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Advanced Journal of Graduate Research

An Experimental Configuration to Probe for Lorentz Symmetry Violation in Electrons Using Trapped Yb+ Ions

Noah Schlossberger, Phil Richerme

Published Apr 4, 2018• 0 citations
Publisher

Abstract

Since extensions of the standard model have been developed that predict violations of local Lorentz invariance (LLI), precision measurement groups have been working to reduce experimental bounds of the associated matrix element. Using an analogue of the Michelson-Morley test with trapped Ca+ ions, the current bound has been set at one part in 1018. However, by instead using Yb+ ions, which have highly stable electronic states for storing quantum information compared to their counterparts and exhibit enhanced effects of LLI breaking asymmetries, we can push the bounds to one part in 1023. In this article, we outline a configuration for such an experiment and offer solutions to experimental concerns. We develop an algorithm for state creation, manipulation, and measurement that minimizes measurement time and transition uncertainty. We also discuss necessary hardware for trapping and manipulating ions including a vacuum system, a Paul trap and the associated electrode voltage supplies, and an optics system for generating and applying transition pulses. The experiment is specifically designed to utilize the existing ion trap hardware in place at the Richerme lab at Indiana University Bloomington.

DOI
10.21467/ajgr.4.1.15-33

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Since extensions of the standard model have been developed that predict violations of local Lorentz invariance (LLI), precision measurement groups have been working to reduce experimental bounds of the associated matrix element. Using an analogue of the Michelson-Morley test with trapped Ca+ ions, the current bound has been set at one part in 1018. However, by instead using Yb+ ions, which have highly stable electronic states for storing quantum information compared to their counterparts and exhibit enhanced effects of LLI breaking asymmetries, we can push the bounds to one part in 1023. In this article, we outline a configuration for such an experiment and offer solutions to experimental concerns. We develop an algorithm for state creation, manipulation, and measurement that minimizes measurement time and transition uncertainty. We also discuss necessary hardware for trapping and manipulating ions including a vacuum system, a Paul trap and the associated electrode voltage supplies, and an optics system for generating and applying transition pulses. The experiment is specifically designed to utilize the existing ion trap hardware in place at the Richerme lab at Indiana University Bloomington.
Abstract In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2 F 7/2 manifold of an Yb + ion, extending the coherence time from 200 μ s to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2 F 7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10 −21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this paper we study how entangled states can be leveraged to enhance a precision test of local Lorentz invariance of the electron. Employing high-fidelity entanglement of a pair of trapped Ca-ions, we find that the sensitivity can be improved by a factor of two. The sensitivity of our measurements nearly reaches the projection noise limit set by quantum mechanics. Our measurements improve the previous best limit for local Lorentz invariance of the electron using Ca-ions by factor of two to about 5×10−195\times10^{-19}5×10−19.
We demonstrate that experiments measuring the transition energies of rare-earth ions doped in crystalline lattices are sensitive to violations of local Lorentz invariance and Einstein's equivalence principle. Using the crystal field of LaCl3{\mathrm{LaCl}}_{3}LaCl3​ as an example, we calculate the frame-dependent energy shifts of the transition frequencies between low-lying states of Ce3+,Nd3+{\mathrm{Ce}}^{3+},\phantom{\rule{0.16em}{0ex}}{\mathrm{Nd}}^{3+}Ce3+,Nd3+, and Er3+{\mathrm{Er}}^{3+}Er3+ dopants in the context of the standard model extension, and show that they have high sensitivity to electron anomalies that break rotational invariance.
