Recoil corrections to the atomic decay rate are considered in the order of Zm/M . The expressions are treated exactly without any expansion over Z alpha. The expressions obtained are valid both for muonic atoms (for which they contribute on the level of a few percent in high Z ions) and for electronic atoms. Explicit results for Lyman-alpha transitions for low-Z of the order (Zm/M)(Z alpha)^2 are also presented.
We study a wide range of neutral atoms and ions suitable for ultra-precise atomic optical clocks with naturally suppressed black body radiation shift of clock transition frequency. Calculations show that scalar polarizabilities of clock states cancel each other for at least one order of magnitude for considered systems. Results for calculations of frequencies, quadrupole moments of the states, clock transition amplitudes and natural widths of upper clock states are presented.
With the development of microwave atomic clocks, the Zeeman shifts for the spectral lines of black-body radiation need to be investigated carefully. In this Letter, the frequency shifts of hyperfine splittings of atomic ground states due to the magnetic field of black-body radiation are reported. The relative frequency shifts of different alkali atoms and alkali-like ions, which could be candidates of microwave atomic clocks, were calculated. The results vary from $-0.977\times10^{-17}[T(K)/300]^{2}$ to $-1.947\times10^{-17}[T(K)/300]^{2}$ for different atoms considered. These results are cons…
Atoms constitute relatively simple many-body systems, making them suitable objects for developing an understanding of basic aspects of many-body physics. Photoabsorption spectroscopy is a prominent method to study the electronic structure of atoms and the inherent many-body interactions. In this article the impact of many-body effects on well-known spectroscopic features such as Rydberg series, Fano resonances, Cooper minima, and giant resonances is studied, and related many-body phenomena in other fields are outlined. To calculate photoabsorption cross sections the time-dependent configuratio…
We investigate black-body induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure and Lamb-shift induced black-body shifts are found to increase with the square of the nuclear charge number, whereas black-body shifts due to virtual transitions decrease with increasing nuclear charge as the fourth power of the nuclear charge. We also investigate the decay width acquired by the ground state of atomic hydrogen, due to interaction with black-body…
Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and descibe their solutions in Coulomb-Sturmian space representation. Although the system contains only long-range Coulomb interactions these equations allow us to reach solution by approximating only some auxiliary short-range type potentials. We outline the method for bound states and demonstrate its power in benchmark calculations. We can report a fast convergence in angular momentum channels.
Three-body resonances in atomic systems are calculated as complex-energy solutions of Faddeev-type integral equations. The homogeneous Faddeev-Merkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green's operator has been calculated as a contour integral of two-body Coulomb Green's matrices. This approximation casts the integral equation into a matrix equation and the complex energies are located as the complex zeros of the Fredholm determinant. We calculated resonances of the e-…
We study three-body recombination in an optically trapped ultracold gas of cesium atoms with precise magnetic control of the s-wave scattering length a. At large positive values of a, we measure the dependence of the rate coefficient on a and confirm the theoretically predicted scaling proportional to a^4. Evidence of recombination heating indicates the formation of very weakly bound molecules in the last bound energy level.
A black-body radiation (BBR) shifts of (nsnp ^3P_0) - (ns^2 ^1S_0) clock transition in divalent atoms Mg, Ca, Sr, and Yb are evaluated. A theory of multipolar BBR shifts is developed and its implications are discussed. At room temperatures, the resulting uncertainties in the BBR shifts are relatively large and substantially affect the projected 10^{-18} fractional accuracy of the optical-lattice-based clocks.
