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Physical Review Letters

Stochastic Cooling of a Trapped Ion by Null Detection of Its Fluorescence

Jürgen Eschner, Bernd Appasamy, P. E. Toschek

Published Mar 27, 1995• 33 citations
Publisher

Abstract

When a single trapped ion is laser excited to a metastable state, its ``quantum jump'' inhibits the laser-excited light scattering on a resonance line. This event, and its inverse, modifies the distribution over the oscillator levels $(n)$ of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease $〈n〉$ to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.

DOI
10.1103/physrevlett.74.2435

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AIP conference proceedings•Jan 1, 1999•0 citations
When a single trapped ion is laser excited to a metastable state, its quantum jump'' inhibits the laser-excited light scattering on a resonance line. This event, and its inverse, modifies the distribution over the oscillator levels $(n)$ of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease $〈n〉$ to sub-Doppler values and may leave the ion in a trapped'' Fock state decoupled from the light.
An ion, or atom, confined in a ‘trap’ and laser-irradiated on its resonance line generates a quasi-continuous flow of scattered light, and makes the line split or shifted. When the ion is probe-laser excited, on a neighbouring dipole-forbidden line to a metastable state, the flow subsides. Also, the shift or dynamic Stark splitting of the resonance and of the dipole-forbidden line vanishes. De-excitation of the ion requires the probe laser to be re-tuned to the unshifted resonance. Cyclic scanning of this laser shows a mean frequency offset of the on-off jumps from the off-on jumps. This random hysteresis may cool or heat the ion, and lock an ensemble in the metastable state.
A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.
Excitation spectra of an individual trapped 138Ba+{}^{138}{\mathrm{Ba}}^{+}138Ba+ ion show sidebands of radial and axial ion vibration in the trap. The second-order sidebands involving radial and axial vibrations would allow swapping these vibrational states; they represent an inverse Raman effect with the role of electronic and vibrational excitation interchanged. Deexcitation sidebands differ from excitation sidebands as the vibrational distribution in the D5/2{D}_{5/2}D5/2​ level is modified by the ion being reduced to this level in null observations of resonance light. Delayed deexcitation goes along with stochastic cooling that makes the ion collapse into the Fock state ∣n=1〉|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1〉∣n=1〉. Sideband modulation is identified as stroboscopic detection of the light-induced nutation on a vibrational transition with $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$.
We briefly discuss the preparation of a single cold ion in an rf trap, and the concept of "quantum jumps" which requires a single atomic particle for verification. Recent corresponding experiments have demonstrated interruptions of the laser-excited resonance fluorescence, which are the signature of the particles performing quantum jumps to and from a metastable level, under weak excitation of the corresponding transition. The time density of the jumps obeys a Poissonian distribution in agreement with theoretical models. With three trapped ions, the high rate of multiple jumps suggests the presence of collective interaction.
A single Sr+ atom was confined in a radio-frequency quadrupole trap and laser cooled with resonant laser light. Examination of the transition Doppler profile indicated an ion kinetic temperature of less than 500 mK. Quantum jumps into and out of the metastable 4d(2)D(5/2) level were observed by laser excitation on the electric-quadrupole-allowed transition from the ground state at 674 nm. The dark and bright periods in the strong fluorescence showed variations owing to the applied driving field on the electric-quadrupole transition. These results provide an improved determination of tau = 372 +/- 25 msec for the natural metastable-state lifetime.
The microwave-induced dynamics of the nuclear spin and the laser-induced dynamics of the centre-of-mass motion of individual ions have been studied: (i) The phase shift of the hyperfine Larmor precession of a ground-state 171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry and quantum ergodicity. Even a single measurement yields (partial) phase information. At the extremes of the fringes, the results of measurements are deterministic where ion probing is compatible with ion preparation, as demonstrated by laser-exciting an ion on an E2 line. (ii) Excitation and de-excitation spectra of the E2 line S1/2−D5/2 of an individual trapped 138Ba+ ion show different first-order sidebands of radial and axial ion vibration in the trap, since the vibrational distribution in the excited D5/2 level is modified by the ion being reduced to this level in null observations of resonance light. Delayed sideband deexcitation eventually leaves the ion in the Fock state |n=1〉 (“stochastic cooling”). Sideband modulation is identified as stroboscopic detection of the light-induced nutation.