This thesis presents the results of my graduate work which has concentrated on applying laser-cooling techniques to molecular ions, specifically CaH⁺ and BH⁺ ions for the study of their rovibronic spectroscopy. The goal of my research has been to control external and internal degrees of freedom of these two ions. Each of these molecules is spectroscopically appealing in its own right. For starters, CaH⁺ has been identified as a potential system for the test for the time variation of fundamental constants, and it's also been speculated to be in space. BH⁺ has a nearly diagonal Franck-Condon structure, and could be directly laser-cooled using only a few lasers. This structure makes it a good candidate for the cooling of internal molecular degrees of freedom. Each of the experiments described in this review involves the trapping and laser-cooling of ions. We cool the molecular ions sympathetically with laser-cooled Ca⁺. The probing techniques used to collect data are mainly: laser induced fluorescence, mass spectrometry, and resonance-enhanced multi-photon dissociation (REMPD). We have demonstrated the ground state sympathetic cooling of CaH⁺ ion to less than 16 $\\mu$K, and we have used to REMPD to measure for the first time four vibronic transitions in CaH⁺ ions. Together, these results are important for future quantum logic experiments on this molecule. Furthermore, we have also made some progress towards trapping and cooling BH⁺ ions by first trapping B⁺ ions with Ca⁺ ions. We use the motional resonance method to detect the B⁺ ions, which can be reacted with H atoms to produce the molecular ions. Following the measurement of the vibronic spectrum of CaH⁺, we have narrowed the linewidth of the laser source to resolve rotational lines.
This thesis presents the results of my graduate work which has concentrated on applying laser-cooling techniques to molecular ions, specifically CaH⁺ and BH⁺ ions for the study of their rovibronic spectroscopy. The goal of my research has been to control external and internal degrees of freedom of these two ions. Each of these molecules is spectroscopically appealing in its own right. For starters, CaH⁺ has been identified as a potential system for the test for the time variation of fundamental constants, and it's also been speculated to be in space. BH⁺ has a nearly diagonal Franck-Condon structure, and could be directly laser-cooled using only a few lasers. This structure makes it a good candidate for the cooling of internal molecular degrees of freedom. Each of the experiments described in this review involves the trapping and laser-cooling of ions. We cool the molecular ions sympathetically with laser-cooled Ca⁺. The probing techniques used to collect data are mainly: laser induced fluorescence, mass spectrometry, and resonance-enhanced multi-photon dissociation (REMPD). We have demonstrated the ground state sympathetic cooling of CaH⁺ ion to less than 16 muK, and we have used to REMPD to measure for the first time four vibronic transitions in CaH⁺ ions. Together, these results are important for future quantum logic experiments on this molecule. Furthermore, we have also made some progress towards trapping and cooling BH⁺ ions by first trapping B⁺ ions with Ca⁺ ions. We use the motional resonance method to detect the B⁺ ions, which can be reacted with H atoms to produce the molecular ions. Following the measurement of the vibronic spectrum of CaH⁺, we have narrowed the linewidth of the laser source to resolve rotational lines.
