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

Journal of Optics B Quantum and Semiclassical Optics

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

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

Published Mar 1, 2004• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/6/3/004

Related papers

Spatial separation of atomic states in a laser cooled ion crystal

Wolfgang Alt, M. Block, P. Seibert +1 more

A laser cooled ion crystal containing several hundred Ca+ ions has been stored in a linear Paul trap. Cooling is provided by a red detund laser at the 4S1/2−4P1/2 resonance transition. A second laser serves for repumping of those ions which decay from the excited 4P1/2 level to the metastable 3D3/2 state. The ions can be additionally excited by a third laser to a long lived metastable 3D5/2 energy level which decouples them from the cooling laser radiation. The light pressure acting upon the laser cooled ions pushes them into the direction of the laser beam. The ions in the metastable 3D5/2 state, however, do not experience any light pressure force and diffuse to the crystal side which points towards the cooling laser. Part of the crystal then appears dark. Depending on the number of ions in the crystal and on the fraction of the excited ions, the spatial separation of the ions in the metastable state and the ions in the cooling cycle can be as large as several hundred microns.

AIP conference proceedings•Jan 1, 1999•0 citations

Raman cooling and heating of two trapped Ba+ ions

Dirk Reiß, Klaus Abich, Werner Neuhauser +2 more

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.

arXiv:quant-ph/0104002•Physical Review A•Apr 12, 2002•33 citations

Studies of trapped, cooled ion ensembles

David Offenberg

This work presents various novel results in the field of experimental and theoretical trapped ion studies. All investigations involve laser-cooled 138Ba+ ions confined in a linear quadrupole ion trap, which serve as coolant for complex molecular ions, as target for collisions with neutral atoms, or as model system in theoretical analyses. The special feature of the apparatus used in this work, is a molecular ion source based on electrospray ionization that allows for the production of gas-phase molecular ions of almost arbitrary species with a maximum mass-to-charge ratio of 2,000 Da. Trapped together with laser-cooled 138Ba+ ions, the molecular ions can be cooled down, kept cold and investigated for many minutes and in principle for up to hours in a nearly collisionless environment. In this work, the sympathetic cooling of complex molecular ions to translational temperatures below 1 K is demonstrated for different types of molecules covering a mass range from 182 to 12,400 Da. Using the example of the protein cytochrome c, with a mass of about 12,400 Da the most massive molecular species sympathetically cooled in an ion trap so far, the methods for detection of successful trapping and cooling, and temperature determination are presented in detail. In one case, multiply protonated molecules of the protein cytochrome c have been cooled to less than 0.75 K. Furthermore, two methods for measuring photodestruction rates of cold, trapped complex molecular ions have been developed that can, for example, be applied in destructive spectroscopy schemes. Both techniques are demonstrated using the example of singly protonated glycyrrhetinic acid molecules (GAH+) dissociated by an ultraviolet (UV) laser. Measurements of the photodestruction rate were performed at different intensities of the UV laser, and rates as low as 0.05 s-1 and less have been determined, which is only possible due to the long ion storage times that can be achieved with this apparatus. For the UV laser wavelength of 266 nm, a destruction cross section of (1.1±0.1)∙10E-17 cm2 for GAH+ has been determined. In this work, feasibility studies towards internal cooling of trapped complex molecular ions have been performed. Such an additional internal cooling could be realized via collisions with laser-cooled neutral atoms. To test their suitability, neutral atoms of Li, Na, K, Rb, Cs, and Yb have been collided with trapped laser-cooled and not cooled Ba+ ions as well as with complex molecular ions. For all species charge exchange reactions with Ba+ ions have been observed excluding these species for collisional cooling. While K, Rb, and Cs showed charge exchange reactions with ground state and laser-excited Ba+ ions, the charge exchange rates of Yb and Ba+ were found to be state dependent. Collisions of neutral Yb atoms were found to be reactive and lead to the formation of adducts and fragments, in contrast to the alkali metals for which no such reactions have been observed. In addition, the motion of cooled, trapped ions has been studied theoretically via simulations. When the translational energy of a trapped ion ensemble is sufficiently reduced, a first-order phase transition from a liquid to a solid state occurs with the ion ensemble changing from a disordered ion cloud to an ordered ion crystal. As ions in a linear quadrupole trap arrange in shell structures, a free motion in radial direction is disabled, and ions can only move to neighboring shells when their kinetic energy is high enough to overcome a certain potential barrier. The simulations have shown that intershell diffusion rates in the considered ion crystals increase exponentially when the ion temperatures exceed values that well agree with the predictions of other established models. Ion ensembles of different ion numbers (300, 500, and 1000 138Ba+ ions) and symmetries (prolate and spherical) have been investigated showing a clear tendency for the phase transition temperatures: The higher the ion number, the lower is the transition temperature.

•Jan 1, 2010•1 citation

Spatial separation of atomic states in a laser-cooled ion crystal

Wolfgang Alt, M. Block, P. Seibert +1 more

We have produced a laser-cooled ion crystal in a linear Paul trap containing several hundred ${\mathrm{Ca}}^{+}$ ions. A portion of the ions can be excited by an additional laser to a long-lived metastable energy level that decouples them from the cooling laser radiation. The light pressure acting upon the remaining laser-cooled ions forces them into the direction of the laser beam, while the ions in the metastable state drift to the crystal side that points toward the cooling laser. Depending on the number of ions in the crystal and on the fraction of the excited ions, the spatial separation of the ions in the metastable state and the ions in the cooling cycle can be as large as several hundred micrometers.

Physical Review A•Jul 1, 1998•12 citations

Addressing and Cooling of Single Ions in Paul Traps

Hanns‐Christoph Nägerl, Christian F. Roos, H. J. Rohde +4 more

The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.

