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Physical Review A

Sympathetic cooling and detection of molecular ions in a Penning trap

Martijn A. van Eijkelenborg, M.E.M Storkey, D. M. Segal, Richard Claude Thompson

Published Nov 1, 1999• 44 citations
Publisher

Abstract

We have trapped and sympathetically cooled the molecular ions ${\mathrm{HCO}}^{+}$ and ${\mathrm{N}}_{2}{\mathrm{H}}^{+}$ in a Penning trap. Through their Coulomb interaction with laser-cooled ${\mathrm{Mg}}^{+}$ ions the molecules were sympathetically cooled to cryogenic temperatures. We identify the molecules through a measurement of their characteristic mass-dependent breathing mode frequencies. From a measurement of the temperature of the ${\mathrm{Mg}}^{+}$ ions we estimate that the final temperature of the sympathetically cooled molecules is 4 K.

DOI
10.1103/physreva.60.3903

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We have trapped and sympathetically cooled the molecular ions HCO+{\mathrm{HCO}}^{+}HCO+ and N2H+{\mathrm{N}}_{2}{\mathrm{H}}^{+}N2​H+ in a Penning trap. Through their Coulomb interaction with laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions the molecules were sympathetically cooled to cryogenic temperatures. We identify the molecules through a measurement of their characteristic mass-dependent breathing mode frequencies. From a measurement of the temperature of the Mg+{\mathrm{Mg}}^{+}Mg+ ions we estimate that the final temperature of the sympathetically cooled molecules is 4 K.
We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N2+{\mathrm{N}}_{2}^{+}N2+​ and CaH+{\mathrm{CaH}}^{+}CaH+ ions were confined in a surface-electrode radio-frequency (rf) ion trap and cooled by the interaction with laser-cooled Ca+{\mathrm{Ca}}^{+}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.
Sympathetic cooling of trapped ions has been demonstrated in an experiment where 198Hg+^{198}\mathrm{Hg}^{+}198Hg+ ions were confined in a Penning ion trap with laser-cooled 9Be+^{9}\mathrm{Be}^{+}9Be+ ions. 198Hg+^{198}\mathrm{Hg}^{+}198Hg+ temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the 9Be+^{9}\mathrm{Be}^{+}9Be+ plasma were observed when the 198Hg+^{198}\mathrm{Hg}^{+}198Hg+ ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.
We have produced and cooled the molecular ions MgH+{\mathrm{MgH}}^{+}MgH+ and MgD+{\mathrm{MgD}}^{+}MgD+ in a linear Paul trap. These ions were generated by the photochemical reactions ${\mathrm{Mg}}^{+}{(3p}^{2}{P}_{3/2})+{\mathrm{H}}_{2} ({\mathrm{D}}_{2})\ensuremath{\rightarrow}{\mathrm{MgH}}^{+} ({\mathrm{MgD}}^{+})+\mathrm{H} (\mathrm{D}),$ and identified by the radial separation in the trap of ions with different charge-to-mass ratios. The molecular translational motion was cooled sympathetically by Coulomb interaction with laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions to a temperature estimated to be below 100 mK. Ordered structures (ion crystals) containing more than 1000 ions, with more than 9595%95 being molecular ions, were obtained. Such translationally cold and well-localized samples of molecular ions could become very useful for molecular physics and chemistry.
We demonstrate sympathetic Doppler cooling and our progress towards sideband cooling of a CaH+^{+}+ ion co-trapped with a Ca+^{+}+ atomic ion in a linear Paul trap. Molecular ions are generally difficult to laser cool due to a lack of closed electronic transitions as a result of vibrational and rotational states. Despite this challenge, they can be cooled indirectly through their Coulombic interaction with a fluorescent atomic ion that is being directly laser cooled. Ions are firstly Doppler cooled to get to the Lamb-Dicke regime, where the ion motion is small relative to the excitation wavelength and then sideband cooled reaching temperatures below 1 μ\muμK. All the ions' axial modes (center of mass and breathing mode) and radial modes ( two center of mass and two tilt modes) are addressed, and the temperature is determined by examining the ratio of sidebands.
Laser-cooled atomic ions have led to an unprecedented amount of control over the quantum states of matter. The Coulombic interaction allows for information to be transferred between neighboring ions, and this interaction can be used to entangle qubits for logic operations in quantum information processors. The same procedure for logic operations can be used for high resolution atomic spectroscopy, and is the basis for the most accurate atomic optical clocks to date. This thesis describes how laser-cooled atomic ions can impact physical chemistry through the development of molecular ion spectroscopy techniques and the simulation of magnetic systems by ion trap quantum computers. \n\t \n\tA new technique developed for spectroscopy, Sympathetic Heating Spectroscopy (SHS), takes advantage of the Coulombic interaction between two trapped ions: the control ion and a spectroscopy ion. SHS uses the back action of the interrogating laser to map spectroscopy ion information onto the Doppler shift of the control ion for measurement. SHS only requires Doppler cooling of the ions and fluorescence measurement and represents a simplification of quantum logic spectroscopy. This technique is demonstrated on two individual isotopes of calcium: Ca-40(+) for cooling and Ca-44(+) as the spectroscopy ion. \n \n\tHaving demonstrated SHS with atomic ions, the next step was to extend the technique by loading and characterizing molecular ions. The identification of an unknown molecular ion is necessary and can be achieved by monitoring the change in motion of the two ion crystal, which is dependent on the molecular ion mass. The motion of two trapped ions is described by their normal modes, which can be accurately measured by performing resolved sideband spectroscopy of the S(1/2)-D(5/2) transition of calcium. The resolved sidebands can be used to identify unknown ions (atomic and molecular) by calculating the mass based on the observed value in axial normal mode frequencies. Again, the trapped molecular ion is sympathetically cooled via the Coulombic interaction between the Ca-40(+) and the unknown molecular ion. The sensitivity of SHS could be improved by implementing sympathetic sideband cooling and determining the heating by measuring single quanta of motion. \n\t \n\tThe ultimate limit of control would be the development of an ion trap quantum computer. Many theoretical quantum computing researchers have made bold claims of the exponential improvement a quantum computer would have over a classical computer for the simulation of physical systems such as molecules. These claims are true in principle for ideal systems, but given non-ideal components it is necessary to consider the scaling due to error correction. An estimate of the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision, is presented. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the quantum logic array architecture. The results show that a significant amount of error correction is required to implement the TIM problem due to the exponential scaling of the computational time with the desired precision of the energy. Comparison of this result to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.
Ultracold molecular hydrogen (D/sub 2//sup +/) is produced by sympathetic cooling in a linear Paul trap. With this method the translational degrees of freedom of the molecules are cooled by Coulomb interaction with laser-cooled /sup 9/Be/sup +/. This work shows that sympathetic cooling and crystallization is possible down to mass ratios of 0.45. Using molecular dynamics simulations, the mass range for sympathetic cooliing is predicted. By employin a light and a heavy species of laser-cooled ions (/sup 9/Be/sup +/ and e.g. /sup 137/Ba/sup +/) the mass range from 2 to 20 000 amu, i.e. from the simplest molecule to complex proteins, can be sympathetically cooled.