Characterization of micro-motion and its influence on systematic frequency shifts of quadrupole transition of Calcium ion trapped in Paul trap

Tato práce se zabývá analýzou mikropohybu zachyceného jednomocného iontu vápníku v lineární Paulově iontové pasti a vlivem zbytkového mikropohybu na systematické posuvy frekvence hodinového přechodu vápníkového iontu. Pomocí teoretického popisu jsou obecně ukázány základní vlastnosti pohybu zachyceného iontu uvnitř lineární Paulovy iontové pasti. Zejména je kladen důraz na mikropohybovou složku celkového pohybu. Na základě výsledků numerického výpočtu elektrických polí uvnitř pasti je představen model popisující mikropohyb v axiálním směru pasti. Tento model je experimentálně porovnán s realitou. Dále je představena foton-korelační metoda detekce mikropohybu, která je následně využita k minimalizaci a odhadu míry zbytkového mikropohybu ve všech prostorových osách. Na základě dosažitelné míry zbytkového mikropohybu jsou odhadnuty systematické frekvenční posuvy způsobené tímto mikropohybem. Ukazuje se, že jsme schopni dosáhnout nejistot relativních frekvenčních posuvů souvisejících s mikropohybem pod úroveň 10^20. Očekáváme, že nejistota celkového systematického frekvenčního posuvu v důsledku pohybu iontu je v našem případě limitována tepelným pohybem.This thesis deals with the analysis of micromotion of a single charged calcium ion trapped inside the linear Paul's ion trap and the influence of residual micromotion on the systematic frequency shifts of the clock transition of calcium ion. The fundamental properties of the motion of an ion confined within linear Paul's ion trap are shown in general using a theoretical description. The micromotion component of the overall motion is especially emphasized. A model expressing micromotion in the axial direction of the trap is introduced on the basis of the results of the numerical calculation of electric fields inside the trap. The model is compared to the reality experimentally. Then, the photon-correlation method of detection of micromotion is introduced and subsequently used to minimize and to estimate a measure of residual micromotion in all spacial directions. According to the achievable measure of residual micromotion, the systematic frequency shifts caused by this micromotion are estimated. It can be seen that we are able to reach uncertainties of the relative frequency shifts due to micromotion below 10^20. We expect that uncertainty of total motional systematic frequency shift is in our case limited by thermal motion.

Sideband thermometry of ion crystals

Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.Comment: 12+5 pages, 9+2 figures, Fig.3(b) was correcte

Sideband Thermometry of Ion Crystals

Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals

Calculation of potentials and simulation of the behavior of calcium ions in Paul´s linear ion trap

Precision of the experiments performed using trapped ion within Paul’s linear ion trap is highly dependent on the magnitude of ion’s residual motion. Two different radiofrequency driving modes of the electrodes are compared with respect to magnitude of the ion’s micromotion in the direction of trap’s axis. This comparison of the trapped ion’s micromotion is carried by numerical calculation using finite element method for geometry, which corresponds to trap located in laboratory of Institute of Scientific Instruments, Czech Academy of Science in Brno. The results of the calculations show that symmetrical driving mode should be more suitable to attenuation of trapped ion’s micromotion’s axial component

Calculation of potentials and simulation of the behavior of calcium ions in Paul's electrical trap

Tato práce se zabývá srovnáním vlastností pohybu zachyceného iontu vápníku v Paulově radiofrekvenční lineární kvadrupólové pasti mezi symetrickým a asymetrickým buzením pasti pomocí numerické simulace. Tyto dva způsoby buzení pasti porovnává zejména z hlediska minimalizace mikropohybu vykonávaného iontem. Detailně analyzuje také sekulární pohyb zachyceného iontu. Společně s vlastnostmi pohybu iontu podrobně ukazuje výsledné průběhy potenciálů v iontové pasti. Pomocí měření sekulárních frekvencí pohybu zachyceného iontu vápníku je ověřena shoda reálného chování iontu s numerickým modelem. Práce také shrnuje a využívá teoretický popis obecných vlastností radiofrekvenčních kvadrupólových pastí.This thesis deals with comparison of motional properties of calcium ion confined in Paul’s radiofrequency linear quadrupole trap between symetrical and asymetrical driving modes of the trap by numerical simulation. It compares these two modes especially with respect to minimization of ion’s micromotion. It also provides detailed analysis of trapped ion’s secular motion. Together with ion’s motional properties it shows obtained shapes of potential in ion trap in detail. Agreement of real behavior of trapped Calcium ion with numerical model is verified via experimental measurement of trapped ion’s secular frequencies. Thesis also summarizes and uses theoretical description of general features of radiofrequency quadrupole ion traps.

Sideband Thermometry of Ion Crystals

Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals