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Rydberg States of Two Valence Electron Atoms

Rydberg States of Two Valence Electron Atoms. W. E Cooke K.A. Safinya W. Sandner F. Gounand P. Pillet N. H. Tran R. Kachru R. R. Jones. Perturbations of bound Rydberg states Interactions with doubly excited states Autoionization Excitation of autoionizing states.

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Rydberg States of Two Valence Electron Atoms

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  1. Rydberg States of TwoValence Electron Atoms W. E Cooke K.A. Safinya W. Sandner F. Gounand P. Pillet N. H. Tran R. Kachru R. R. Jones

  2. Perturbations of bound Rydberg states Interactions with doubly excited states Autoionization Excitation of autoionizing states

  3. Effective quantum numbers of the Ba 6snd states near n=25 a Lu-Fano plot showing the perturbation of energy levels n=21 n=27

  4. The interaction with the 5d7d state perturbs the 6snd series 6snd 5d7d Higher lying levels are pushed up and lower lying ones pushed down.

  5. The properties of the 6snd states are also perturbed.

  6. The slope of the Lu-Fano plot gives the character of the states The squared amplitude ratio is given by the derivative of the Lu Fano plot

  7. It is a level crossing problem. large No interaction(----) small

  8. Effective quantum numbers of the Ba 6snd states near n=25 a Lu-Fano plot n=21 n=27 5d7d

  9. Both level shifts and perturbed lifetimes are due to the interaction of the Rydberg states with a state converging to a higher limit. They are related to autoionization above the limit White 1934

  10. The similarity of series perturbations to autoionization the phenomenon of Forced Autoionization-Sandner et al

  11. Forced Autoionization Sandner et al q=∞ q=0

  12. Spectra taken via paths A and B on zero field and 4.8 kV/cm Path A Path B q=∞ q=0

  13. Ba two electrons outside a closed shell Ba++ core Ba+ is isoelectronic to Cs, one electron outside the closed shell core, and the energy levels are similar. 6d 7s 6p 5d 6s Ba is simpler than He since the ion levels are nondegenerate.

  14. To each of these Ba+ levels we add the second electron, producing the energy levels shown below.

  15. We can write the Hamiltonian for the Ba atom, ignoring spin, as Where r1 and r2 are the positions of the two electrons, r12 is their separation, and f(r) Is the potential an electron feels from the Ba++ ion. As r→∞ f(r)→2/r. If we use only H0 the Schrodinger equation is separable. hydrogen Ba+

  16. Without the coupling between the electrons provided by H1 the excited states would only decay by radiative decay of each of the two electrons.

  17. We introduce the coupling between the electrons If r1 < r2 we can use f(r2)=2/r2 and write H1 as Interaction between the dipole of the core and the field from the outer electron Interaction between the quadrupole of the core and the field gradient from the outer electron

  18. H1 introduces the coupling, between states of the same parity and angular momentum, leading to both series perturbations and autoionization. 6s 6p The 6pnd state is coupled to the 6sεf and 6sεp continua by the dipole coupling. It is also coupled to continua by the quadrupole coupling, which we ignore for simplicity.

  19. Autoionization broadens a level coupled to a continuum The full width at half maximum is the autoionization rate There is also a phase shift of the continuum

  20. The autoionization rate is given by Fermi’s golden rule, for example, the Autoionization rate from the 6pnd state to the 6sεf continuum is The continuum state is normalized per unit energy. This expression is a product of an angular factor, of order 1, and two radial matrix elements From the latter we can see that the autoionization rates scale as 1/n3 The matrix element for the outer electron, 2, depends on the small r part of its wavefunction, which is why it has the 1/n3/2 scaling. Due to the centrifugal barrier which keeps high ℓ electrons from the core, autoionization rates fall rapidly with ℓ.

  21. A simple classical picture of autoionization Each time the Rydberg electron comes by the core it has a finite probability of superelastic scattering, deexciting the core from 6p to 6s and leaving with its energy The frequency with which the elecron comes to the core is 1/n3 The autoionization rate is thus proportional to 1/n3 How likely the outer electron is to deexcite the core on an orbit depends on the eccentricity of the orbit. Hence the ℓ dependence.

  22. Absorption spectrum of Barium ground state atoms, showing the autoionizing 6pns and 6pnd states converging to both the 6p1/2 and 6p3/2 limits.

  23. The spectrum is composed of odd, certainly not Lorentzian, shapes superimposed on a non zero background There are two interfering pathways to the continuum, direct continuum excitation and excitation of the autoionizing state. The result is a Fano profile. 6s6s

  24. There are two excitation amplitudes, to the broadened discrete state, and to the continuum, which are added, then squared, to obtain the transition probability. discrete amplitude 0 continuum Photon energy

  25. The ratio of the discrete to the continuum amplitudes is q, which defines the lineshape. The lineshapes are as shown. q=∞ and q=0 are Lorentzian Peaks and dips. Any other q results In the asymmetric Fano profiles shown. They are observed in many contexts.