This dissertation reports on precision measurements of the atomic structure of calcium ions (40Ca+), application of trapped 40Ca+ ions as a probe for a violation of fundamental symmetry and prospects of performing quantum simulations with trapped ion.We demonstrate a novel technique to perform spectroscopy on the dipole transition of 40Ca+ that circumvents usual difficulties from dark resonances and Doppler heating. The center of the atomic transition can be detected to a precision of 200 kHz or less with an integration time of 10 minutes. We apply this method to directly measure the influence of micromotion on the fluorescence spectra and confirm the dependence of the modulation index on the radial trap frequency. We measure the branching fraction of the excited 2P1/2 state of 40Ca+ to be 0.93565(7) using a simple experimental scheme readily applicable to many other ion species. Our result for 40Ca+ distinguishes well among various theoretically calculated values, which is important in guiding further developments of the theoretical work.We apply the Ramsey spectroscopy technique based on a pair of correlated ions to probe the effect of the violation of local Lorentz invariance (LLI). The energy difference between the two components of the Bell state |PsiB> = |mJ=5/2,mJ=-5/2>+|mJ=1/2,mJ=-1/2> in the D5/2 manifold of 40Ca+ is monitored for 12 hours. We found that the energy component related to the violation of LLI varies less than 17±22 mHz. Assuming a hydrogen-like model of 40Ca+, the measurement result provides us the bound of the LLI parameter C(2)0 to be 1.7±2.2x10-17.Based on numerical simulations, we show that the Aubry transition in the Frenkel-Kontorova model with trapped ion can be observed for practical experimental parameters such as the strength and wavelength of the optical lattice, which serves as an external perturbing periodic potential. Moreover, we also show that the normal mode structure of ion chain can change significantly as we vary the strength of the optical lattice.
Trapped ions in linear Paul traps are largely isolated from interaction with the environment. This property of trapped ions make them a primary choice for quantum technology. \nOver the last decade, trapped atomic ions in linear radio frequency Paul traps have shown to be an important tool to implement quantum algorithms. The scalability of linear ion \ntraps is required to handle large numbers of qubits, in order to implement useful quantum computation. Advance micro-fabrication technology allows the realisation of scalable ion traps. Further developments of micro-trap designs, for the purpose of scalable quantum technology, requires inter-disciplinary investigations of ion traps. Micro-scale ion trap designs typically require a versatile experimental setup. The first part of this thesis describes such an experimental setup including a chip bracket that can host macroscopic ion traps as well as advanced symmetric and asymmetric ion trap chips with up to 90 control electrodes. The system provides versatile optical access for both type of traps and the vacuum chamber is designed in a way so the ion traps can be replaced within a short amount of time. To test the working of the setup, a macroscopic ion trap with an ion-electrode distance of 310±10 μm is used to trap ytterbium ions (Yb+). The trap is characterised by measuring the heating rate, (n•), and spectral noise density SE(ω). A \nphotoionisation technique is used to ionise the different isotopes of Yb in our trap. Isotope selective photoionisation requires exact measurements of 1So↔1P1 transition for the different Yb isotopes. A technique to measure these resonant frequencies is described. \nThis technique works by observing and aligning fluorescence spots and by using this technique, the 1So↔1P1 transition frequencies for stable isotopes of Yb were measured with an accuracy of 60 MHz. These new measured transition frequencies for stable Yb isotopes differ from previously published work by 660 MHz. Furthermore, this technique can also be used to obtain the transition frequencies at different laser-atomic beam angles, typical for non-perpendicular laser-atomic beam angles. The second part of this thesis discusses the optimisation of surface trap geometries as they are being used to implement scalable ion trap designs which consist of a large number of trapping zones. The trap depth in surface traps is low compared to symmetric traps of similar dimensions. How to optimise the trap geometry to achieve maximum trap depth for a given ion height above the trap electrodes, is discussed. Fast and adiabatic ion shuttling operations in one dimension as well as ion separation and recombination processes are important for many quantum information implementations. The maximum speed of separation of trapped ions for adiabatic shuttling operations depends on the secular frequencies, the trapped ion experiences in the process. It will be shown how such ion trap structures have to be designed for fast ion separation process and linear shuttling. Numerical results of adiabatic shuttling operations for trapped ions in such trap structures are also presented.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.