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Engineering quantum states and non-equilibrium quantum matter in open quantum many-body systems
Haack, Casey
Haack, Casey
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2025
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Abstract
Open quantum systems are quantum systems that interact with an environment whose state is not known and whose interactions can not be controlled or monitored easily. Even though open quantum systems are ubiquitous in nature, they are less understood than their closed counterparts. Improved understanding of open quantum systems could help elucidate the sources of decoherence in quantum computers and simulators. Moreover, if the dissipation on an open quantum system can be controlled and engineered, one may create new phases of quantum matter or novel many-body entangled state that are hard to prepare for a closed quantum system. In this thesis, I describe my research efforts to understand and engineer open quantum many-body systems with a particular focus on quantum simulators using trapped atomic ions.
In Chapter 2, I propose an experiment for trapped-ion quantum simulators that could observe a novel driven-dissipative phase transition in a long-range transverse field Ising model (TFIM) for the first time. I present two experimentally practical protocols to engineer the required dissipation on the Ising model. One scheme simulates continuous dissipation by continuous optical pumping with carefully chosen laser configurations. The other scheme involves a periodic, probabilistic, measurement procedure that creates effective dissipation in a Floquet manner. In this proposed experiment, the competition between the drive and the dissipation makes the steady state of the system non-equilibrium, leading to novel features that cannot be observed in thermal equilibrium. These features can be captured by measuring two-time correlation functions in the steady state, and I provide a practical experimental method to measure these two-time correlations. With these two-time correlations, I show that the non-equilibrium features of the model can be observed for small or intermediate system sizes, making the results highly relevant for near-future experiments.
In Chapter 3, I generalize the above-mentioned idea of engineering dissipation via Floquet dynamics to realize more complicated open quantum many-body models. I show that Floquet dissipative maps can generate a large class of Lindblad master equations. Moreover, they can be used to simulate novel types of dissipation that are not easily accessible through existing methods, such as correlated dissipation or asymmetric/chiral dissipative transport processes. Through numerical simulations, I also find that the Floquet dissipation creates qualitatively similar steady states compared to continuous dissipation even with a moderately large period, making experimental realizations within reach.
In Chapter 4, I discuss a collaborative work with an ion-trap experimental group where I modeled an experimental quantum simulator as an open quantum many-body system. In the experiment, my collaborators worked to prepare a continuous symmetry breaking phase of a long-range transverse field Ising model. They find that their prepared state has the expected long-range correlations from the continuous symmetry breaking, but the observed correlations are much smaller than those predicted from my theoretical simulations using the experimental parameters if no decoherence is included. I then developed a microscopic model to include the most likely decoherence processes in the experiment and fit the decoherence rates from experimental data. I find that my model well reproduces the experimental measurement data, and I attribute the remaining difference between the theory and experiment to error sources that cannot be modeled with a standard Lindblad master equation, as well as a sub-optimal ramping function used in the preparation of the ground state.
In Chapter 5, I propose to modify the experimental setup in the previous chapter to prepare the ground-state of a spin-1 anti-ferromagnetic long-range Heisenberg model that exhibit a symmetry protected topological order. This ground state is much more challenging to prepare. I explore how to best optimize the ramping function used to prepare the state, applying a method based on adiabatic state preparation and a second, more sophisticated method based on gradient descent. I also model the effects of an expected shot-to-shot magnetic field noise that could be detrimental in our efforts to prepare the ground-state. I explore two distinct methods to mitigate this field noise: either by applying a large transverse field or applying spin-echo pulses. I show that spin-echo pulses can improve state fidelity, but unwanted resonance effects generated by the pulses could result in poor state fidelity. Such negative effects can be suppressed by a careful choice of the number of echo pulses applied. While I find that a large magnetic field appears to be a simpler yet effective way to mitigate this noise, this large field could introduce additional errors due to unwanted spin-phonon entanglement. How to suppress such phonon induced errors in the presence of a large field remains an important open question in trapped-ion quantum simulators.
In Chapter 6, I summarize my PhD research and point out several future direction my research can lead to. These include further collaboration with trapped-ion experimentalists to implement the aforementioned proposals, efforts to model correlated dissipation and shot-to-shot fluctuations in ion-trap quantum simulators, and protocols to simulate non-Hermitian many-body Hamiltonians using measurement feedback and post-selection.
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