Microwave spectrometer for Rydberg state atoms: Last improvements

With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ (R < RF) this dependence transforms to the formula for electric dipole interaction energy ΔEd − d = C3/R3 and for R > RF it transforms to the formula for the van der Waals interaction energy ΔEVdW = −C6/R6. The van der Waals constant C6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J. The numerical values of the irreducible components of tensor C6 were calculated for rubidium atoms in the same Rydberg states |nlJM〉 with large quantum numbers n. We present the calculated resonance interaction energy of two rubidium atoms in the states |43D5/2M〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P3/2M〉 and of the other in the state |41F7/2M〉.

Rydberg states of atoms and molecules are very sensitive to electric fields. This property makes them ideal electric-field sensors but is detrimental to applications of Rydberg states in quantum optics, quantum-information processing, and quantum simulation because of inhomogeneous Stark broadening and the resulting loss of quantum coherence. We demonstrate, with the example of Rydberg states of 39K, the existence of Rydberg-Rydberg transitions with extremely small differential dc Stark shifts, which we call dc-field-magic Rydberg-Rydberg transitions. These transitions hardly exhibit any Stark broadening, even when the electric-field strength varies by as much as 10 V cm-1 over the experimental volume. We present a systematic study of dc-field-magic Rydberg-Rydberg transitions combining experiment and calculations and classify them in three main types, which should also be encountered in the other alkali-metal atoms, in alkaline-earth-metal atoms, and even in molecules. The observed insensitivity to dc electric fields does not reduce the interactions between Rydberg atoms, even if they are dominantly electric dipole-dipole in nature. Rydberg states coupled by dc-field-magic Rydberg-Rydberg transitions, therefore, have great potential as qubits.

New features of the blackbody-induced radiation processes on Rydberg atoms were discovered on the basis of numerical data for the blackbody-induced decay Pdnl(T), excitation Penl(T) and ionization Pionnl(T) rates of nS, nP and nD Rydberg states calculated together with the spontaneous decay rates Pspnl in neutral hydrogen, and singlet and triplet helium atoms for some values of the principal quantum number n from 10 to 500 at temperatures from T = 100 K to 2000 K. The fractional rates Rd(e, ion)nl(T) = Pnld(e, ion)(T)/Pspnl equal to the ratio of the induced decay (excitation, ionization) rates to the rate of spontaneous decay were determined as functions of T and n in every series of states with a given angular momentum l = 0, 1, 2. The calculated data reveal an essential difference between the asymptotic dependence of the ionization rate Pionnl(T) and the rates of decay and excitation Pd(e)nl(T)∝T/n2. The departures appear in each Rydberg series for n > 100 and introduce appreciable corrections to the formula of Cooke and Gallagher. Two different approximation formulae are proposed on the basis of the numerical data, one for Rd(e)nl(T) and another one for Rionnl(T), which reproduce the calculated values in wide ranges of principal quantum number from n = 10 to 1000 and temperatures between T = 100 K and T = 2000 K with an accuracy of 2% or better. Modified Fues' model potential approach was used for calculating matrix elements of bound–bound and bound–free radiation transitions in helium.

The Stark effect in molecular Rydberg states is qualitatively different from the Stark effect in atomic Rydberg states because of the anisotropy of the ion core and the existence of rotational and vibrational degrees of freedom. These uniquely molecular features cause the electric-field-induced decoupling of the Rydberg electron from the body frame to proceed in several stages in a molecule. Because the transition dipole moment among the same-n* Rydberg states is much larger than the permanent dipole moment of the ion core, the decoupling of the Rydberg electron from the ion core proceeds gradually. In the first stage, analyzed in detail in this paper, l and N are mixed by the external electric field, while N+ is conserved. In the further stages, as the external electric field increases, N+, n*, and v+ are expected to undergo mixing. We have characterized these stages in n*=13, v+=1 states of CaF. The large permanent dipole moment of CaF+ makes CaF qualitatively different from the other molecules in which the Stark effect in Rydberg states has been described (H2, Na2, Li2, NO, and H3) and makes it an ideal testbed for documenting the competition between the external and CaF+ dipole electric fields. We use the weak-field Stark effect to gain access to the lowest-N rotational levels of f, g, and h states and to assign their actual or nominal N+ quantum number. Lowest-N rotational levels provide information needed to disentangle the short-range and long-range interactions between the Rydberg electron and the ion core. We diagonalize an effective Hamiltonian matrix to determine the l-characters of the 3 < or = l < or = 5 core-nonpenetrating 2Sigma+ states and to characterize their mixing with the core-penetrating states. We conclude that the mixing of the l=4, N-N+=-4(g(-4)) state with lower-l 2Sigma+ states is stronger than documented in our previous multichannel quantum defect theory and long-range fits to zero-field spectra.

