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Register a new userDescription of two-electron atoms with correct cusp conditions
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New sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Katos cusp conditions. The new functions are special linear combinations of Hylleraas- and/or Kinoshita-type terms. Standard variational calculation, leading to matrix eigenvalue problem, can be carried out to calculate the energies of the system. There is no need for optimization with constraints to satisfy the cusp conditions. In the numerical examples the ground state energy of the He atom is considered.
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Alkaline-earth-like~(AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states $|0rangle$ and $|1rangle$ are excited to Rydberg states $|rrangle$ with detuning $Delta$ and 0, respectively, where a MHz-scale detuning $Delta$ arises from a weak magnetic field on the order of 1~G. With a proper ratio between $Delta$ and $Omega$, the qubit state $|1rangle$ can be fully excited to the Rydberg state while $|0rangle$ remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.
The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state changes smoothly into a shape resonance as Z crosses the critical value. Using variational calculations combined with the complex coordinate rotation method, we study the energy and width of the resonance for Z textless{} Zc, thus providing direct evidence of the validity of this hypothesis. The variation of the resonance width with Z is found to be in good agreement with a model derived from analysis of the 1/Z perturbation series.
We report on kinematically complete measurements and ab initio non-perturbative calculations of double ionization of He and H2 by a single 800 eV circularly polarized photon. We confirm the quasifree mechanism of photoionization for H2 and show how it originates from the two-electron cusp in the ground state of a two-electron target. Our approach establishes a new method for mapping electrons relative to each other and provides valuable insight into photoionization beyond the electric-dipole approximation.
We study the electron-loss-to-continuum (ELC) cusp experimentally and theoretically by comparing the ionization of U$^{89+}$ projectiles in collisions with N$_2$ and Xe targets, at a beam energy of 75.91 MeV/u. The coincidence measurement between the singly ionized projectile and the energy of the emitted electron is used to compare the shape of the ELC cusp at weak and strong perturbations. A significant energy shift for the centroid of the electron cusp is observed for the heavy target of Xe as compared to the light target of N$_2$. Our results provide a stringent test for fully relativistic calculations of double-differential cross sections performed in the first-order approximation and in the continuum-distorted-wave approach.
We study an integrated silicon photonic chip, composed of several sub-wavelength ridge waveguides, and immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observe that the waveguide transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. Due to the enhanced electric field in the waveguide cladding, the atomic transition can be saturated at a photon number $approx$ 80 times less than a free-propagating beam case. The non-linearity of the atom-clad Si-waveguide is about 4 orders of magnitude larger than maximum achievable value in doped Si photonics. The measured spectra corroborate well with a generalized effective susceptibility model that includes the Casimir-Polder potentials, due to the dielectric surface, and the transient interaction between flying atoms and the evanescent waveguide mode. This work paves the way towards a miniaturized, low-power, and integrated hybrid atomic-photonic system compatible with CMOS technologies.
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