arXiv:1008.1858 · Physical Review A

Ion-assisted ground-state cooling of a trapped polar molecule

Zbigniew Idziaszek, Tommaso Calarco, P. Zoller

Published May 12, 2011• 10 citations

Abstract

We propose and analyze a scheme for sympathetic cooling of the translational motion of polar molecules confined in the wells of a deep optical lattice and interacting one by one with laser-cooled ions in a radio-frequency trap. The energy gap between the excitation spectra of the particles in their respective trapping potentials is bridged by means of a parametric resonance, provided by the additional modulation of the rf field. We analyze two scenarios: simultaneous laser cooling and energy exchange between the ion and the molecule, and a scheme where these two processes take place separately. We calculate the lowest final energy of the molecule and the cooling rate depending on the amplitude of the parametric modulation. For small parametric modulation, the dynamics can be solved analytically within the rotating wave approximation.

DOI: 10.1103/physreva.83.053413

Related papers

Rotational laser cooling of vibrationally and translationally cold molecular ions

Anders Kragh Hansen, Peter Frøhlich Staanum, Klaus Højbjerre +5 more

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)May 1, 20115 citations

Sympathetic cooling of a mass-mismatched two-ion chain in a double-well trap potential

Taro Hasegawa

Physical Review AMay 6, 20112 citations

Rotational cooling of molecular ions through laser-induced coupling to the collective modes of a two-ion Coulomb crystal

Ivan R. Vogelius, Lars Bojer Madsen, Michael Drewsen

Journal of Physics B Atomic Molecular and Optical PhysicsSep 25, 200618 citations

Laser cooling of trapped ions with polarization gradients

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

Physical Review AAug 1, 199320 citations

Sideband cooling of ions in radio-frequency traps

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

Physical Review AJul 1, 199990 citations

Sympathetic cooling of molecular ions in a surface-electrode ion trap

Arezoo Mokhberi, Stefan Willitsch

arXiv:1404.4292Physical Review AAug 4, 201410 citations

arXiv:1008.1858 · Physical Review A

Ion-assisted ground-state cooling of a trapped polar molecule

Zbigniew Idziaszek, Tommaso Calarco, P. Zoller

Published May 12, 2011• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.83.053413

Related papers

Rotational laser cooling of vibrationally and translationally cold molecular ions

Anders Kragh Hansen, Peter Frøhlich Staanum, Klaus Højbjerre +5 more

Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)May 1, 20115 citations

Sympathetic cooling of a mass-mismatched two-ion chain in a double-well trap potential

Taro Hasegawa

Sympathetic cooling of two-ion system, in which one is laser-cooled and the other is sympathetically cooled and their masses are mismatched, in a linear rf trap with a double-well potential is proposed. The double-well potential consists of two wells, and there is one ion in each well. The axial frequencies of the two wells and the spatial interval between them are experimentally controllable. By theoretical analysis, the normal modes of the small oscillations around the equilibrium are derived, and a measure of the sympathetic cooling rate is obtained. As a result, it is found that the sympathetic cooling rate is fast when the frequency of the axial motion of the sympathetically cooled ion is close to that of the laser-cooled ion. In the double-well potential, the sympathetic cooling rate of the ion species whose mass is much heavier or lighter than that of the laser-cooled ion can be fast. The sympathetic cooling rate of ${\mathrm{C}}_{60}$ ${}^{+}$ by the laser-cooled Ba ${}^{+}$ in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.Sympathetic cooling of two-ion system, in which one is laser-cooled and the other is sympathetically cooled and their masses are mismatched, in a linear rf trap with a double-well potential is proposed. The double-well potential consists of two wells, and there is one ion in each well. The axial frequencies of the two wells and the spatial interval between them are experimentally controllable. By theoretical analysis, the normal modes of the small oscillations around the equilibrium are derived, and a measure of the sympathetic cooling rate is obtained. As a result, it is found that the sympathetic cooling rate is fast when the frequency of the axial motion of the sympathetically cooled ion is close to that of the laser-cooled ion. In the double-well potential, the sympathetic cooling rate of the ion species whose mass is much heavier or lighter than that of the laser-cooled ion can be fast. The sympathetic cooling rate of ${\mathrm{C}}_{60}$${}^{+}$ by the laser-cooled Ba${}^{+}$ in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.

Physical Review AMay 6, 20112 citations

Rotational cooling of molecular ions through laser-induced coupling to the collective modes of a two-ion Coulomb crystal

Ivan R. Vogelius, Lars Bojer Madsen, Michael Drewsen

We show that the rotational degree of freedom of a polar heteronuclear molecular ion can be cooled through an optical coupling to the collective motional modes of the molecular ion and a simultaneously trapped and laser cooled atomic ion. Since the dissipative part of the rotational cooling is realized through laser cooling of the two-ion systems motional modes, the scheme should be applicable to a large range of molecules. As a test case for our cooling scheme we consider rotational cooling of a MgH + ion trapped with a laser cooled 40 Ca + ion.We show that the rotational degree of freedom of a polar heteronuclear molecular ion can be cooled through an optical coupling to the collective motional modes of the molecular ion and a simultaneously trapped and laser cooled atomic ion. Since the dissipative part of the rotational cooling is realized through laser cooling of the two-ion systems motional modes, the scheme should be applicable to a large range of molecules. As a test case for our cooling scheme we consider rotational cooling of a MgH + ion trapped with a laser cooled 40 Ca + ion.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 25, 200618 citations

Laser cooling of trapped ions with polarization gradients

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is ${\mathit{J}}_{\mathit{g}}$ =1/2\ensuremath{\rightarrow} ${\mathit{J}}_{\mathit{e}}$ =3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.

Physical Review AAug 1, 199320 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

Sympathetic cooling of molecular ions in a surface-electrode ion trap

Arezoo Mokhberi, Stefan Willitsch

We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. ${\mathrm{N}}_{2}^{+}$ and ${\mathrm{CaH}}^{+}$ ions were confined in a surface-electrode radio-frequency (rf) ion trap and cooled by the interaction with laser-cooled ${\mathrm{Ca}}^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to cold molecular ions with potential applications in mass spectrometry, chemistry, quantum information science, and spectroscopy.We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. ${\mathrm{N}}_{2}^{+}$ and ${\mathrm{CaH}}^{+}$ ions were confined in a surface-electrode radio-frequency (rf) ion trap and cooled by the interaction with laser-cooled ${\mathrm{Ca}}^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to cold molecular ions with potential applications in mass spectrometry, chemistry, quantum information science, and spectroscopy.

arXiv:1404.4292Physical Review AAug 4, 201410 citations

{\mathrm{C}}_{60}

{}^{+}

by the laser-cooled Ba

{}^{+}

in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.

{\mathit{J}}_{\mathit{g}}

=1/2\ensuremath{\rightarrow}

{\mathit{J}}_{\mathit{e}}

=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.

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.

We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip.

{\mathrm{N}}_{2}^{+}

and

{\mathrm{CaH}}^{+}

ions were confined in a surface-electrode radio-frequency (rf) ion trap and cooled by the interaction with laser-cooled

{\mathrm{Ca}}^{+}

ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to cold molecular ions with potential applications in mass spectrometry, chemistry, quantum information science, and spectroscopy.