This thesis reports on the setup of a new ion trap apparatus designed for experiments with single ⁴⁰Ca⁺ ions to perform molecular spectroscopy. The calcium ion is laser cooled, allowing for sympathetic cooling of the nonfluorescing molecular ion. The aim of these experiments is to explore loading and identifying molecular ions in RF-Paul traps, as well as developing new spectroscopic tools to measure transitions of molecular ions via the fluorescence of co-trapped ⁴⁰Ca⁺ ions. Ground state cooling of a mixed ion pair is implemented as a first step towards increasing the sensitivity of our technique to the level necessary to measure transitions with low scattering rates (like those present in molecular ions). Doppler cooling on the S(1/2)->P(1/2) transition of the calcium ion results in the formation of a Coulomb crystal, the behavior of which may be used to infer properties of the molecular ion. Following cooling, sideband spectroscopy on the narrow S(1/2)->D(5/2) quadrupole transition of calcium may be used to identify the mass of single molecular ions. This method is verified via a non-destructive measurement on ⁴⁰CaH⁺ and ⁴⁰Ca¹⁶O⁺. The normal modes of the Coulomb crystal can also be used to extract information from the target ion to the control ion. By driving the blue side of a transition, laser induced heating can be put into the two ion system, which leads to changes in fluorescence of the ⁴⁰Ca⁺ ion, first demonstrated with two Ca⁺ isotopes. Increasing the sensitivity of this technique requires ground state cooling of both the ⁴⁰Ca⁺ ion and the ion of interest, enabling the transfer of the ion's motional state into the ground state with high probability. This thesis demonstrates ground state cooling of the atomic ion and sympathetic cooling of a second ion (⁴⁴Ca⁺). Once in the ground state, heating of the Coulomb crystal by scattering photons off of the spectroscopy ion can be measured by monitoring the resolved motional sidebands of the S(1/2)->D(5/2) transition of ⁴⁰Ca⁺, allowing for spectral lines to be inferred. Future experiments will investigate this technique with molecular ions.
In recent years there has been much progress in the field of cold and ultracold molecular physics and a variety of experimental techniques for producing cold matter now exist. In particular, the generation of trapped molecular ions at mK temperatures has been achieved by sympathetic-cooling with laser-cooled atomic ions. By implementing schemes to selectively prepare and control the internal quantum state of molecular ions, and developing detection techniques, it will be increasingly possible to study cold state-selected chemical collisions in an ion-trap. Most molecular species produced in a selected rovibrational state have a lifetime of a few seconds, before the population is redistributed across numerous rovibrational states by interaction with the ambient blackbody radiation (BBR). Consequently, the investigation of state-selected reaction dynamics at low temperatures in experiments where long time scales (minutes to hours) are required, is hindered. This thesis looks into developing strategies that maintain state selection in molecular ions, allowing one to observe state-selected reactions in cold environments, in particular the state-selected reaction between C2H+2 and ND3. Examining reactive ion molecule collisions under cold conditions provides insight into fundamental reaction dynamics, which are thermally averaged out at higher temperatures. A theoretical model is used to investigate laser-driven, blackbody-mediated, rotational cooling schemes for several 1Σ and 2Π diatomic species. The rotational cooling is particularly effective for DCl+ and HCl+, for which 92% and >99% (respectively) of the population can be driven into the rovibrational ground state. For the other systems a broadband optical pumping source is found to enhance the population that can be accumulated in the rovibrational ground state by up to 29% more than that achieved when exciting a single transition. The influence of the rotational constant, dipole moments and electronic state of the diatomics on the achievable rotational cooling is also studied. This approach is extended to consider the BBR interaction and rotational cooling of a linear polyatomic ion, C2H+2, which has a 2Π electronic ground state. The (1-0) band of the ν5 cis-bending mode is infrared active and strongly overlaps the 300 K blackbody spectrum. Hence the lifetimes of state-selected rotational levels are found to be short compared to the typical timescale of ion trapping experiments. Laser cooling schemes are proposed that could be experimentally viable, which involves simultaneous pumping of a set of closely spaced Q-branch transitions on the 2Δ5/2-2Π3/2 band together with two 2Σ+– 2Π1/2 lines. It is shown that this should lead to >70% of total population in the lowest rotational level at 300 K and over 99% at 77 K. In order to identify states of the acetylene ion that could be trapped sufficiently long enough for state-selected reactions in the ion trap with decelerated ND3, the theoretical work has been complemented by experimental investigations into the production of C2H+2 in selected states, and ion trapping of the same using sinusoidal