in Ponderomotive Bottle Beam Traps.

We demonstrate three-dimensional trapping of individual Rydberg atoms in holographic optical bottle beam traps. Starting with cold, ground-state ^{87}Rb atoms held in standard optical tweezers, we excite them to nS_{1/2}, nP_{1/2}, or nD_{3/2} Rydberg states and transfer them to a hollow trap at 850nm. For principal quantum numbers 60≤n≤90, the measured trapping time coincides with the Rydberg state lifetime in a 300K environment. We show that these traps are compatible with quantum information and simulation tasks by performing single qubit microwave Rabi flopping, as well as by measuring the interaction-induced, coherent spin-exchange dynamics between two trapped Rydberg atoms separated by 40 μm. These results will find applications in the realization of high-fidelity quantum simulations and quantum logic operations with Rydberg atoms.

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.

Scheme of a hydrogen-molecule quantum simulator based on two ultracold rubidium atoms

A scheme is proposed for implementing a hydrogen-molecule quantum simulator based on two ultracold rubidium atoms trapped into spatially separated optical dipole traps. The scheme includes the adiabatic preparation of the initial quantum state of two atoms and the iterative quantum phase estimation. The accuracy of measuring the ground state energy of a molecule is numerically calculated as a function of the number of iterations. The simulation is performed using two-qubit gates based on the dipole blockade effect under short-term excitation of atoms into the Rydberg states with allowance for the finite lifetime of Rydberg states and the finite energies of the van der Waals interaction.

Laser-stimulated deexcitation of Rydberg antihydrogen atoms

Antihydrogen atoms are routinely formed at CERN in a broad range of Rydberg states. Ground-state anti-atoms, those useful for precision measurements, are eventually produced through spontaneous decay. However given the long lifetime of Rydberg states the number of ground-state antihydrogen atoms usable is small, in particular for experiments relying on the production of a beam of antihydrogen atoms. Therefore, it is of high interest to efficiently stimulate the decay in order to retain a higher fraction of ground-state atoms for measurements. We propose a method that optimally mixes the high angular momentum states with low ones enabling to stimulate, using a broadband frequency laser, the deexcitation toward low-lying states, which then spontaneously decay to ground-state. We evaluated the method in realistic antihydrogen experimental conditions. For instance, starting with an initial distribution of atoms within the $n=20-30$ manifolds, as formed through charge exchange mechanism, we show that more than 80\% of antihydrogen atoms will be deexcited to the ground-state within 100 ns using a laser producing 2 J at 828 nm.

Transport on flexible Rydberg aggregates using circular states

Assemblies of interacting Rydberg atoms show promise for the quantum simulation of transport phenomena, quantum chemistry and condensed matter systems. Such schemes are typically limited by the finite lifetime of Rydberg states. Circular Rydberg states have the longest lifetimes among Rydberg states but lack the energetic isolation in the spectrum characteristic of low angular momentum states. The latter is required to obtain simple transport models with few electronic states per atom. Simple models can however even be realized with circular states, by exploiting dipole-dipole selection rules or external fields. We show here that this approach can be particularly fruitful for scenarios where quantum transport is coupled to atomic motion, in adiabatic excitation transport or quantum simulations of electron-phonon coupling in light harvesting. Additionally, we explore practical limitations of flexible Rydberg aggregates with circular states and to which extent interactions among circular Rydberg atoms can be described using classical models.

Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states

We study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically-driven Rabi oscillations between ground and Rydberg states of a single atom. Finite contrast is due to preparation and detection errors and we show how to model and measure them accurately. Part of these errors originates from the finite lifetime of Rydberg states and we observe its $n^3$-scaling with the principal quantum number $n$. To explain the damping of Rabi oscillations, we use simple numerical models, taking into account independently measured experimental imperfections, and show that the observed damping actually results from the accumulation of several small effects, each at the level of a few percents. We discuss prospects for improving the coherence of ground-Rydberg Rabi oscillations in view of applications in quantum simulation and quantum information processing with arrays of single Rydberg atoms.

