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AIP conference proceedings

Optical lamb-dicke confinement of a Ba+ mono-ion oscillator

Warren Nagourney, HANS G. DEHMELT, G. R. Janik

Published Jan 1, 1986• 0 citations
Publisher

Abstract

We demonstrate the confinement of a single laser cooled Ba+ ion, held in a radiofrequency trap, to a region of space whose linear dimensions are much less than the wavelength of the interrogating light divided by 2π (Lamb‐Dicke regime1). This is the condition for the complete freedom from first order Doppler shifts. From the absence of observable Doppler sidebands on a narrow, two‐photon feature in the spectrum of Ba+, we infer an upper bound on the ion orbit radius of 165 nm. This is the first clear demonstration of Lamb‐Dicke confinement in the visible.2

DOI
10.1063/1.35754

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Zero‐point level confinement in a trap is the quantum‐mechanical equivalent of the classical single particle at rest in free space. Such confinement has been demonstrated—by the Continuous Stern‐Gerlach Effect—for only the 150 GHz cyclotron motion in geonium, a single electron permanently confined in a cold Penning trap. This confinement made possible a new determination of the radius of the electron, some 10 000 times smaller than the accepted upper limit of ≊10−16 cm. Localizing the electron to ≊60 μm in the node of a standing wave in the trap cavity approximated free space, however decreasing spontaneous emission ten‐fold. Driving the 60 MHz axial motion on a side band higher by the ≊12 kHz magnetron frequency, forced the magnetron motion to absorb the excess photon energy, and shrank its radius to ≊15 μm. Analogous laser cooling has reduced the oscillation amplitude of a Ba+ ion in a Paul rf trap to <120 nm. As in Nuclear Magnetic Resonance, confinement here is much smaller than the wave length and side bands disappear. Quantum jumps to and from an electronic metastable level of Ba+ have been demonstrated. Using In+ or similar, these techniques may make a mono‐ion oscillator optical frequency standard with a 1000‐day reproducibility of 10−18 possible. Further experiments are proposed.

AIP conference proceedings•Jan 1, 1987•1 citation
We demonstrate the confinement of a single laser cooled Ba+ ion, held in a radiofrequency trap, to a region of space whose linear dimensions are much less than the wavelength of the interrogating light divided by 2π (Lamb‐Dicke regime1). This is the condition for the complete freedom from first order Doppler shifts. From the absence of observable Doppler sidebands on a narrow, two‐photon feature in the spectrum of Ba+, we infer an upper bound on the ion orbit radius of 165 nm. This is the first clear demonstration of Lamb‐Dicke confinement in the visible.2
Laser fluorescence spectroscopy has been performed on the two-photon 62S1/2 to 52D3/2 transition in Ba+. Using signals from an individual laser-cooled ion in a rf trap, a laser limited linewidth of less than 3 MHz has been achieved with an effective wavelength of 2.07 μm. The absence of any sidebands in the spectra spaced at the 5.5-MHz oscillation frequency of the ion in the rf quadrupole trap indicates that the ion vibrational motion must be well into the Lamb–Dicke regime. An upper limit of 165 nm is given to the vibrational amplitude.
A single Hg+ ion that is confined in an rf (Paul) trap can be laser cooled so that the amplitude of its motion is much less than an optical wavelength (the Dicke limit for optical transitions).1 More recently, we used the technique of sideband cooling to reach the zero point of motion.2 This realizes for the first time, we believe, the fundamental limit of laser cooling and the ideal of an isolated atomic particle at rest in free space to within the quantum mechanical limits imposed by the surrounding apparatus. In both limits, Doppler effects to all orders become negligible, the interrogation time is arbitrarily long, and the fundamental shot noise limit of a single atom is readily attained. We report these results and our progress toward the 2S1/2—2D5/2 282-nm transition with a resolution approaching the 2-Hz natural linewidth.
The electric quadrupole transition of confined Ca/sup +/ ions has been proposed as a frequency standard in the visible domain. To access metrologic conditions, we have built a cylindrical miniature trap, allowing to obtain high frequencies of motion and preparing the access to the Lamb-Dicke regime where the first order Doppler broadening is suppressed. Laser cooling and interrogation of the confined ions require lasers at 397 nm and at 729 nm. We propose the generation of these wavelengths using multimode laser diodes and a frequency-doubling set-up.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
Zero‐point level confinement in a trap is the quantum‐mechanical equivalent of the classical single particle at rest in free space. Such confinement has been demonstrated—by the Continuous Stern‐Gerlach Effect—for only the 150 GHz cyclotron motion in geonium, a single electron permanently confined in a cold Penning trap. This confinement made possible a new determination of the radius of the electron, some 10 000 times smaller than the accepted upper limit of ≊10−16 cm. Localizing the electron to ≊60 μm in the node of a standing wave in the trap cavity approximated free space, however decreasing spontaneous emission ten‐fold. Driving the 60 MHz axial motion on a side band higher by the ≊12 kHz magnetron frequency, forced the magnetron motion to absorb the excess photon energy, and shrank its radius to ≊15 μm. Analogous laser cooling has reduced the oscillation amplitude of a Ba+ ion in a Paul rf trap to <120 nm. As in Nuclear Magnetic Resonance, confinement here is much smaller than the wave length and side bands disappear. Quantum jumps to and from an electronic metastable level of Ba+ have been demonstrated. Using In+ or similar, these techniques may make a mono‐ion oscillator optical frequency standard with a 1000‐day reproducibility of 10−18 possible. Further experiments are proposed.