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

arXiv:quant-ph/0104002 · Physical Review A

Raman cooling and heating of two trapped Ba+ ions

Dirk Reiß, Klaus Abich, Werner Neuhauser, Ch. Wunderlich, P. E. Toschek

Published Apr 12, 2002• 33 citations
arXivHTMLPDF

Abstract

We study cooling of the collective vibrational motion of two ${}^{138}{\mathrm{Ba}}^{+}$ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (493 nm) and ${P}_{1/2}\ensuremath{-}{D}_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split ${S}_{1/2}\ensuremath{-}{D}_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.

DOI
10.1103/physreva.65.053401

Related papers

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

Many-Body Effects in Dark-State Laser Cooling

Muhammad Miskeen Khan, David Wellnitz, Bhuvanesh Sundar +6 more

We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a $Λ$ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.

quant-pharXiv:2601.09180•Jan 15, 2026•0 citations

Raman sideband cooling of a Ba+138 ion using a Zeeman interval

Christopher M. Seck, Mark Kokish, Matthew Dietrich +1 more

Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for $^{138}\mathrm{Ba}^{+}$ of sufficient fidelity for QLS without an extremely narrow-band laser or the use of a species with hyperfine structure. We use the two ${S}_{1/2}$ Zeeman sublevels of $^{138}\mathrm{Ba}^{+}$ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, continuous near-resonant Raman sideband cooling of $^{138}\mathrm{Ba}^{+}$ requires only the Doppler cooling lasers and two additional acousto-optic modulators. Observing the near-resonant Raman optical pumping fluorescence, we extract relevant experimental parameters and demonstrate a final average motional quantum number $\overline{n}\ensuremath{\ll}1$. We additionally employ a second, far-off-resonant laser driving Raman $\ensuremath{\pi}$ pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final $\overline{n}=0.15(6)$.

arXiv:1603.09322•Physical Review A•May 17, 2016•10 citations

Thermally activated hopping of two ions trapped in a bistable potential well

Klaus Abich, Albert Keil, Dirk Reiß +3 more

With two ions in a spheroidal Paul trap, the harmonic trapping potential turns, by Coulomb repulsion, into a bistable well. Two Ba ions have been confined, laser-cooled, and observed, via their laser-excited resonance scattering, by a spatially resolving photomultiplier, or intensifying CCD camera. A repump laser releases the ions from a metastable state. Well-cooled ions are found localized. When the laser is detuned, the Raman cooling rate and the ions’ temperature vary. A transition from the crystallized state to a toroidal gas takes place. The ions are discriminated when one (i) gets excited into a non-fluorescing metastable state, or (ii) is of another isotopic species. Hopping rates of 1 s −1 are found at high thermal excitation. Elsewhere, the rates drop by two orders of magnitude, and vary resonantly with temperature near potential energy/kinetic energy = 15, where the bright ion’s hopping upstream of the laser beam is five times more likely than downstream. Two discernible ions in a trap represent a microscopic model system for the study of reaction kinetics.

Journal of Optics B Quantum and Semiclassical Optics•Mar 1, 2004•9 citations

Raman sideband cooling of a 138Ba+ ion using a single Zeeman interval

Christopher M. Seck, Mark Kokish, Matthew Dietrich +1 more

Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for $^{138}$Ba$^+$ of sufficient fidelity for QLS without an extremely narrowband laser or the use of a species with hyperfine structure. We use the two S$_{1/2}$ Zeeman sublevels of $^{138}$Ba$^+$ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, near-resonant Raman sideband cooling of $^{138}$Ba$^+$ requires only the Doppler cooling lasers and two additional AOMs. Observing the near-resonant Raman optical pumping fluorescence, we estimate a final average motional quantum number $\bar{n}\approx0.17$. We additionally employ a second, far-off-resonant laser driving Raman $\pi$-pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final $\bar{n} = 0.15(6)$.