We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating…
The next-to-leading order black-body radiation(BBR) shift to atomic energy-levels, namely $ (Zα)^2αT^2/m $ correction, was studied by using the nonrelativistic quantum electrodynamics(NRQED). We also estimate the one-loop contribution of quadrupole and the two-loop contributions of BBR-shift of the thermal(real) photon. These corrections have not been investigated before. The order of magnitude BBR-shift indicates the one-loop contribution of quadrupole is stronger than the previous result. And the two-loop contribution of BBR-shift of the thermal(real) photon is tiny, but this next-to-leading…
We present a detailed study of the Flambaum-Ginges radiative potential method which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms, ions, and molecules over the range 10<=Z<=120, where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s, p, and d waves over the series of alkali atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many…
We have developed an efficient approach for treating low-dimensional few-body processes in confined geometry of atomic and hybrid atom-ion traps. It based on the split-operator method in 2D discrete-variable representation (DVR) suggested by V. Melezhik for integration of the few-dimensional time-dependent Schrödinger equation. We give a brief review of the application to resonant ultracold atomic processes and discuss our latest results on hybrid atomic-ion systems. Prospects for the application of the method in other hot problems of the physics of low-dimensional few-particle systems are als…
In this review we study the level of accuracy of the electronic wave functions which is necessary to describe properly the atomic effects during nuclear beta-decay. In the case of the beta- decay in the Li atom into Be+ ion we compare the numerical values of the transition probabilities from the S-, P-, D-low-lying states of the initial atom and final ion calculated using both Hylleraas-Configuration Interaction (Hy-CI) and Configuration Interaction (CI) with Slater orbitals wave functions. In addition using the CI method the transition probabilities from F, G, H and I low-lying states have be…
The effect of finite nuclear mass on the magnetic-dipole transition probabilities between fine-structure levels of the same term is investigated. Based on a rigorous QED approach a nonrelativistic formula for the recoil correction to first order in m_e/M is derived. Numerical results for transitions of experimental interest are presented.
Properties of some few-body systems which include one positively charged muon $μ^{+}$ and two electrons $e^{-}$ are discussed. In particular, we consider the negatively charged muonium ion Mu$^{-}$ (or $μ^{+} e^{-}_{2}$) and four-body MuPs (or $μ^{+} e^{-}_{2} e^{+}$) systems each of which has only one stable bound (ground) state. The problem of annihilation of the electron-positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is $Δ\approx$ 23.05758 $…
Corrections from Breit interaction to basic properties of atomic 133Cs are determined in the framework of third-order relativistic many-body perturbation theory. The corrections to energies, hyperfine-structure constants, off-diagonal hyperfine 6S-7S amplitude, and electric-dipole matrix elements are tabulated. It is demonstrated that the Breit corrections to correlations are comparable to the Breit corrections at the Dirac-Hartree-Fock level. Modification of the parity-nonconserving (PNC) 6S-7S amplitude due to Breit interaction is also evaluated; the resulting weak charge of $^{133}$Cs shows…
We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single $X$H molecular state when $X$ is one of the bosonic alkali atoms: $^7$Li, $^{23}$Na, $^{39}$K, $^{87}$Rb and $^{133}$Cs. As a result, the {\em only} recombination process is the one that leads to formation of $X$H molecules, H+H+$X$$\rightarrow$$X$H+H, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision induced dissociation as well as the elastic cross-s…
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P$_{3/2}$ level of the barium ion, with precision below $0.5\%$. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition pr…
The spectral properties of an interacting many-body system may display critical character and have potential applications in precision metrology. Here, we demonstrate such many-body enhanced metrology for microwave (MW) electric fields in a non-equilibrium Rydberg atomic gas. Near criticality the high sensitivity of Rydberg atoms to external MW electric fields, combined with many-body enhancement induces significant changes in the optical transmission. We quantify this behavior using the Fisher information. For continuous optical transmission at the critical point, the Fisher information is th…
We report an optical inelastic-wave-mixing-enhanced atomic magnetometry technique that results in nT-level magnetic field detection at temperatures compatible with the human body without magnetic shielding, zero-field compensation, or high-frequency modulated phase-locking spectroscopy. Using Gaussian magnetic pulses that mimic the transient magnetic field produced by an action potential on a frog's nerve, we demonstrate more than 300,000-fold (550-fold) enhancement of magneto-optical rotation signal power spectral-density (power amplitude) over the conventional single-beam $Λ-$scheme atomic m…
Manipulating expressions in many-body perturbation theory becomes unwieldily with increasing order of the perturbation theory. Here I derive a set of theorems for efficient simplification of such expressions. The derived rules are specifically designed for implementing with symbolic algebra tools. As an illustration, we count the numbers of Brueckner-Goldstone diagrams in the first several orders of many-body perturbation theory for matrix elements between two states of a mono-valent system.
Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} μ^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $μ^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} μ^{-} e^{-}$. In particular, we determine the hyperfine stru…
We study the excitation redistribution from cesium $7\mathrm{P}_{1/2}$ or $7\mathrm{P}_{3/2}$ to neighboring energy levels by Black Body Radiation (BBR) and inter atomic collisions using pump-probe spectroscopy inside a vapor cell. At low vapor densities we measure redistribution of the initial, velocity-selected, atomic excitation by BBR. This preserves the selected atomic velocities allowing us to perform high resolution spectroscopy of the $\mathrm{6D\rightarrow 7F}$ transitions. This transfer mechanism could also be used to perform sub-Doppler spectroscopy of the cesium highly-excited $\ma…
On the basis of general theoretical results developed previously in [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we analyze spontaneous decay of a single atom inside cold atomic clouds under conditions when the averaged interatomic separation is less or comparable with the wavelength of quasi resonant radiation. Beyond the decay dynamics we analyze shifts of resonance as well as distortion of the spectral shape of the atomic transition.
Spontaneous decay of an excited atomic state is a fundamental process that originates from the interaction between matter and vacuum modes of the electromagnetic field. The rate of decay can thus be engineered by modifying the density of final states of the joint atom-photon system. Imposing suitable boundary conditions on the electromagnetic field has been shown to alter the density of vacuum modes near the atomic transition, resulting in modified atomic decay rates. Here we report the first experimental demonstration of suppression of atomic radiative decay by reducing the density of availab…
Probabilities of various final states are determined numerically for a number of ß- decaying light atoms. In our evaluations of the final state probabilities we have used the highly accurate atomic wave functions constructed for each few-electron atom/ion. We also discuss an experimental possibility to observe negatively charged ions which form during the nuclear ß+ decays. High order corrections to the results obtained for ß+/- decays in few-electron atoms with the use of sudden approximation are considered.
The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transiti…
In dense atomic gases the interaction between transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged forces. Despite decades of research, a full understanding of this paradigmatic many-body problem is still lacking. Here, we put forward and explore a scenario in which a dense atomic gas is weakly excited by an off-resonant laser field. We develop the theory for describing such dressed many-body ensembles and show that collective excitations are responsible for the emergence of many-body interactions, i.e. effective potentials that …
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any specific order of the perturbation theory or to calculate similar terms in other areas of the many-body theory, like e.g. terms in the coupled-cluster equations. The use of the algorithm is illustrated by calculating the second and third order correlation corrections to the removal energies of electrons from the ground state of sodium, copper and gallium and by cal…
Pair collisions in atomic gases lead to decoherence and decay. Assuming that all the atoms in the gas are equally likely to collide one is led to consider Lindbladian of mean field type where the evolution in the limit of many atoms reduces to a single qudit Lindbladian with quadratic non-linearity. We describe three smoking guns for non-linear evolutions: Power law decay and dephasing rates; Dephasing rates that take a continuous range of values depending on the initial data and finally, anomalous flow of the Bloch ball towards a hemisphere.
We report on three-body recombination of a single trapped Rb^+ ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K_3 depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is…
Two-photon decay rates in simple atoms such as hydrogenlike systems represent rather interesting fundamental problems in atomic physics. The sum of the energies of the two emitted photons has to fulfill an energy conservation condition, the decay takes place via intermediate virtual states, and the total decay rate is obtained after an integration over the energy of one of the emitted photons. Here, we investigate cases with a virtual state having an energy intermediate between the initial and the final state of the decay process, and we show that due to non-uniform convergence, only a careful…
In Efimov physics, a three-body parameter (3BP), previously regarded as nonuniversal, uniquely defines bound and scattering properties of three particles. A universal 3BP, however, have been recently shown in experiments and theory in ultracold homonuclear gases. Our present study further predicts a universal 3BP for heteronuclear atomic systems near broad Feshbach resonances, and provides physical interpretations for its origin. We show that for a system composed of two light and one heavy atoms, the physical origin of the universal 3BP is similar to the homonuclear case while for systems com…
We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used as a predictor of spontaneous decay rates for one-electron atoms. The CE is constructed from the Fourier transform of the atomic probability density. For the hydrogen atom with degenerate states labeled with the principal quantum number n, we obtain a scaling law relating the n-averaged decay rates to the respective CE. The scaling law allows us to predict the n-averaged decay rate without relying …
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long-range, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio …
