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.
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.
From the first demonstration of a quantum logic gate in 1995 to the actualizationof a “quantum advantage” over classical technology a few years ago, the field of quantum information has made remarkable progress during my lifetime. Multiple quantum technology platforms have developed to the point that companies and governments are investing heavily in the industry. A primary focus is the development of fault-tolerant error correction, a technology expected to be necessary for large-scale digital quantum computers. Meanwhile analog quantum simulators, a subclass of quantum computers that apply unitary evolutions instead of digitized gates, are at the forefront of controllable quantum system sizes. In place of algorithms, analog quantum simulators are naturally suited to study many-body physics and model certain materials and transport phenomena. In this thesis I discuss an analog quantum simulator based on trapped +Yb171 ions and its use for studying dynamics and thermalizing properties of the non-integrable long-range Ising model with system sizes near the limit of classical tractability. In addition to the technical properties of the simulator, I present three select experiments that I worked on during my PhD. The first is an observation of a phenomenon in nonequilibrium physics, a dynamical phase transition (DPT). While equilibrium phase transitions follow robust universal principles, DPTs are challenging to describe with conventional thermodynamics. We present an experimental observation and characterization of a DPT with up to 53 qubits. We also explore the system’s ability to simulate physics beyond its own by implementing a quasiparticle confinement Hamiltonian. Here we see that the natural long-range interactions present in the simulator induce an effective confining potential on pairs of domain-wall quasiparticles, which behave similarly to quarks bound into mesons. We measure post-quench dynamics to identify how confinement introduces low-energy bound states and inhibits thermalization. Lastly, we use the individual-addressing capabilities of our simulator to implement Stark many-body localization (MBL) with a linear potential gradient. Stark MBL provides a novel, disorder-free method for localizing a quantum system that would otherwise thermalize under evolution. We explore how the localized phase depends on the gradient strength and uncover the presence of correlations using interferrometric double electron-electron resonance (DEER) measurements. These experiments show the capability of our experiment to study complex quantum dynamics in systems near 50 qubits and above.
While realizing a fully functional quantum computer presents a long term technical goal, in the present, there are small to mid-sized quantum simulators (up to ∼100 qubits), that are capable of approaching specialized problems. The quantum simulator discussed here uses trapped ions to act as qubits and is housed in a cryogenically cooled vacuum chamber in order to reduce the background pressure, thereby increasing ion chain length and life-time. The details of performance and characterization of this cryogenic apparatus are discussed, and this system is used to study many-body dephasing in a finite-sized quantum spin system. How a closed quantum many-body system relaxes and dephases as a function of time is important to understand when dealing with many-body spin systems. In this work, the first experimental observation of persistent temporal fluctuations after a quantum quench is presented with a tunable long-range interacting transverse-field Ising Hamiltonian. The fluctuations in the average magnetization of a finite-size system of spin-1/2 particles are measured presenting a direct measurement of relaxation dynamics in a non-integrable system. This experiment is in the regime where the properties of the system are closely related to the integrable Hamiltonian with global coupling. The system size is varied in order to investigate the dependence on finite-size scaling, and the system size scaling exponent extracted from the measured fluctuations is consistent with theoretical prediction.
Trapped-ion systems are among the most promising hardware candidates for large scale quantum computing and quantum simulation. In order to scale up such devices, it is necessary to engineer extreme-high vacuum (XHV) environments to prevent background gas from disrupting the ion crystal. Here we present a new cryogenic ion trapping system designed for long time storage of large ion chains. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap and hold over 100 171 Yb + ions for hours in a linear configuration, due to low background gas pressure from differential cryo-pumping. We characterize the XHV cryogenic environment measuring pressures below by recording both inelastic and elastic collisions between the ion chain and the molecular background gas. We also demonstrate coherent one and two-qubit operations and nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials, in order to enable better detection and single ion addressing in large ion arrays. We anticipate that this reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of models that are intractable with classical computer modeling.
While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.
Certain classes of quantum many-body systems, including those supporting phenomena like high-Tc superconductivity and spin liquids, are believed to be fundamentally intractable to classical modeling. Quantum simulations, in which synthetic materials are engineered by inducing well-controlled quantum systems like ultracold atoms to obey many-body Hamiltonians of interest, are a promising new approach to study this type of physics. In this work, I present several advances toward this ultimate goal of large-scale, highly controllable quantum simulations of many-body spin physics. We simulate long-range Ising and XY spin models in the presence of transverse and longitudinal magnetic fields using chains of up to 18 ultracold 171Yb+ ions held in a linear Paul trap, where two hyperfine levels in each ion encode spin-1/2 states. The tunable spin-spin interactions and effective magnetic fields are engineered using laser fields, and the individual spin states are directly imaged with state-dependent fluorescence. The results in this thesis address several of the ongoing challenges in the development of synthetic quantum matter platforms. One such challenge is establishing more flexible capabilities in the sorts of Hamiltonians we can model. By observing suppression of the ground state spin ordering, we have demonstrated our ability to continuously tune the interaction range in a power-law interaction pattern, and hence the amount of frustration present in the spin system. We have additionally begun developing tools to study particles of higher spin, which could eventually be used to create and study topological phases of matter. Another challenge is the necessity of identifying problems that the next generation of experiments, with flexible (but not arbitrary) controls and classically intractable (but not infinitely large) system sizes, can feasibly shed new light on. We have made measurements of how the range of interaction affects dynamics of spin correlations propagating through the chain, and the excellent agreement between our observations and numerical simulations indicate that at larger sizes, our experiment can meaningfully contribute to the open question of the fundamental speed limit on the transfer of information through such a spin chain. Finally, for classically intractable system sizes, it will be crucial to have multiple techniques at our disposal for validating our understanding of the exact microscopic model being implemented. We have developed and demonstrated an MRI-like spectroscopic technique for probing the energies of the many-body Hamiltonian, which serves as a new method for validating quantum simulations of the transverse Ising model. Our experiments can potentially be scaled up in the near future to study fully connected lattice spin models with several tens of spins, where classical computation begins to fail, and the results described in this thesis contribute to the effort to build experiments that can break new ground in the study of quantum many-body physics.
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.