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.
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.
Zero-point level confinement1 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—only for the 150-GHz cyclotron motion in geonium, a single electron permanently confined in a cold Penning trap. Localizing the electron to ≈ 60 μm in the node of a standing wave in the trap cavity approximated free space, but decreased spontaneous emission tenfold. Driving the 60-MHz axial motion on a sideband higher by the ≈ 12-kHz magnetron frequency forced the magnetron motion to absorb the excess photon energy, shrinking its radius to ~ 15μm. 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 is now much smaller than the wavelength and sidebands disappear. Quantum jumps to and from an electronic metastable level of Ba+ have been demonstrated. Using In+ or a similar ion, this may make a monoion oscillator optical frequency standard with a 1000-day reproducibility of 10-18 possible.
Zero-point confinement in a suitable trap is briefly discussed as a quantum-mechanical equivalent of the classical single particle at rest in free space. So far, such confinement has been realized only for the 150 GHz cyclotron motion in geonium, a single electron permanently confined in a Penning trap. The most important result of mono-ion spectroscopy is a new, 10 000 times smaller, radius for the electron. This result was obtained by analyzing our g-factor data, g/2 = 1.001 159 652 193 (4), on the basis of a near-Dirac particle model. RF spectroscopy in geonium relies on the Continuous Stem Gerlach Effect in which a spin flip is detected as a small change in the ~ 60 MHz axial oscillation frequency of the electron in the trap. The Kaufmann Effect or relativistic mass shift may become a superior alternative : operating a geonium apparatus as a frequency selective mini-synchro-cyclotron has produced an easily detectable shift in the axial frequency. Like in Habann's 1926 split-anode magnetron, energy is quickly transferred from the oscillating electron to a resonant circuit, but by us for the purpose of detection, damping and cooling of the oscillatory motion. Conversely, localizing the electron to ~ 60 μm in the node of a standing wave in the trap cavity, where this cavity looks like a short, when it is resonant with the cyclotron motion, has made it possible to decrease the natural line width ten-fold. By driving the axial frequency not on resonance but on a side band higher by the ~ 12 kHz magnetron frequency, it has been possible to force the magnetron motion to absorb the excess in the photon energy and thereby shrink the magnetron radius to ~ 15 μm. By an analogous laser spectroscopic procedure the oscillation amplitude of a Ba+ ion in a different trap has been reduced to ~ 120 nm or less. Like in Nuclear Magnetic Resonance, confinement is now much smaller than the wave length and no motional side bands appear in the optical spectrum. Such a mono-ion oscillator, but using Tl+ or a similar ion, may make an optical frequency standard with a 1 000-day reproducibility of 10 -18 possible and thereby allow one to watch the expansion of the universe from one's laboratory.
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.
This article surveys experiments with individual closely confined atomic particles since their beginning in 1973. Such experiments have improved information on the size of an elementary particle on the same level as a quark, the electron, by at least three orders of magnitude. Their extension to the optical region promises atomic clocks of a reproducibility improved up to 100 000 times. The most important of the techniques developed for continuously detecting, cooling, and spin-state analyzing a permanently confined individual electron are described in some detail. The electron, trapped in ultrahigh vacuum at liquid helium temperature, is profitably viewed as a man-made atom, geonium.
An individual atomic ion localized in the center of a small Paul rf quadrupole trap is a promising object for ultimate resolution laser spectroscopy because, broadly speaking, the ion may be brought to "A State of Complete Rest in Free Space" by side band cooling. As a consequence, all Doppler shifts vanish. "Free Space" is approximated insofar as the electric trapping field vanishes in the center of the trap and there is no Stark effect. Neither need there be a Zeeman Effect as magnetic fields may be controlled down to the micro-Gauss range. Naturally, there is no transit time broadening. Minute laser powers provided by harmonic generators suffice for saturation of optical transitions as well focused beams may be used. Millionfold atomic amplification of the single-ion fluorescence from a metastable level may bring resolutions of 1 part in 1018 within reach. Furthermore, the close localization of an atomic particle in space is one of the most fundamental problems in physics and worthy of study on its own merit.
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g/2 = 1.00115965218073(28)[0.28 ppt], and the fine structure constant, α −1 = 137.035999084(51)[0.37 ppb], both significantly improved from prior results. The static magnetic and electric fields of a Penning trap confine the electron, and a 100 mK dilution refrigerator cools its cyclotron motion to the quantum-mechanical ground state. A quantum nondemolition measurement allows resolution of single cyclotron jumps and spin flips by coupling the cyclotron and spin energies to the frequency of the axial motion, which is self-excited and detected with a cryogenic amplifier. The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 timesthe free-space rate and shiftthe cyclotron frequency, a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculable couplingsto cyclotron motion. Two independent methods use the cyclotron damping rate of an electron plasma or of the single electron itself as probes of the cavity mode structure and allow the identification ofthe modes by their geometries and couplings, the quantification of an offset between the mode and electrostatic centers, and the reduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at four magnetic fields with cavity shifts spanning thirty times the final g-value uncertainty provides a check on the calculated cavity shifts. Magnetic field fluctuations limit the measurement of g by adding a noise-model dependence to the extraction of the cyclotron and anomaly frequencies from their resonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty. New techniques promise to increase field stability, narrow the resonance lines, and accelerate the measurement cycle. The measured g allows tests for physics beyond the Standard Model through searches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structure constant.