In the present paper by using Mathematica system a symbolic programming method for generation of the expressions of the expansion terms of atomic stationary perturbation theory (PT) is presented. For this purpose, the package named as NCoperators was developed. In producing the PT terms, this package accommodates the features of the Rayleigh-Schrödinger perturbation theory (RSPT), the second quantization method (SQR) and angular momentum theory (AMT). The package was built in such a way that it could be applicable in various areas of theoretical atomic spectroscopy. Many functions of the NCope…
Collective excitations (spinwaves) of long-lived atomic hyperfine states can be synthesized into a Bose-Hubbard model in momentum space. We explore many-body ground states and dynamics of a two-leg momentum-space lattice formed by two coupled hyperfine states. Essential ingredients of this setting are a staggered artificial magnetic field engineered by lasers that couple the spinwave states, and a state-dependent long-range interaction, which is induced by laser-dressing a hyperfine state to a Rydberg state. The Rydberg dressed two-body interaction gives rise to a state-dependent blockade in m…
Three-body recombination is a prime example of the fundamental interaction between three particles. Due to the complexity of this process it has resisted a comprehensive description. Experimental investigations have mainly focussed on the observation of corresponding loss rates without revealing information on the reaction products. Here, we provide the first general experimental study on the population distribution of molecular quantum states after three-body recombination in a non-resonant regime. We have developed a highly sensitive detection scheme which combines photoionization of the mol…
Systems of three particles show a surprising feature in their bound state spectrum: a series of geometrically scaled states, known as Efimov states. These states have not yet been observed directly, but many recent experiments show indirect evidence of their existence via the so-called recombination process. The theories that predict the Efimov states also predicts either resonant enhancement of the recombination process or suppression by destructive interference, depending on the sign of the interaction between the particles. The theories predict universal features for the Efimov states, for …
The one-loop correction and two-loop contribution to black-body radiation (BBR) shift are restudied. The S-matrix approach and nonrelativistic quantum electrodynamics (NRQED) are adopted in finite temperature case. The relativistic correction to one-loop BBR-shift has a $(Zα)^{2}αT^2/m$-order contribution. In the two-loop case, the pure thermal (real) photon part is too tiny to be detected; while the corrections induced by the thermal and virtual mixing diagram are at $(Zα)^{2}α^2 T^2/m$ order. We calculate the relativistic correction to one-loop BBR-shift in the ground state of hydrogen and i…
We study the modification of the atomic spontaneous emission rate, i.e. Purcell effect, of $^{87}$Rb in the vicinity of an optical nanofiber ($\sim$500 nm diameter). We observe enhancement and inhibition of the atomic decay rate depending on the alignment of the induced atomic dipole relative to the nanofiber. Finite-difference time-domain simulations are in quantitative agreement with the measurements when considering the atoms as simple oscillating linear dipoles. This is surprising since the multi-level nature of the atoms should produce a different radiation pattern, predicting smaller mod…
We present an alternative, univocal characterization of the continuous transition from atomic to molecular shape in the Coulomb system constituted by two identical particles and a third particle with the opposite charge, as the mass ratio of the particles varies. Applying a marginal-conditional exact factorization to a variationally optimized wavefunction, we construct a nonadiabatic potential energy surface for the relative motion between the single particle and each of the identical particles in the ground state. The transition is revealed through the evolution with the mass ratio of the top…
We address the microscopic origin of the universal three-body parameter that fixes the spectrum of three-atom systems in the Efimov regime. We identify it with the van der Waals two-body correlation, which causes the three-atom system to deform when the three atoms come within the distance of the van der Waals length, effectively preventing them from coming closer due to the kinetic-energy cost associated with this three-body deformation. This deformation mechanism explains the universal ratio of the scattering length at the triatomic resonance to the van der Waals length observed in several e…
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting p…
We benchmark three standard approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. These configuration-interaction calculations used up to $2 \times 10^8$ uncoupled basis states, equivalent to $ 10^7$ coupled basis states (configuration state functions.) Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approx…
We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $γ$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $κ$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty…
We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering len…
Strongly correlated many-body systems often display the emergence of simple patterns and regular behaviour of their global properties. Phenomena such as clusterization, collective motion and appearance of shell structures are commonly observed across different size, time, and energy scales in our universe. Although at the microscopic level their individual parts are described by complex interactions, the collective behaviour of these systems can exhibit strikingly regular patterns. This contribution provides an overview of the experimental signatures that are commonly used to identify the emer…
Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterise these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunabl…
