Trapped ions have been a staple resource of quantum simulation for the past decade. By taking advantage of the spin motion coupling provided by the Coulomb interaction, trapped ions have been used to study quantum phase transitions of highly frustrated spins, many body localization, as well as discrete time crystals. However, all of these simulations involve decoupling the ion motion from spin at the end of the experimental procedure. Here we present progress towards driving bosonic interference between occupied phonon modes. This thesis details a tool box for manipulating the motional states of a chain of trapped ions. Taking advantage of spin motion interaction of tightly trapped chains of 171Yb+ ions with two photon Raman transition, we show how to prepare a specic number state of a given normal mode of motion. This is achieved without traditional individual addressing but instead by using composite pulse sequences and ion transport. This involves a stage of quantum state distillation, and we also show preservation of phonon and spin coherence after this distillation step. This Fock state preparation sets the stage to observe bosonic interference of different phonon modes. We use stimulated Raman transitions to create a parametric drive; this drive will couple different normal modes of motion. To observe the bosonic nature of the phonons, we preform a Hong-Ou-Mandel (HOM) interference experiment on two singly occupied normal modes. We use the same spin motion coupling to read out the spin states of individual ions as a witness for this interaction. We also describe a process to use stimulated rapid adiabatic passage (STIRAP) to read out normal mode occupation. The toolbox presented here will be useful for future experiments towards boson sampling using trapped ions.
Trapped ions have been a staple resource of quantum simulation for the past decade. By taking advantage of the spin motion coupling provided by the Coulomb interaction, trapped ions have been used to study quantum phase transitions of highly frustrated spins, many body localization, as well as discrete time crystals. However, all of these simulations involve decoupling the ion motion from spin at the end of the experimental procedure. Here we present progress towards driving bosonic interference between occupied phonon modes. This thesis details a tool box for manipulating the motional states of a chain of trapped ions. Taking advantage of spin motion interaction of tightly trapped chains of 171Yb+ ions with two photon Raman transition, we show how to prepare a specic number state of a given normal mode of motion. This is achieved without traditional individual addressing but instead by using composite pulse sequences and ion transport. This involves a stage of quantum state distillation, and we also show preservation of phonon and spin coherence after this distillation step. This Fock state preparation sets the stage to observe bosonic interference of different phonon modes. We use stimulated Raman transitions to create a parametric drive; this drive will couple different normal modes of motion. To observe the bosonic nature of the phonons, we preform a Hong-Ou-Mandel (HOM) interference experiment on two singly occupied normal modes. We use the same spin motion coupling to read out the spin states of individual ions as a witness for this interaction. We also describe a process to use stimulated rapid adiabatic passage (STIRAP) to read out normal mode occupation. The toolbox presented here will be useful for future experiments towards boson sampling using trapped ions.
