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

AIP conference proceedings

Quantum measurement and nonclassical vibration of an ion in a trap

R. Huesmann, Ch. Balzer, Bernd Appasamy, Yves Stalgies, P. E. Toschek

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.57447

Related papers

Single-Atom Interferometry

R. Huesmann, Chr. Balzer, Ph. W. Courteille +2 more

The phase shift of the hyperfine Larmor precession of an individual ground-state ${}^{171}{\mathrm{Yb}}^{+}$ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an $E2$ line.

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•0 citations

Measurement-Induced Vibrational Dynamics of a Trapped Ion

Bernd Appasamy, Yves Stalgies, P. E. Toschek

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 $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$.

Physical Review Letters•Mar 30, 1998•20 citations

Single-Atom Interferometry

R. Huesmann, Ch. Balzer, Ph. W. Courteille +2 more

The phase shift of the hyperfine Larmor precession of an individual ground-state ${}^{171}{\mathrm{Yb}}^{+}$ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an $E2$ line.

Physical Review Letters•Feb 22, 1999•33 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

Quantum dynamics of small numbers of ions in a penning trap

G. Stutter

Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of $97\%$, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.

•Nov 1, 2015•1 citation

Microwave-Optical Double Resonance on a Single Laser-Cooled 171 Yb + Ion

V. Enders, Ph. W. Courteille, R. Huesmann +4 more

A single ion whose energy levels are hyperfine split, 171 Yb + , was electrodynamically trapped and laser cooled. The residual energy of both its driven motion and its secular motion was 11 μeV. Radiofrequency-optical double-resonance excitation yields spectra whose 40 Hz wide lines are determined so far by the duration of the ion's interaction with the 12.6 GHz radiation. These results prove that a microwave clock is feasible with its fractional systematic uncertainty not exceeding 10 −16 .

Europhysics Letters (EPL)•Nov 10, 1993•18 citations
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.
The phase shift of the hyperfine Larmor precession of an individual ground-state 171Yb+{}^{171}{\mathrm{Yb}}^{+}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. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an E2E2E2 line.
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 $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$.
The phase shift of the hyperfine Larmor precession of an individual ground-state 171Yb+{}^{171}{\mathrm{Yb}}^{+}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. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an E2E2E2 line.
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.
Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of 97%97\%97%, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.
A single ion whose energy levels are hyperfine split, 171 Yb + , was electrodynamically trapped and laser cooled. The residual energy of both its driven motion and its secular motion was 11 μeV. Radiofrequency-optical double-resonance excitation yields spectra whose 40 Hz wide lines are determined so far by the duration of the ion's interaction with the 12.6 GHz radiation. These results prove that a microwave clock is feasible with its fractional systematic uncertainty not exceeding 10 −16 .