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 $\ensuremath{\Delta}n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$.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 LettersMar 30, 199820 citations

Reconstructing the Vibrational State of a Trapped Ion

Benedetto Militello, Anna Napoli, Antonio Messina

arXiv:quant-ph/0211044Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20040 citations

Spectroscopy of Trapped Ions

Richard Claude Thompson

Advances in atomic, molecular, and optical physicsJan 1, 199363 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.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 AJul 1, 199990 citations

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.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 proceedingsJan 1, 19990 citations

Trapped Ion Spectroscopy

Frank Schlawin

Springer thesesSep 10, 20163 citations

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

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.