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arXiv:2205.11178 · Physical Review X

Quantum Simulations of Interacting Systems with Broken Time-Reversal Symmetry

Yotam Shapira, Tom Manovitz, Nitzan Akerman, Ady Stern, Roee Ozeri

Published May 9, 2023• 20 citations
arXivHTMLPDF

Abstract

Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics.Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation.Of these, platforms with universal quantum control can experimentally access a wide range of physical properties.However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging.Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor.Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trappedion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems.Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions.Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.

DOI
10.1103/physrevx.13.021021

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Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics.Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation.Of these, platforms with universal quantum control can experimentally access a wide range of physical properties.However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging.Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor.Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trappedion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems.Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions.Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.
Quantum many-body systems in which time-reversal symmetry is broken give rise to a wealth of exotic phases, and thus constitute one of the frontiers of modern condensed matter physics. Quantum simulation allows us to better understand many-body systems with huge Hilbert space, where classical simulation is usually inefficient. With superconducting quantum circuit as a platform for quantum simulation, we realize synthetic Abelian gauge fields by using microwave drive and tunable coupling in loop configurations to break the time-reversal symmetry of the system. Based on high-precision manipulation and readout of circuit-QED architecture, we demonstrate the chiral ground spin current of a time-reversal symmetry broken system with nontrivial interactions. Our work is a significant attempt to simulate quantum many-body systems with time-reversal symmetry breaking in multi-qubit superconducting processors.
We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.
Certain classes of quantum many-body systems, including those supporting phenomena like high-TcT_cTc​ 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 171^{171}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.
In recent decades, the rapid development of quantum technologies has led to a new era of programmable platforms, enabling the realizations of quantum simulation and quantum computation. This dissertation is motivated by recent experimental progress on controlling individual quantum degrees of freedom in systems such as trapped ions and Rydberg atom arrays. By tailoring the interactions in these quantum systems, we study analog quantum simulations of various physical phenomena, including non-equilibrium quantum dynamics and nontrivial topological physics. In the first part of the dissertation, we study slow quantum many-body dynamics in trapped-ion systems and Rydberg atom arrays. We first show that either the long-range interactions or an additional symmetry-breaking field can give rise to a confining potential. Such a potential can couple domain wall quasiparticles into mesonic or baryonic bound states. These confined quasiparticles strongly suppress the quantum information dynamics and lead to slow thermalization. In thelimit of strict domain-wall confinement, the full Hilbert space is fragmented into exponentially many disconnected subspaces. Furthermore, we demonstrate that thermalization can be halted by quantum engineering a uniformly increasing field in the trapped-ion quantum simulator. The second part of the dissertation focuses on topologically relevant phenomena in quantum simulators. We first study the effect of experimentally relevant disorder in 2D Rydberg atom arrays. We find that there are three distinct localization regimes due to the presence of nontrivial topological bands. We further study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We show that the interplay of anyonic statistics and interactions can give rise to spatially asymmetric quantum dynamics. Finally, we use Nielsen’s geometric approach to quantify circuit complexity in topological models. We find that the circuit complexities of ground states and non-equilibrium steady states both exhibit nonanalytical behavior at topological transition points.
Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space time in general relativity to modern theories of quantum gravity. In quantum many-body systems, the entanglement structure can change if the constituents are connected differently, leading to altered bounds for correlation growth and difficulties for classical computers to simulate large systems. While a universal quantum computer can perform digital simulations, an analog-digital hybrid quantum processor offers advantages such as parallelism. Here, we engineer a class of high-dimensional Ising interactions using a linear one-dimensional ion chain with up to eight qubits through stroboscopic sequences of commuting Hamiltonians. In addition, we extend this method to noncommuting circuits and demonstrate the quantum XY and Heisenberg models using Floquet periodic drives with tunable symmetries. The realization of higher-dimensional spin models offers new opportunities ranging from studying topological phases of matter or quantum spin glasses to future fault-tolerant quantum computation.
<!--HTML-->Despite the importance of gauge theories for modern physics, solving their out-of-equilibrium dynamics on classical computers is extremely challenging. This difficulty is currently stimulating a worldwide effort to implement them in dedicated quantum simulators. In this talk, I will discuss recent progress towards quantum simulation of gauge theories using ultracold atoms. I will show recent breakthroughs to overcome the main challenge, the realization of a dynamics that respects gauge symmetry. In particular, I will present a recent experiment based on engineering of suitable energy penalties in an optical lattice, which has realized a many-body gauge theory in a 71-site Hubbard model and has certified the fulfilment of Gauss’s law for the first time. Further, I will discuss recent progress in understanding gauge breaking errors in this and related models as well as possibilities to mitigate them. I will also illustrate some of the fascinating physics attainable in quantum simulators of gauge theories even for simple target models and with realistic resources, such as dynamical topological quantum phase transitions. Finally, I will discuss the state of art and common issues of gauge quantum simulation, and thus aim at outlining a roadmap towards mature and practically relevant quantum simulation of gauge theories.