Ultrashort, nearly unipolar electric field pulses are used to produce novel dynamic states in Rydberg atoms. A single 500 fsec field pulse redistributes essentially all of the population from a single stationary Rydberg state to hundreds of different final states. The dynamic evolution of the nonstationary wave packet is monitored using a second, time-delayed pulse. The time-dependent momentum-space probability distribution of the wave packet can be retrieved experimentally using a classical impulse approximation.

The authors have studied phenomena related to the ionisation of indium Rydberg atoms by an external electric field. The indium atoms are excited in an atomic beam apparatus by pulsed dye laser light. The high-lying states are populated in one step from the ground state by an ultraviolet, frequency-doubled dye laser or by stepwise excitation using two dye lasers in the visible region. Shortly after the excitation, an electric field is applied in the interaction region which causes ionisation of the highly excited atoms. The authors have investigated (i) the lowest adiabatic ionisation threshold over a wide range of n values and compared the results with model predictions, (ii) the structure in the adiabatic part of the ionisation spectrum, and (iii) the transition from adiabatic to diabatic ionisation as a function of the slew rate of the ionising field pulse and the quantum defect and quantum numbers of the atomic state concerned. The ionisation signal is demonstrated to shift considerably towards higher field strengths with increasing slew rate. A qualitative explanation is presented and consequences for the detection efficiency are mentioned. Differences in the field ionisation behaviour between nearly degenerate excited states are demonstrated and exploited to achieve selective detection of fine-structure and even hyperfine-structure states.

One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr–Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus- and arsenic-doped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times—key to many well known schemes for quantum computing qubits—for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.

Application of laser induced photoemission electron in time-of-flight mass spectrometry

Uncontrollable sporadic distortions of global positioning system (GPS) satellite signals, caused by phase and group delays in the propagation of electromagnetic radiation through a medium, take place during periods of high solar activity and formation of geomagnetic disturbances in the Earth’s ionosphere. Determining ways of ensuring sustainability of GPS systems is a fundamental scientific and technical challenge.Above-background incoherent ultra-high frequency (UHF) radiation is formed at altitudes of the E and D layers of the Earth’s ionosphere. Wavelengths of this radiation correspond to a range from 1 dm to 1 mm. This emission is caused by transitions between Rydberg states of atoms and molecules, which are excited by electrons in plasma and are surrounded by a neutral particle environment. Reliable information about UHF radiation flux power in this wavelength range is not currently available. The answer to this question depends entirely on the knowledge of impact and radiation quenching of Rydberg state dynamics and the kinetics of their location in a lower ionosphere, i.e., on the quantum optical properties of a perturbed environment. Analysis of existing experimental data has shown that UHF radiation is formed in the atmospheric layer located at altitudes of 60–110 km. A physical mechanism of satellite signal delay is caused by cascade resonance re-emissions of electromagnetic waves in the decimeter range while passing through this layer over a set of Rydberg states. The most promising approach to studies of medium optical quantum properties can be a simultaneous analysis of background additional noise and GPS signal propagation time delay, which determines a positioning error. Using standard methods of noise measurement, one cannot detect physical and chemical processes responsible for noise formation and errors affecting positioning. Therefore, the problem can be solved if the level of a background noise is considered as a noise of the measured GPS signal because propagation delays of the latter are caused by one of the most important atmospheric collisional process, i.e., the orbital degeneracy of highly excited states. For this purpose, it is advisable to use the S/N ratio where a signal corresponds to a level of a signal obtained by the GPS receiver and a noise corresponds to a GPS signal fluctuation.In this chapter, a current state theory is examined, and manners of its further development are discussed. These are associated with the progress of theoretical methods for describing medium neutral particle impact effects on the dynamics of collision and radiation quenching focusing primarily on elementary processes involving molecules of nitrogen and oxygen. It has been shown that preliminary calculations of nonadiabatic transition dynamics between potential energy surfaces (PES) of Rydberg complexes, construction of appropriate electronic wave functions, calculations of allowed transition dipole moments, and determination of emission line shapes are necessary for the quantitative estimation of the influence of excited particles on a spectrum of incoherent UHF radiation of the atmosphere. These results should be included in the total kinetic scheme, which establishes the dependence of UHF radiation on temperature and density of the lower ionosphere. Then satellite-monitoring data of infrared (IR) radiation, which accompanies UHF radiation, can be directly used for the detection of Rydberg states and diagnostics of plasma parameters.KeywordsHighly excited states of atoms and moleculesD and Е layers of lower Earth’s ionosphereNeutral particles of mediumRydberg complexes l mixingNonequilibrium two-temperature plasmaUHF microwave radiation