The quantum simulation of complex many body systems holds promise for understanding the origin of emergent properties of strongly correlated systems, such as high-Tc superconductors and spin liquids. Cold atomic systems provide an almost ideal platform for quantum simulation due to their excellent quantum coherence, initialization and readout properties, and their ability to support several forms of interactions. In this thesis, I present experiments on the quantum simulation of long range Ising models in the presence of transverse magnetic fields with a chain of up to sixteen ultracold 171-Yb+ ions trapped in a linear radio frequency Paul trap. Two hyperfine levels in each of the 171-Yb+ ions serve as the spin-1/2 systems. We detect the spin states of the individual ions by observing state-dependent fluorescence with single site resolution, and can directly measure any possible spin correlation function. The spin-spin interactions are engineered by applying dipole forces from precisely tuned lasers whose beatnotes induce stimulated Raman transitions that couple virtually to collective phonon modes of the ion motion. The Ising couplings are controlled, both in sign and strength with respect to the effective transverse field, and adiabatically manipulated to study various aspects of this spin model, such as the emergence of a quantum phase transition in the ground state and spin frustration due to competing antiferromagnetic interactions. Spin frustration often gives rise to a massive degeneracy in the ground state, which can lead to entanglement in the spin system. We detect and characterize this frustration induced entanglement in a system of three spins, demonstrating the first direct experimental connection between frustration and entanglement. With larger numbers of spins we also vary the range of the antiferromagnetic couplings through appropriate laser tunings and observe that longer range interactions reduce the excitation energy and thereby frustrate the ground state order. This system can potentially be scaled up to study a wide range of fully connected spin networks with a few dozens of spins, where the underlying theory becomes intractable on a classical computer.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
Trapped ions offer a controlled and versatile platform for the simulation of spin and spin-boson quantum systems. The Coulomb interaction between ions trapped in a harmonic potential can be used to mediate interactions between effective spins in the ion chain. Generally, coherent operations on ions are performed on ground-state qubits encoded in magnetically insensitive hyperfine sublevels. In this thesis, we extend this toolbox with the aim of simultaneously manipulating both ground-state and optical qubits, with the latter encoded in metastable optically excited states. The optical qubit provides another set of coherent and dissipative operations that can be performed on the ions, opening new avenues for quantum computing and simulation. In our experiment, we use 171Yb+ and 172Yb+ ions to encode ground-state and optical qubits. We discuss the laser setup needed to address the narrow quadrupole transition from 2S1/2 →2 D3/2 of 3.02 Hz linewidth, and we describe spectroscopy techniques to study this transition in both the isotopes. We describe how the low linewidth allows resolved sideband cooling on the shared motional modes in an ion chain, enabling sympathetic cooling with one ion, 172Yb+ , while simultaneously performing coherent operations on the 171Yb+ ion. Finally, we discuss the prospects of using this tool for light-shift entangling gates, showing the flexibility of this trapped-ion system for simulating coherent as well as dissipative quantum systems.
Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in 25 Mg + , implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal probability distribution of motional states the STIRAP population transfer is more efficient than a stimulated Raman Rabi pulse on a motional sideband. In contrast to previous implementations, a large detuning of more than 200 times the natural linewidth of the transition is used. This approach renders STIRAP suitable for atoms in which resonant laser fields would populate nearby fluorescing excited states and thus impede the STIRAP process. We use the technique to measure the wavefunction overlap of excited motional states with the motional ground state. This is an important application for force sensing applications using trapped ions, such as photon recoil spectroscopy, in which the signal is proportional to the depletion of motional ground state population. Furthermore, a determination of the ground state population enables a simple measurement of the ion's temperature.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of en-tangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demon-strating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss exper-iments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
Trapped ions are a powerful and flexible platform used for scientific applications ranging from studies of fundamental physics and precision spectroscopy to quantum simulation and quantum information processing. These applications are enabled by the excellent control that can be exerted over the long-lived atomic states of trapped ions using electromagnetic fields. In crystals containing multiple ions, the shared motion is used as a mediator to couple the atomic states of distant ions. This thesis focuses on improving the control over ion motion, and in particular for crystals that contain multiple ion species. The first set of experiments discussed in this thesis is the application of a ground-state cooling method known as electromagnetically-induced-transparency (EIT) cooling to 25Mg+. This ion has a complex hyperfine structure which enables the implementation of a long-lived qubit. By demonstrating EIT cooling on 25Mg+, it is shown that such qubit ions are also compatible with this resource-efficient sub-Doppler cooling method. The normal modes of trapped-ion motion are well-described by quantum harmonic oscillators, and the second set of experiments described in this thesis covers the direct, rapid, and parametric coupling between two harmonic oscillators in the motion modes of multi-ion crystals. This coupling can be used to indirectly cool ion modes that are otherwise difficult or inefficient to cool. It can also be used to perform mid-circuit non-destructive readout of trapped-ion motion, which is useful for the study of states encoded in the ion motion, such as those used for bosonic error correction.