  26. Excitation of Autoionizing states from the Rydberg states Isolated Core Excitation With the last laser the ion 6s-6p transition is excited The outer electron is a spectator. The Fano q parameter is infinity. Lorentzian lines

  27. We ignore the direct continuum excitation. Why? The 6s-6p transition is the strongest transition in the Ba+ ion. It is spread over the width of the 6p15d state, yielding a cross section of 10-13 cm2. The direct photoionization of the 15d state has a cross section of 10-22 cm2

  28. lasers Ion signal 0 1 Time (µs) detector ions atoms Field pulse lasers Detect the ions from the rapid decay of the autoionizing 6p15d state as the third laser frequency is swept.

  29. The result: a Lorentzian line centered on the 6p15d state It is straightforward to determine the width, 15 cm-1 and the energy. Two photon resonance due to third laser.

  30. By changing the bound nd state it is straightforward to confirm the 1/n3 dependence of the autoionization rate. Autoionization widths of the Ba 6pnd states

  31. It is straightforward to populate the low ℓ 6snℓ bound states to study their Autoionizing 6pnℓ analogues, but can we study the higher ℓ states as well? 6snp 6snd 6sns 6snℓ ? 6s6p 6s6s

  32. The Stark switching technique– excite a bound Stark state. Reduce the field Adiabatically to zero, producing the desired high ℓ 6snℓ state.-Freeman and Kleppner Field ramps lasers Ion signal 0 1 Time (µs) Pruvost et al, Jones

  33. Recordings of the 6s13ℓ to 6p1/213ℓ and 6s13ℓ to 6p3/213ℓ transitions for different ℓ Splitting of the 6p3/213ℓ states is due to the quadrupole interaction of H1 Pruvost et al

  34. Scaled Decay rates, n3Γ, in atomic units of the Ba 6p1/212ℓ states Showing the rapid decrease with ℓ Radiative decay rate of the 6p ion

  35. Simple time domain classical picture of autoionization If the probability of superelastic scattering per orbit is 60% you would expect in the time domain to see the population decay in linear segments, one per orbit, and the rate to decrease like a stairstep. Jones et al population time

  36. Excite atoms from the Ca 4snd State to the 4pn state with a fs laser Monitor the population by pumping 4pnd atoms to 4dnd with another fs laser And detecting 7.1 eV electrons

  37. The lines are at the Kepler periods Linear piecewise decay

  38. Can we use the core transition to manipulate bound Rydberg atoms? Yes, if we can avoid autoionization.

  39. The radiative decay rate is the decay rate of the Ba+ 6p state, 1.6x108 s-1. The autoionization rates decrease with n and ℓ 6p1/212ℓ decay rates 100 10 1 0.1 Autoionization Decay rate ℓ=10 radiative ℓ

  40. 6p1/228ℓ decay rates For high ℓ many excitations Possible without autoionization 10 1 0.1 0.01 autoionization ℓ=7 Decay rate radiative ℓ

  41. Cooling, trapping, and imaging of high n, high ℓ states using the core transition 6p1/228ℓ>10 493 nm 6s28ℓ>10

  42. Imaging an Interacting Rydberg Gas—Killian et al Rice Populate Sr 5s50s and drive the core transition ai 5p50ℓ 5p 5p50s Sr 493 nm wait 5s50s 5s50ℓ 5s fluorescence 5s5p Sr+ 5s5s

  43. Imaging an Interacting Rydberg Gas 3 ms Excitation 2 ms excitation Evolution time (ms) 0.6 2.9 5.1 7.3 Evolution time (ms) 0.6 2.9 5.1 7.3 • Penning ionization • Collisional l-mixing • electron-collision ionization • auto-ionization 5s50s1S0 5s50d1D2 5s 2P1/2 5s5p1P1 422 nm evolution time 5s21S0 5s 2S1/2 Sr neutral Ground State Sr+ ion or Sr Rydberg core Killian et al 3 mm

  44. Cooling or trapping of high n, high ℓ states using the core transition 6p1/228ℓ>10 493 nm 5d3/228ℓ>10 6s28ℓ>10 The autoioization rates of 6p1/228ℓ>10 and 5d3/228ℓ>10 states are similar. Radiative decay of the latter is 106 slower.

  45. Cooling, trapping, and imaging of high n, high ℓ states using the core transition 6p1/228ℓ>10 650 nm 493 nm 5d3/228ℓ>10 6s28ℓ>10 The autoioization rates of 6p1/228ℓ>10 and 5d3/228ℓ>10 states are similar. Radiative decay of the latter is 106 slower.

  46. Far off resonance trap based on ICE 6p15d Laser red detuned from 455 nm 6s15d

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