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.
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.
Trapped ions are currently one of the most promising architectures for realising the quantum information processor. The long lived internal states are ideal for representing qubit states and, through controlled interactions with electromagnetic radiation, ions can be manipulated to execute coherent logic operations. In this thesis an experiment capable of trapping Yb+ ions, including 171Yb+, is presented. Since ion energy can limit the coherence of qubit manipulations, characterisation of an ion trap heating rate is vital. Using a trapped 174Yb+ ion a heating rate consistent with previous measurements of other ion species in similar ion traps is obtained. This result shows abnormal heating of Yb+ does not occur, further solidifying the suitability of this species for quantum information processing. Efficient creation, and cooling of trapped ions requires exact wavelengths for the ionising, cooling and repump transitions. A simple technique to measure the 1S0 ? 1P1 transition wavelengths, required for isotope selective photoionisation of neutral Yb, is developed. Using the technique new wavelengths, accurate to 60 MHz, are obtained and differ from previously published results by 660 MHz. Through a simple modification the technique can also predict Doppler shifted transition frequencies, which may be required in non-perpendicular atom-laser interactions. Using trapped ions, the 2S1=2 ? 2P1/2 Doppler cooling and 2D3/2 ? 2D[3/2]1/2 repump transitions are also measured to a greater accuracy than previously reported. Many experiments require wavelengths which can only be obtained using complex expensive laser systems. To remedy this a simple cost effective laser is developed to enable laser diodes to be operated at sub zero temperatures, extending the range of obtainable wavelengths. Additional diode modulation capabilities allow for the manipulation of atoms and ions with hyperfine structures. The laser is shown to be suitable for manipulating Yb+ ions by cooling a diode from 372 nm to 369 nm and simultaneously generating 2.1 GHz frequency sidebands. Coherent manipulation such as arbitrary qubit rotations, motional coupling and ground state cooling, are required for trapped ion quantum computing. Two photon stimulated Raman transitions are identified as a suitable technique to implement all of these requirements and an investigation into implementing this technique with 171Yb+ is conducted. The possibility of exciting a Raman transition via either a dipole or quadrupole transitions in 171Yb+ is analysed, with dipole transitions preferred because quadrupole transitions are found to be too demanding experimentally. An inexpensive setup, utilising a dipole transition, is designed and tested. Although currently limited the setup shows potential to be an inexpensive, high fidelity method of exciting a Raman transition.
Quantum computing promises solutions to some of the world's most important problems that classical computers have failed to address. The trapped-ion-based quantum computing platform has a lot of advantages for doing so: ions are perfectly identical and near-perfectly isolated, feature long coherent times, and allow high-fidelity individual laser-controlled operations. One of the greatest remaining obstacles in trapped-ion-based quantum computing is the issue of scalability. The approach that we take to address this issue is a modular architecture: separate ion traps, each with a manageable number of ions, are interconnected via photonic links. To avoid photon-generated crosstalk between qubits and utilize advantages of different kinds of ions for each role, we use two distinct species - ¹⁷¹Yb⁺ as memory qubits and ¹³⁸Ba⁺ as communication qubits. The qubits based on ¹⁷¹Yb⁺ are defined within the hyperfine "clock" states characterized by a very long coherence time while ¹³⁸Ba⁺ ions feature visible-range wavelength emission lines. Current optical and fiber technologies are more efficient in this range than at shorter wavelengths. We present a theoretical description and experimental demonstration of the key elements of a quantum network based on the mixed-species paradigm. The first one is entanglement between an atomic qubit and the polarization degree of freedom of a pure single photon. We observe a value of the second-order correlation function g⁽²⁾(0) = (8.1 ± 2.3)⨉10⁻⁵ without background subtraction, which is consistent with the lowest reported value in any system. Next, we show mixed-species entangling gates with two ions using the Mølmer-Sørensen and Cirac-Zoller protocols. Finally, we theoretically generalize mixed-species entangling gates to long ion chains and characterize the roles of normal modes there. In addition, we explore sympathetic cooling efficiency in such mixed-species crystals. Besides these developments, we demonstrate new techniques for manipulating states within the D₃⸝₂-manifold of zero-nuclear-spin ions - a part of a protected qubit scheme promising seconds-long coherence times proposed by Aharon et al. in 2013. As a next step, we provide a detailed description of the protocols for three- and four-node networks with mixed species, along with a novel design for the third trap with in-vacuum optics to optimize light collection.