•Mar 30, 2016•0 citations

Stimulated Raman transitions for cooling atoms in an optical dipole trap

Joseph D. Miller, Robert A. Cline, Daniel J. Heinzen

Optical dipole traps can provide strong, state-independent confinement of atoms. Unfortunately, the spatially dependent light shifts of optical transitions in dipole traps can interfere with conventional laser cooling techniques. These limitations may be overcome by cooling trapped atoms with stimulated Raman transitions. In particular, the lights shifts of ground state sublevels can be equal, so that the Raman cooling transition is unperturbed. Cooling in the sideband limit, to the quantum ground state of motion, should be possible. We have confined {sup 85}Rb atoms in a far-detuned optical dipole trap, and indirectly measured extremely low heating rates of the trapped atoms. We have also driven velocity-sensitive stimulated Raman transitions of the trapped atoms. The high resolution of these stimulated Raman resonances should allow us to resolve the motional sidebands and to directly cool the trapped atoms.

Bulletin of the American Physical Society•May 1, 1993•0 citations
We study cooling of the collective vibrational motion of two 138Ba+{}^{138}{\mathrm{Ba}}^{+}138Ba+ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances S1/2\ensuremath−P1/2{S}_{1/2}\ensuremath{-}{P}_{1/2}S1/2​\ensuremath−P1/2​ (493 nm) and P1/2\ensuremath−D3/2{P}_{1/2}\ensuremath{-}{D}_{3/2}P1/2​\ensuremath−D3/2​ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split S1/2\ensuremath−D3/2{S}_{1/2}\ensuremath{-}{D}_{3/2}S1/2​\ensuremath−D3/2​ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.
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.
We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a ΛΛΛ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ of sufficient fidelity for QLS without an extremely narrow-band laser or the use of a species with hyperfine structure. We use the two S1/2{S}_{1/2}S1/2​ Zeeman sublevels of 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, continuous near-resonant Raman sideband cooling of 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ requires only the Doppler cooling lasers and two additional acousto-optic modulators. Observing the near-resonant Raman optical pumping fluorescence, we extract relevant experimental parameters and demonstrate a final average motional quantum number $\overline{n}\ensuremath{\ll}1$. We additionally employ a second, far-off-resonant laser driving Raman $\ensuremath{\pi}$ pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final n‾=0.15(6)\overline{n}=0.15(6)n=0.15(6).
With two ions in a spheroidal Paul trap, the harmonic trapping potential turns, by Coulomb repulsion, into a bistable well. Two Ba ions have been confined, laser-cooled, and observed, via their laser-excited resonance scattering, by a spatially resolving photomultiplier, or intensifying CCD camera. A repump laser releases the ions from a metastable state. Well-cooled ions are found localized. When the laser is detuned, the Raman cooling rate and the ions’ temperature vary. A transition from the crystallized state to a toroidal gas takes place. The ions are discriminated when one (i) gets excited into a non-fluorescing metastable state, or (ii) is of another isotopic species. Hopping rates of 1 s −1 are found at high thermal excitation. Elsewhere, the rates drop by two orders of magnitude, and vary resonantly with temperature near potential energy/kinetic energy = 15, where the bright ion’s hopping upstream of the laser beam is five times more likely than downstream. Two discernible ions in a trap represent a microscopic model system for the study of reaction kinetics.
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for 138^{138}138Ba+^++ of sufficient fidelity for QLS without an extremely narrowband laser or the use of a species with hyperfine structure. We use the two S1/2_{1/2}1/2​ Zeeman sublevels of 138^{138}138Ba+^++ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, near-resonant Raman sideband cooling of 138^{138}138Ba+^++ requires only the Doppler cooling lasers and two additional AOMs. Observing the near-resonant Raman optical pumping fluorescence, we estimate a final average motional quantum number nˉ≈0.17\bar{n}\approx0.17nˉ≈0.17. We additionally employ a second, far-off-resonant laser driving Raman π\piπ-pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final nˉ=0.15(6)\bar{n} = 0.15(6)nˉ=0.15(6).
Optical dipole traps can provide strong, state-independent confinement of atoms. Unfortunately, the spatially dependent light shifts of optical transitions in dipole traps can interfere with conventional laser cooling techniques. These limitations may be overcome by cooling trapped atoms with stimulated Raman transitions. In particular, the lights shifts of ground state sublevels can be equal, so that the Raman cooling transition is unperturbed. Cooling in the sideband limit, to the quantum ground state of motion, should be possible. We have confined {sup 85}Rb atoms in a far-detuned optical dipole trap, and indirectly measured extremely low heating rates of the trapped atoms. We have also driven velocity-sensitive stimulated Raman transitions of the trapped atoms. The high resolution of these stimulated Raman resonances should allow us to resolve the motional sidebands and to directly cool the trapped atoms.