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Title: XUV frequency-comb metrology on the ground state of helium

Abstract

The operation of a frequency comb at extreme ultraviolet (xuv) wavelengths based on pairwise amplification and nonlinear upconversion to the 15th harmonic of pulses from a frequency-comb laser in the near-infrared range is reported. It is experimentally demonstrated that the resulting spectrum at 51 nm is fully phase coherent and can be applied to precision metrology. The pulses are used in a scheme of direct-frequency-comb excitation of helium atoms from the ground state to the 1s4p and 1s5p {sup 1} P{sub 1} states. Laser ionization by auxiliary 1064 nm pulses is used to detect the excited-state population, resulting in a cosine-like signal as a function of the repetition rate of the frequency comb with a modulation contrast of up to 55%. Analysis of the visibility of this comb structure, thereby using the helium atom as a precision phase ruler, yields an estimated timing jitter between the two upconverted-comb laser pulses of 50 attoseconds, which is equivalent to a phase jitter of 0.38 (6) cycles in the xuv at 51 nm. This sets a quantitative figure of merit for the operation of the xuv comb and indicates that extension to even shorter wavelengths should be feasible. The helium metrology investigation resultsmore » in transition frequencies of 5 740 806 993 (10) and 5 814 248 672 (6) MHz for excitation of the 1s4p and 1s5p {sup 1} P{sub 1} states, respectively. This constitutes an important frequency measurement in the xuv, attaining high accuracy in this windowless part of the electromagnetic spectrum. From the measured transition frequencies an eight-fold-improved {sup 4}He ionization energy of 5 945 204 212 (6) MHz is derived. Also, a new value for the {sup 4}He ground-state Lamb shift is found of 41 247 (6) MHz. This experimental value is in agreement with recent theoretical calculations up to order m{alpha}{sup 6} and m{sup 2}/M{alpha}{sup 5}, but with a six-times-higher precision, therewith providing a stringent test of quantum electrodynamics in bound two-electron systems.« less

Authors:
; ; ; ;  [1]
  1. LaserLaB Amsterdam, VU University, De Boelelaan 1081, NL-1081HV Amsterdam (Netherlands)
Publication Date:
OSTI Identifier:
22095604
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 84; Journal Issue: 6; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; AMPLIFICATION; ATOMS; ELECTRONS; EXCITATION; EXCITED STATES; EXTREME ULTRAVIOLET RADIATION; FREQUENCY MEASUREMENT; GROUND STATES; HELIUM; HELIUM 4; IONIZATION; LAMB SHIFT; MHZ RANGE; MODULATION; NONLINEAR PROBLEMS; P STATES; QUANTUM ELECTRODYNAMICS