High-fidelity Rydberg quantum gate via a two-atom dark state

We propose a two-qubit gate for neutral atoms in which one of the logical state components adiabatically follows a two-atom dark state formed by the laser coupling to a Rydberg state and a strong, resonant dipole-dipole exchange interaction between two Rydberg excited atoms. Our gate exhibits optimal scaling of the intrinsic error probability $E \propto (B\tau)^{-1}$ with the interatomic interaction strength $B$ and the Rydberg state lifetime $\tau$. Moreover, the gate is resilient to variations in the interaction strength, and even for finite probability of double Rydberg excitation, the gate does not excite atomic motion and experiences no decoherence due to internal-translational entanglement.

Two-way interconversion of millimeter-wave and optical fields in Rydberg gases

We show that cold Rydberg gases enable an efficient six-wave mixing process where terahertz or microwave fields are coherently converted into optical fields and vice versa. This process is made possible by the long lifetime of Rydberg states, the strong coupling of millimeter waves to Rydberg transitions and by a quantum interference effect related to electromagnetically induced transparency. Our frequency conversion scheme applies to a broad spectrum of millimeter waves due to the abundance of transitions within the Rydberg manifold, and we discuss two possible implementations based on focussed terahertz beams and millimeter wave fields confined by a waveguide, respectively. We analyse a realistic example for the interconversion of terahertz and optical fields in rubidium atoms and find that the conversion efficiency can in principle exceed 90%.

UV + V UV double-resonance studies of autoionizing Rydberg states of the hydroxyl radical.

The hydroxyl radical (OH) is a key oxidant in atmospheric and combustion chemistry. Recently, a sensitive and state-selective ionization method has been developed for detection of the OH radical that utilizes UV excitation on the A(2)Σ(+)-X(2)Π transition followed by fixed 118 nm vacuum ultraviolet (VUV) radiation to access autoionizing Rydberg states [J. M. Beames et al., J. Chem. Phys. 134, 241102 (2011)]. The present study uses tunable VUV radiation generated by four-wave mixing to examine the origin of the enhanced ionization efficiency observed for OH radicals prepared in specific A(2)Σ(+) intermediate levels. The enhancement is shown to arise from resonant excitation to distinct rotational and fine structure levels of two newly identified (2)Π Rydberg states with an A(3)Π cationic core and a 3d electron followed by ionization. Spectroscopic constants are derived and effects due to uncoupling of the Rydberg electron are revealed for the OH (2)Π Rydberg states. The linewidths indicate a Rydberg state lifetime due to autoionization on the order of a picosecond.

Lifetimes of Rydberg states of Eu atoms**Project supported by the National Natural Science Foundation of China (Grant No. 11174218).

The radiative lifetimes of the Eu 4f76snp (8PJ or 10PJ) Rydberg states with J = 5/2 and 11/2 are investigated with a combination of multi-step laser excitation and pulsed electric field ionization, from which their dependence on the effective principal quantum number is observed. The lifetimes of 21 states are reported along with an evaluation of their experimental uncertainty. The influence of blackbody radiation, due to the oven temperature, on the lifetime of the higher-n states is detected. The non-hydrogen behavior of the investigated states is also observed.

Lifetimes of Rydberg states in ions of the group II elements

Total probabilities Anl of spontaneous radiative transitions, which determine lifetimes τnl = 1/Anl of nS-, nP-, nD- and nF-states in singly charged ions of the group IIa (Be+, Mg+, Ca+, Sr+, Ba+) and IIb (Zn+, Cd+, Hg+) elements, were calculated in the single-electron Fues’ model potential (FMP) method. An asymptotic dependence is determined for highly excited states with small angular momentums and presented in the form τnl = τl(0)n3Ql(1/n) and numerical values of the factors τl(0) and coefficients of the cubic polynomial Ql(x) are calculated, which approximate results of numerical computations with relative error below 2% in the range of states with principal quantum numbers from n = 7 to n ≈ 2000. The comparison of the numerical results with data in literature is presented, and applicability and reliability of single-electron model calculations are discussed in detail for positive singly charged ions of the group II elements.