and digital trapping voltages. Appropriate (2+1) REMPI (Resonance Enhanced Multiphoton Ionization) schemes are used to produce C2H+2 in different quantum states, with (1+1) Resonance Enhanced Multiphoton Dissociation (REMPD) employed to detect the ion thus produced. The concept of digital ion trapping for ejection onto MCPs is introduced. A comprehensive comparison between sinusoidal and digital trapping fields has been performed with respect to trap depth and stability regions. Programs have been developed to calculate the stability regions for different ions under varying experimental conditions. The trap depth has been derived for both digital and sinusoidal trapping fields. It is observed that as τ increases, the trap depth of a digital trap increases. For τ = 0.293, the trap depth and stability diagram for both sinusoidal and digital trapping fields would be equivalent. The trap depth at which the sinusoidal trap operates experimentally in our research group is ˜1.36 eV. In contrast, the experimental parameters at which the digital trap operates generates a trap depth of 1.21 eV. Ca+ Coulomb crystals have been formed, stably trapped and stored for extended periods of time in both sinusoidally and digitally time-varying trapping fields. The sympathetic cooling of a diverse range of ions into Ca+ Coulomb crystals is demonstrated, again using both sinusoidal and digital trapping fields. Mass spectrometric detection of ionic reaction products using a novel ejection scheme has been developed, where ejection is achieved by switching off the trapping voltage and converting the quadrupole trap into an extractor-repeller pair by providing the ion trap electrodes with appropriate ejection pulses. This technique is developed using a digital trapping voltage rather than the sinusoidal trapping voltage, as ejection with sinusoidal trapping voltages is not clean (resonance circuitry used in the electronics induces ringing after switching off the trapping voltage). Coulomb crystals, both pure Ca+ and multi-component crystals, are ejected from the ion trap and the TOF trace obtained is recorded on an oscilloscope. When the integrated, base-line subtracted TOF peak is plotted against the number of ions in a Ca+ crystal and sympathetically-cooled Ca+ – CaF+ crystal, a linear relationship is obtained. This technique is found to be well mass-resolved, with the signal arising from CaOH+ (57 amu) and CaOD+ (58 amu) resolvable on the TOF trace. This technique would enable one to monitor a reaction in a Coulomb crystal where the reactant and product species are both either lighter or heavier than calcium, such as the reaction between C2H+2 and ND3, something which has not been previously possible. It is, also, potentially a very important technique for reactions with many product channels.
Stationary molecules in well-defined internal states are of broad interest in both physics and chemistry. Through high-resolution spectroscopy, fundamental physics can be tested and lead to, e.g., improved values of the electron-to-proton mass ratio [1], new boundaries on the electron electric dipole moment [2] and observation of the potential evolution of the fine structure constant over time [3]. Translationally and internally cold molecules have as well been considered promising candidates for qubits in new quantum computing senarios [4], and molecular ions could in the future likely become an excellent alternative to atomic qubits in the realization of a practical ion trap based quantum computer due to favourable internal state decoherence rates. In chemistry, state prepared molecular targets are an ideal starting point for uni-molecular reactions, including coherent control of photofragmentation through the application of various laser sources [5,6]. In cold bi-molecular reactions, where the effect of even tiny potential barriers becomes significant, experiments with state prepared molecules can yield important information on the details of the potential curves of the molecular complexes [7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling results imply that, through this technique, cold molecular-ion experiments can now be carried out at cryogenic temperatures in room-temperature set-ups. References [1] Koelemeij, J. C. J., Roth, B., Wicht, A., Ernsting, I. and Schiller, S., Phys. Rev. Lett. 98, 173002 (2007). [2] Hudson, J. J., Sauer, B. E., Tarbutt, M. R. and Hinds, E. A., Phys. Rev. Lett. 89, 023003 (2002). [3] Hudson, E. R., Lewandowski, H. J., Sawyer, B. C. and Ye, J, Phys. Rev. Lett. 96, 143004 (2006). [4] DeMille, D, Phys. Rev. Lett. 88, 067901 (2002). [5] Rice, S. A. and Zaho, M. Optical control of molecular dynamics (Wiley, New York, 2000). [6] Shapiro, M. and Brumer, P. W. Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003). [7] Willitsch, S., Bell, M. T., Gingell, A. D. and Softley, T. P., Phys. Chem. Chem. Phys. 10, 7200 ( 2008). [8] Krems, R. V., Phys. Chem. Chem. Phys. 10, 4079 (2008). [9] Smith, I. W. M., Low temperatures and cold molecules (Imperial College Press, London, 2008). [10] Staanum, P. F., Højbjerre, K., Skyt, P.S., Hansen, A. K. and Drewsen, M., Nat. Phys. 6, 271 (2010). [11] Vogelius, I. S., Madsen, L. B. and Drewsen, M., Phys. Rev. Lett. 89, 173003 (2002).