We predict the possibility of ‘triply magic’ optical lattice trapping of neutral divalent atoms. In such a lattice, the and clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation out of the motional ground state as a result of the excitations between the clock and the Rydberg states. We also calculate trapping laser-induced photoionization rates of divalent Rydberg atoms at magic frequencies. We find that such rates are below the radiative spontaneous-emission rates, due to the presence of Cooper minima in photoionization cross-sections.

This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.

The atomic triply excited double Rydberg states (TEDRS) of La have been studied both experimentally and theoretically. It is revealed that in such an asymmetric four-body system where three electrons have very different orbital energies, the electronic correlations can be understood by means of decomposing into different dielectronic correlations that play different roles time-dependently. The correlations depend strongly on the relative excited orbital energies of three valence electrons. Our theoretical approach based on a semiclassical model is able to interpret the two observed patterns of ${\mathrm{La}}^{+}$ ion distributions among high Rydberg states resulted from the decay of TEDRS.

Cold Rydberg atoms, known for their long lifetimes and strong dipole-dipole interactions that lead to the Rydberg blockade phenomenon, are among the most promising platforms for quantum simulations, quantum computation and quantum networks. However, a major limitation to the performance of Rydberg atom-based platforms is dephasing, which can be caused by atomic motion within the trap. Here, we propose a trap for 87Rb cold atoms that confines both the electronic ground state and a Rydberg state, engineered to minimize the differential light shifts between the two states. This is achieved by combining a fictitious magnetic field induced by optical nanofiber (ONF) guided light and an external bias magnetic field. We calculate trap potentials for the cases of one- and two-guided modes with quasi-linear and quasi-circular polarizations, and calculate trap depths and trap frequencies for different values of laser power and bias fields. Moreover, we discuss the impact of the quadrupole polarisability of the Rydberg atoms on the trap potential and demonstrate how the size of a Rydberg atom influences the ponderomotive potential generated by the nanofiber-guided light field. This work expands on the idea of light-induced fictitious magnetic field traps and presents a practical approach for creating quantum networks using Rydberg atoms integrated with ONFs to generate 1D atom arrays.

Laser-controlled charge exchange is a promising method for producing cold antihydrogen. Caesium atoms in Rydberg states collide with positrons and create positronium. These positronium atoms then interact with antiprotons, forming antihydrogen. Laser excitation of the caesium atoms is essential to increase the cross section of the charge-exchange collisions. This method was demonstrated in 2004 by the ATRAP collaboration by using an available copper vapour laser. For a second generation of charge-exchange experiments we have designed a new semiconductor laser system that features several improvements compared to the copper vapour laser. We describe this new laser system and show the results from the excitation of caesium atoms to Rydberg states within the strong magnetic fields in the ATRAP apparatus.

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