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.
Quantum simulation is the process of using a highly controllable quantum system to simulate another less controllable system. Quantum simulation can provide insights into the properties and dynamics of complex many-body systems. Trapped ion platform is one of the leading candidates for a quantum simulator due to its properties such as ease of isolation, preparation and manipulation. Simulating high dimensional spin systems enables us to study the various physical phenomena in higher geometries. Previous proposals for simulating higher dimensions require experimental resources that don't scale favourably with the system. In this thesis, we propose a hybrid (digital-analog) approach to simulate an effective 2D lattice from a 1D chain of trapped ions. In the initial geometry, the ions interact with each other through a flip-flop kind of interactions generated using a global Molmer-Sorensen scheme. A series of single qubit gates are used to rescale and suppress the interactions in the initial chain to simulate the target geometry. These gates are applied using a laser field gradient which generates a site-dependent AC stark shift. I discuss the construction of this protocol in detail and the theoretical results for the case of 6, 9 and 16 ions. I also show that the number of gates and also the Stark gradient scale linearly with the system size. \n \nExperimental implementation of an ion trap quantum simulator has various challenges, one of the which is the laser frequency stabilization within a fraction of transition linewidth. Traditionally, this is done by locking the lasers to an atomic transition. In this thesis, I discuss two alternative schemes for locking the laser frequencies used to build a 171Yb+ ion quantum simulator. One of these solutions uses a commercial wavemeter as a measuring device for the frequency and feedbacks the lasers based on this measurement. I discuss the layout of this scheme and some results. Other solution uses a Fabry Perot (FP) cavity to transfer the stability of a stable laser to an unstable laser. In this thesis, I discuss the construction, optical layout and transmission measurements of a home-built FP cavity.
One of the useful applications of a quantum computer is quantum simulation. While the quest for a universal quantum computer is still undergoing research, analog quantum simulators can study specific quantum models that are classically challenging or even intractable. These quantum simulators provide the opportunity to test particular quantum models and scale up the system size to gain insight into more exciting physics. The analog quantum simulator featured in this thesis is a cryogenic trapped-ion system. It serves the purpose of a large-scale quantum simulation by reducing the background pressure for storing a large ion chain with a long lifetime. This work presents the construction and characterization of this cryogenic apparatus and its performance as a trapped-ion quantum simulator. Quantum information is encoded in the atomic state of the ion chain. The entangling operation in trapped ions uses the collective motion of the ion chain for quantum simulation. Therefore, it is imperative to develop a cooling mechanism to prepare the ion chain to near motional ground-state for achieving high fidelity operations. Here, with this system, we explore another ground-state cooling mechanism with electromagnetically induced transparency (EIT) in a four-level system (171Yb+). EIT cooling allows simultaneous ground-state cooling across a bandwidth of motional modes, which it is useful in a large ion chain. Finally, we report the observation of magnetic domain-wall confinement in interacting spins chains. Such confinement is analogous to the color confinement in quantum chromodynamics (QCD), where hadrons are produced by quark confinement. We study the implications of such confinement in many-body spin system by observing the information propagation after applying a quantum quench of the confinement Hamiltonian. We also measure the excitation energy of domain-wall bound states from non-equilibrium quench dynamics. At the end of this experiment, we explore the number of domain wall excitations created with different quench parameters, which can be challenging to model with classical computers.
Abstract The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems that describe many dissipative processes in physical, chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models, by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons, respectively. We demonstrate a fully programmable method to simulate dissipative dynamics of spin-boson models using a chain of trapped ions, where the initial temperature and the spectral densities of the boson bath are engineered by controlling the state of the motional modes and their coupling with qubit states. Our method provides a versatile and precise experimental tool for studying open quantum systems.