Citation Formats

Kandula, Dominik Z., Gohle, Christoph, Pinkert, Tjeerd J., Ubachs, Wim, and Eikema, Kjeld S. E.. XUV frequency-comb metrology on the ground state of helium. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.062512.
Kandula, Dominik Z., Gohle, Christoph, Pinkert, Tjeerd J., Ubachs, Wim, & Eikema, Kjeld S. E.. XUV frequency-comb metrology on the ground state of helium. United States. doi:10.1103/PHYSREVA.84.062512.
Kandula, Dominik Z., Gohle, Christoph, Pinkert, Tjeerd J., Ubachs, Wim, and Eikema, Kjeld S. E.. 2011. "XUV frequency-comb metrology on the ground state of helium". United States. doi:10.1103/PHYSREVA.84.062512.
@article{osti_22095604,
title = {XUV frequency-comb metrology on the ground state of helium},
author = {Kandula, Dominik Z. and Gohle, Christoph and Pinkert, Tjeerd J. and Ubachs, Wim and Eikema, Kjeld S. E.},
abstractNote = {The operation of a frequency comb at extreme ultraviolet (xuv) wavelengths based on pairwise amplification and nonlinear upconversion to the 15th harmonic of pulses from a frequency-comb laser in the near-infrared range is reported. It is experimentally demonstrated that the resulting spectrum at 51 nm is fully phase coherent and can be applied to precision metrology. The pulses are used in a scheme of direct-frequency-comb excitation of helium atoms from the ground state to the 1s4p and 1s5p {sup 1} P{sub 1} states. Laser ionization by auxiliary 1064 nm pulses is used to detect the excited-state population, resulting in a cosine-like signal as a function of the repetition rate of the frequency comb with a modulation contrast of up to 55%. Analysis of the visibility of this comb structure, thereby using the helium atom as a precision phase ruler, yields an estimated timing jitter between the two upconverted-comb laser pulses of 50 attoseconds, which is equivalent to a phase jitter of 0.38 (6) cycles in the xuv at 51 nm. This sets a quantitative figure of merit for the operation of the xuv comb and indicates that extension to even shorter wavelengths should be feasible. The helium metrology investigation results in transition frequencies of 5 740 806 993 (10) and 5 814 248 672 (6) MHz for excitation of the 1s4p and 1s5p {sup 1} P{sub 1} states, respectively. This constitutes an important frequency measurement in the xuv, attaining high accuracy in this windowless part of the electromagnetic spectrum. From the measured transition frequencies an eight-fold-improved {sup 4}He ionization energy of 5 945 204 212 (6) MHz is derived. Also, a new value for the {sup 4}He ground-state Lamb shift is found of 41 247 (6) MHz. This experimental value is in agreement with recent theoretical calculations up to order m{alpha}{sup 6} and m{sup 2}/M{alpha}{sup 5}, but with a six-times-higher precision, therewith providing a stringent test of quantum electrodynamics in bound two-electron systems.},
doi = {10.1103/PHYSREVA.84.062512},
journal = {Physical Review. A},
number = 6,
volume = 84,
place = {United States},
year = 2011,
month =
}
  • The asymptotic behavior of ground states of two-electron atoms is investigated. Suppose psi(x/sub 1/,x/sub 2/) is the ground state of helium, rho(x/sub 1/) = ..integral..psi/sup 2/(x/sub 1/,x/sub 2/) dx/sub 2/ the corresponding electron density, and Phi(x/sub 2/) the ground state of He/sup +/. We show that in the L/sup 2/(dx/sub 2/)-sense, lim/sub vertical-barx//sub 1/Vertical Bar..-->..infinity psi(x/sub 1/,x/sub 2/)(rho(x/sub 1/))/sup -1/2/ = Phi(x/sub 2/), and that psi(rho(x/sub 1/))/sup -1/2/ solves for large Vertical Barx/sub 1/Vertical Bar the Schroedinger equation for He/sup +/ in the quadratic form sense. The rate of convergence of these limits is also discussed.
  • An x-ray free-electron laser oscillator (XFELO) is a next-generation x-ray source, similar to free-electron laser oscillators at VUV and longer wavelengths but using crystals as high-reflectivity x-ray mirrors. Each output pulse from an XFELO is fully coherent with high spectral purity. The temporal coherence length can further be increased drastically, from picoseconds to microseconds or even longer, by phase-locking successive XFELO output pulses, using the narrow nuclear resonance lines of nuclei such as ⁵⁷Fe as a reference. We show that the phase fluctuation due to the seismic activities is controllable and that due to spontaneous emission is small. The fluctuationmore » of electron-bunch spacing contributes mainly to the envelope fluctuation but not to the phase fluctuation. By counting the number of standing-wave maxima formed by the output of the nuclear-resonance-stabilized (NRS) XFELO over an optically known length, the wavelength of the nuclear resonance can be accurately measured, possibly leading to a new length or frequency standard at x-ray wavelengths. A NRS-XFELO will be an ideal source for experimental x-ray quantum optics as well as other fundamental physics. The technique can be refined for other, narrower resonances such as ¹⁸¹Ta or ⁴⁵Sc.« less
  • An x-ray free-electron laser oscillator (XFELO) is a next-generation x-ray source, similar to free-electron laser oscillators at VUV and longer wavelengths but using crystals as high-reflectivity x-ray mirrors. Each output pulse from an XFELO is fully coherent with high spectral purity. The temporal coherence length can further be increased drastically, from picoseconds to microseconds or even longer, by phase-locking successive XFELO output pulses, using the narrow nuclear resonance lines of nuclei such as ⁵⁷Fe as a reference. We show that the phase fluctuation due to the seismic activities is controllable and that due to spontaneous emission is small. The fluctuationmore » of electron-bunch spacing contributes mainly to the envelope fluctuation but not to the phase fluctuation. By counting the number of standing-wave maxima formed by the output of the nuclear-resonance-stabilized (NRS) XFELO over an optically known length, the wavelength of the nuclear resonance can be accurately measured, possibly leading to a new length or frequency standard at x-ray wavelengths. A NRS-XFELO will be an ideal source for experimental x-ray quantum optics as well as other fundamental physics. The technique can be refined for other, narrower resonances such as ¹⁸¹Ta or ⁴⁵Sc.« less
  • An x-ray free-electron laser oscillator (XFELO) is a next-generation x-ray source, similar to free-electron laser oscillators at VUV and longer wavelengths but using crystals as high-reflectivity x-ray mirrors. Each output pulse from an XFELO is fully coherent with high spectral purity. The temporal coherence length can further be increased drastically, from picoseconds to microseconds or even longer, by phase-locking successive XFELO output pulses, using the narrow nuclear resonance lines of nuclei such as Fe-57 as a reference. We show that the phase fluctuation due to the seismic activities is controllable and that due to spontaneous emission is small. The fluctuationmore » of electron-bunch spacing contributes mainly to the envelope fluctuation but not to the phase fluctuation. By counting the number of standing-wave maxima formed by the output of the nuclear-resonance-stabilized (NRS) XFELO over an optically known length, the wavelength of the nuclear resonance can be accurately measured, possibly leading to a new length or frequency standard at x-ray wavelengths. A NRS-XFELO will be an ideal source for experimental x-ray quantum optics as well as other fundamental physics. The technique can be refined for other, narrower resonances such as Ta-181 or Sc-45.« less