Fortschritte der Physik•May 1, 2000•18 citations

Hopping of an impurity defect in ion crystals in linear traps

Jie Liang, P. C. Haljan

Laser-cooled arrays or crystals of $^{171}\mathrm{Yb}$${}^{+}$ ions containing a single impurity, $^{172}\mathrm{Yb}$${}^{+}$ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the $^{171}\mathrm{Yb}$${}^{+}$ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.

Physical Review A•Jun 6, 2011•6 citations
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.
A laser cooled ion crystal containing several hundred Ca+ ions has been stored in a linear Paul trap. Cooling is provided by a red detund laser at the 4S1/2−4P1/2 resonance transition. A second laser serves for repumping of those ions which decay from the excited 4P1/2 level to the metastable 3D3/2 state. The ions can be additionally excited by a third laser to a long lived metastable 3D5/2 energy level which decouples them from the cooling laser radiation. The light pressure acting upon the laser cooled ions pushes them into the direction of the laser beam. The ions in the metastable 3D5/2 state, however, do not experience any light pressure force and diffuse to the crystal side which points towards the cooling laser. Part of the crystal then appears dark. Depending on the number of ions in the crystal and on the fraction of the excited ions, the spatial separation of the ions in the metastable state and the ions in the cooling cycle can be as large as several hundred microns.
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 ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (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.
This work presents various novel results in the field of experimental and theoretical trapped ion studies. All investigations involve laser-cooled 138Ba+ ions confined in a linear quadrupole ion trap, which serve as coolant for complex molecular ions, as target for collisions with neutral atoms, or as model system in theoretical analyses. The special feature of the apparatus used in this work, is a molecular ion source based on electrospray ionization that allows for the production of gas-phase molecular ions of almost arbitrary species with a maximum mass-to-charge ratio of 2,000 Da. Trapped together with laser-cooled 138Ba+ ions, the molecular ions can be cooled down, kept cold and investigated for many minutes and in principle for up to hours in a nearly collisionless environment. In this work, the sympathetic cooling of complex molecular ions to translational temperatures below 1 K is demonstrated for different types of molecules covering a mass range from 182 to 12,400 Da. Using the example of the protein cytochrome c, with a mass of about 12,400 Da the most massive molecular species sympathetically cooled in an ion trap so far, the methods for detection of successful trapping and cooling, and temperature determination are presented in detail. In one case, multiply protonated molecules of the protein cytochrome c have been cooled to less than 0.75 K. Furthermore, two methods for measuring photodestruction rates of cold, trapped complex molecular ions have been developed that can, for example, be applied in destructive spectroscopy schemes. Both techniques are demonstrated using the example of singly protonated glycyrrhetinic acid molecules (GAH+) dissociated by an ultraviolet (UV) laser. Measurements of the photodestruction rate were performed at different intensities of the UV laser, and rates as low as 0.05 s-1 and less have been determined, which is only possible due to the long ion storage times that can be achieved with this apparatus. For the UV laser wavelength of 266 nm, a destruction cross section of (1.1±0.1)∙10E-17 cm2 for GAH+ has been determined. In this work, feasibility studies towards internal cooling of trapped complex molecular ions have been performed. Such an additional internal cooling could be realized via collisions with laser-cooled neutral atoms. To test their suitability, neutral atoms of Li, Na, K, Rb, Cs, and Yb have been collided with trapped laser-cooled and not cooled Ba+ ions as well as with complex molecular ions. For all species charge exchange reactions with Ba+ ions have been observed excluding these species for collisional cooling. While K, Rb, and Cs showed charge exchange reactions with ground state and laser-excited Ba+ ions, the charge exchange rates of Yb and Ba+ were found to be state dependent. Collisions of neutral Yb atoms were found to be reactive and lead to the formation of adducts and fragments, in contrast to the alkali metals for which no such reactions have been observed. In addition, the motion of cooled, trapped ions has been studied theoretically via simulations. When the translational energy of a trapped ion ensemble is sufficiently reduced, a first-order phase transition from a liquid to a solid state occurs with the ion ensemble changing from a disordered ion cloud to an ordered ion crystal. As ions in a linear quadrupole trap arrange in shell structures, a free motion in radial direction is disabled, and ions can only move to neighboring shells when their kinetic energy is high enough to overcome a certain potential barrier. The simulations have shown that intershell diffusion rates in the considered ion crystals increase exponentially when the ion temperatures exceed values that well agree with the predictions of other established models. Ion ensembles of different ion numbers (300, 500, and 1000 138Ba+ ions) and symmetries (prolate and spherical) have been investigated showing a clear tendency for the phase transition temperatures: The higher the ion number, the lower is the transition temperature.
We have produced a laser-cooled ion crystal in a linear Paul trap containing several hundred Ca+{\mathrm{Ca}}^{+}Ca+ ions. A portion of the ions can be excited by an additional laser to a long-lived metastable energy level that decouples them from the cooling laser radiation. The light pressure acting upon the remaining laser-cooled ions forces them into the direction of the laser beam, while the ions in the metastable state drift to the crystal side that points toward the cooling laser. Depending on the number of ions in the crystal and on the fraction of the excited ions, the spatial separation of the ions in the metastable state and the ions in the cooling cycle can be as large as several hundred micrometers.
The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.
Laser-cooled arrays or crystals of 171Yb^{171}\mathrm{Yb}171Yb+{}^{+}+ ions containing a single impurity, 172Yb^{172}\mathrm{Yb}172Yb+{}^{+}+ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the 171Yb^{171}\mathrm{Yb}171Yb+{}^{+}+ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.