Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Measurement-Induced Vibrational Dynamics of a Trapped Ion

Bernd Appasamy, Yves Stalgies, P. E. Toschek

Published Mar 30, 1998• 20 citations
Publisher

Abstract

Excitation spectra of an individual trapped ${}^{138}{\mathrm{Ba}}^{+}$ 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 ${D}_{5/2}$ 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 $|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1〉$. Sideband modulation is identified as stroboscopic detection of the light-induced nutation on a vibrational transition with $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$.

DOI
10.1103/physrevlett.80.2805

Related papers

Quantum measurement and nonclassical vibration of an ion in a trap

R. Huesmann, Ch. Balzer, Bernd Appasamy +2 more

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.

AIP conference proceedings•Jan 1, 1999•0 citations

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

Jürgen Eschner, Bernd Appasamy, P. E. Toschek

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.

Physical Review Letters•Mar 27, 1995•33 citations

Influence of second sideband excitation on the dynamics of trapped ions in a cavity

Xiang Liu, 方卯发

We study the dynamics of a trapped ion placed at an antinode of the standing wave inside a high finesse cavity with consideration of the second sideband excitation between the ionic internal levels and the light field. We investigate the entanglement of the three subsystems embodying the ionic internal levels, the vibrational mode of the ion and the cavity field.

中国物理B：英文版•Mar 16, 2005•0 citations

Influence of second sideband excitation on the dynamics of trapped ions in a cavity

Liu Xiang, Mao-Fa Fang

We study the dynamics of a trapped ion placed at an antinode of the standing wave inside a high finesse cavity with consideration of the second sideband excitation between the ionic internal levels and the light field. We investigate the entanglement of the three subsystems embodying the ionic internal levels, the vibrational mode of the ion and the cavity field.

Chinese Physics•Jun 24, 2003•2 citations

Sideband cooling of ions in radio-frequency traps

E. Peik, J. Abel, Th. Becker +2 more

An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. ${\mathrm{In}}^{+}$ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers $〈n〉<1$ by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of $〈n〉$. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.

Physical Review A•Jul 1, 1999•90 citations

Decoherence in ion traps

Sara Schneider, Gerard J Milburn

Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
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 \ensuremathΔn=\ifmmode±\else\textpm\fi1\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1\ensuremathΔn=\ifmmode±\else\textpm\fi1.
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.
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)(n)(n) of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease 〈n〉〈n〉〈n〉 to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.