ion in a radiofrequency ion trap is studied theoretically using molecular-dynamics simulations based on multilevel rate equations. The inhomogeneous magnetic field couples the different components of the ion motion and introduces position-dependent Zeeman splittings. Nonetheless, laser cooling is still found to work efficiently as the ion samples different magnetic field strengths and directions along its trajectory. Offsetting the centres of the two traps generates a linear magnetic-field gradient so that multiple lasers are required to address the resulting range of Zeeman splittings in order to ensure efficient cooling. The present study yields detailed insights into the ion cooling dynamics in combined magnetic and radiofrequency electric fields relevant for the characterisation and optimisation of hybrid trapping experiments.

DOI: 10.48550/arxiv.2212.11863

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Laser cooling of trapped ions in strongly inhomogeneous magnetic fields

Richard Karl, Yanning Yin, Stefan Willitsch

Hybrid traps for the simultaneous confinement of neutrals and ions have recently emerged as versatile tools for studying interactions between these species at very low temperatures.Such traps rely on the combination of different types of external fields for the confinement of either species raising the question of interactions between the individual traps.Here, the influence of a strongly inhomogeneous magnetic field used for trapping neutrals on the trapping and laser cooling of a single Ca + ion in a radiofrequency ion trap is studied theoretically using molecular-dynamics simulations based on multilevel rate equations.The inhomogeneous magnetic field couples the different components of the ion motion and introduces position-dependent Zeeman splittings.Nonetheless, laser cooling is still found to work efficiently as the ion samples different magnetic field strengths and directions along its trajectory.Offsetting the centres of the two traps generates a linear magnetic-field gradient so that multiple lasers are required to address the resulting range of Zeeman splittings in order to ensure efficient cooling.The present study yields detailed insights into the ion cooling dynamics in combined magnetic and radiofrequency electric fields relevant for the characterisation and optimisation of hybrid trapping experiments.Hybrid traps for the simultaneous confinement of neutrals and ions have recently emerged as versatile tools for studying interactions between these species at very low temperatures.Such traps rely on the combination of different types of external fields for the confinement of either species raising the question of interactions between the individual traps.Here, the influence of a strongly inhomogeneous magnetic field used for trapping neutrals on the trapping and laser cooling of a single Ca + ion in a radiofrequency ion trap is studied theoretically using molecular-dynamics simulations based on multilevel rate equations.The inhomogeneous magnetic field couples the different components of the ion motion and introduces position-dependent Zeeman splittings.Nonetheless, laser cooling is still found to work efficiently as the ion samples different magnetic field strengths and directions along its trajectory.Offsetting the centres of the two traps generates a linear magnetic-field gradient so that multiple lasers are required to address the resulting range of Zeeman splittings in order to ensure efficient cooling.The present study yields detailed insights into the ion cooling dynamics in combined magnetic and radiofrequency electric fields relevant for the characterisation and optimisation of hybrid trapping experiments.

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Experimental implementation of laser cooling of trapped ions in strongly inhomogeneous magnetic fields

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We demonstrate the Doppler laser cooling of $^{40}\mathrm{Ca}^{+}$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.We demonstrate the Doppler laser cooling of $^{40}\mathrm{Ca}^{+}$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.

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A Cryogenic Molecular Ion-Neutral Hybrid Trap

Claudio von Planta

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Jan 1, 20200 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

Cold ion–neutral collisions in a hybrid trap

W. W. Smith, Oleg P. Makarov, Jian Lin

A dual hybrid ion–neutral trap has been built to study collisions between a cloud of ultracold atoms and small numbers of co-trapped atomic or molecular ions, in a common volume. Ultracold Na atoms are trapped in a vapour-cell magneto-optical trap (MOT), via a single-mode frequency-stabilized ring-dye laser, with repumping. A linear rf quadrupole Paul ion trap, centred on the MOT, co-traps selected atomic or molecular ions, for example Ca+. Control of the initial ion temperature involves laser cooling Ca+ ions via the resonant Fraunhofer K line at 397 nm. We showed the rf ion trap can operate simultaneously with the MOT without destroying the ultracold atom cloud. The goal is to investigate the physics of ion–neutral sympathetic cooling, the cooling by neutrals of translationally cold and vibrorotationally hot molecular ions (e.g. Na2 +(v*, J*)), and the observation of other ion–neutral processes near 0 K, of potential interest in astrophysics.A dual hybrid ion–neutral trap has been built to study collisions between a cloud of ultracold atoms and small numbers of co-trapped atomic or molecular ions, in a common volume. Ultracold Na atoms are trapped in a vapour-cell magneto-optical trap (MOT), via a single-mode frequency-stabilized ring-dye laser, with repumping. A linear rf quadrupole Paul ion trap, centred on the MOT, co-traps selected atomic or molecular ions, for example Ca+. Control of the initial ion temperature involves laser cooling Ca+ ions via the resonant Fraunhofer K line at 397 nm. We showed the rf ion trap can operate simultaneously with the MOT without destroying the ultracold atom cloud. The goal is to investigate the physics of ion–neutral sympathetic cooling, the cooling by neutrals of translationally cold and vibrorotationally hot molecular ions (e.g. Na2 +(v*, J*)), and the observation of other ion–neutral processes near 0 K, of potential interest in astrophysics.

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Ion dynamics in a linear radio-frequency trap with a single cooling laser

Mathieu Marciante, C. Champenois, A. Calisti +2 more

We analyze the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use molecular dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature on the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudopotential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudopotential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organize as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.We analyze the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use molecular dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature on the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudopotential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudopotential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organize as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.

arXiv:1004.5202Physical Review ASep 9, 201023 citations

^+

We demonstrate the Doppler laser cooling of

^{40}\mathrm{Ca}^{+}

ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.

{\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.