This thesis describes the study of a range of ion-molecule reactions at very low collision energies using a newly developed experimental technique which involves the reaction of velocity-selected beams of translationally cold neutral molecules with very low kinetic energy ion ensembles. These studies have been enabled by the construction of a new apparatus for trapping and laser-cooling gas phase atomic ions (40Ca⁺). The laser-cooling process results in the formation of ordered, low kinetic energy, lattice-like ion structures, also known as "Coulomb crystals". The properties of single and multicomponent Coulomb crystals (which may also involve molecular ions), and their manipulation via modulation of the applied fields, are explored experimentally and with the use of molecular dynamics simulations. Variations in the laser-cooling parameters are shown to result in different steady-state populations of the electronic states of 40Ca⁺ involved with the laser cooling cycle, and these are modelled within an appropriate theoretical framework. The imaging of 40Ca⁺ fluorescence as a function of time allows the study of various ion-molecule reactions at collision energies around 300 K, with single ion sensitivity. These reaction studies are extended to low-temperature (collision energies close to 1 K), by combination of the ion trap apparatus with a bent quadrupole guide velocity-selector. Ion-molecule collision energies are shown to be variable over a short range through a change in the quadrupole guide voltage, or the ion trapping parameters; the effect of these modulations on the rate constant is explored for Ca⁺ + CH₃F. Bimolecular rate constants for the reactions of 40Ca⁺ with CH₃F, CH₂F₂ and CH₃Cl have been determined for a range of 40Ca⁺ state populations, allowing resolution of the global rate contributions from the ground and combined excited states. These results are analysed in the context of capture theories and ab initio electronic structure calculations. In each case, suppression of the ground state rate constant is explained by the presence of either a submerged or real barrier on the ground state potential surface. Rates of reaction from the combined excited states are generally found to be in line with capture theories, and in some cases variation is found between the high and low collision energy regimes. Molecular product ions generated in these experiments have been shown to be sympathetically-cooled into the crystal structure, and subsequently identified through resonance-excitation mass spectrometry. Molecular ions were also produced by multiphoton laser ionisation of a thermal background gas of OCS molecules. An ion-molecule reaction involving a molecular ion, that of charge transfer between OCS⁺ and ND₃, has been studied at a collision energy near 1 K for the first time using sympathetically-cooled OCS⁺ and velocity-selected ND₃. These experiments illustrate the generality of the techniques described herein, and should lead to many possibilities for future studies.
Trapped laser-cooled atomic ions are a new tool for understanding cold molecular ions. The atomic ions not only sympathetically cool the molecular ions to millikelvin temperatures, but the bright atomic ion fluorescence can also serve as a detector of both molecular reactions and molecular spectra. We are working towards the detection of single molecular ion spectra by sympathetic heating spectroscopy. Sympathetic heating spectroscopy uses the coupled motion of two trapped ions to measure the spectra of one ion by observing changes in the fluorescence of the other ion. Sympathetic heating spectroscopy is a generalization of quantum logic spectroscopy, but does not require ions in the motional ground state or coherent control of the ion internal states. We have recently demonstrated this technique using two isotopes of Ca+ [Phys. Rev. A, 81, 043428 (2010)]. Limits of the method and potential applications for molecular spectroscopy are discussed.
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.