arXiv subjects

Alexander Schuckert

Publications and source records attributed to Alexander Schuckert.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum simulation of bubble nucleation across a quantum phase transition

The liquid-vapor transition is a classic example of a discontinuous (first-order) phase transition. Such transitions underlie many phenomena in cosmology, nuclear and particle physics, and condensed-matter physics. They give rise to long-lived metastable states, whose decay can be driven by either thermal or quantum fluctuations. Yet, direct experimental observations of how these states collapse into a stable phase remain elusive in the quantum regime. Here, we use a trapped-ion quantum simulator to observe the real-time dynamics of ``bubble nucleation'' induced by quantum fluctuations. Bubbles are localized domains of the stable phase which spontaneously form, or nucleate, and expand as the system is driven across a discontinuous quantum phase transition. Implementing a mixed-field Ising spin model with tunable and time-dependent interactions, we track the microscopic evolution of the metastable state as the Hamiltonian parameters are varied in time with various speeds, bringing the system out of equilibrium. Site-resolved measurements reveal the emergence and evolution of finite-size quantum bubbles, providing direct insight into the mechanism by which the metastable phase decays. We also identify nonequilibrium scaling behavior near the transition, consistent with a generalized Kibble-Zurek mechanism. Our results demonstrate the power of quantum simulators to probe out-of-equilibrium many-body physics, including quantum bubble nucleation, a key feature of discontinuous quantum phase transitions, with application to studies of matter formation in the early universe.

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arXiv2025

Multi-Target Rydberg Gates via Spatial Blockade Engineering

Multi-target gates offer the potential to reduce gate depth in syndrome extraction for quantum error correction. Although neutral-atom quantum computers have demonstrated native multi-qubit gates, existing approaches that avoid additional control or multiple atomic species have been limited to single-target gates. We propose single-control-multi-target CZ^{\otimes N}) gates on a single-species neutral-atom platform that require no extra control and have gate durations comparable to standard CZ gates. Our approach leverages tailored interatomic distances to create an asymmetric blockade between the control and target atoms. Using a GPU-accelerated pulse synthesis protocol, we design smooth control pulses for CZZ and CZZZ gates, achieving fidelities of up to 99.55% and 99.24%, respectively, even in the presence of simulated atom placement errors and Rydberg-state decay. This work presents a practical path to implementing multi-target gates in neutral-atom systems, significantly reducing the resource overhead for syndrome extraction.

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arXiv2025

Emergence of Fermi's Golden Rule in the Probing of a Quantum Many-Body System

Fermi's Golden Rule (FGR) is one of the most impactful formulas in quantum mechanics, providing a link between easy-to-measure observables - such as transition rates - and fundamental microscopic properties - such as density of states or spectral functions. Its validity relies on three key assumptions: the existence of a continuum, an appropriate time window, and a weak coupling. Understanding the regime of validity of FGR is critical for the proper interpretation of most spectroscopic experiments. While the assumptions underlying FGR are straightforward to analyze in simple models, their applicability is significantly more complex in quantum many-body systems. Here, we observe the emergence and breakdown of FGR, using a strongly interacting homogeneous spin-$1/2$ Fermi gas coupled to a radio-frequency (rf) field. Measuring the transition probability into an outcoupled internal state, we map the system's dynamical response diagram versus the rf-pulse duration $t$ and Rabi frequency $Ω_0$. For weak drives, we identify three regimes: an early-time regime where the transition probability takes off as $t^2$, an intermediate-time FGR regime, and a long-time non-perturbative regime. Beyond a threshold Rabi frequency, Rabi oscillations appear. Our results provide a blueprint for the applicability of linear response theory to the spectroscopy of quantum many-body systems.

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arXiv2025

Constrained many-body phases in a $\mathbb{Z}_2$-Higgs lattice gauge theory

We study the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping and the confinement of single particles. The pair hopping results in a bunching state with superextensive energy and macroscopic particle number fluctuations at strong electric field strengths and weak on-site interactions. The bunching state crosses over into a pair superfluid phase as the on-site interaction increases, characterized by a finite superfluid density and powerlaw-decaying pair correlations. At large on-site interaction strengths and driven by effective interactions induced by the gauge constraint, the superfluid transitions into an incompressible pair Mott insulator phase. At weak field strengths and on-site interactions, we find a plasma-like region, where single bosons exhibit large short-range correlations and the ground state is composed almost equally of states with even and odd local boson occupation. The presence of a bunching state with large number fluctuations, which is difficult to study using classical numerics, motivates experimental realizations in hybrid boson-qubit quantum simulation platforms such as circuit QED, neutral atoms, and trapped ions. Our findings highlight the rich interplay between gauge fields and soft-core bosonic matter.

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arXiv2024

Observation of string-breaking dynamics in a quantum simulator

Spontaneous particle-pair formation is a fundamental phenomenon in nature. It can, for example, appear when the potential energy between two particles increases with separation, as if they were connected by a tense string. Beyond a critical separation, new particle pairs can form, causing the string to break. String-breaking dynamics in quantum chromodynamics play a vital role in high-energy particle collisions and early universe evolution. Simulating string evolution and hadron formation is, therefore, a grand challenge in modern physics. Quantum simulators, well-suited for studying dynamics, are expected to outperform classical computing methods. However, the required experimental capabilities to simulate string-breaking dynamics have not yet been demonstrated, even for simpler models of the strong force. We experimentally probe, for the first time, the spatiotemporal dynamics of string-breaking in a (1+1)-dimensional $\mathbb{Z}_2$ lattice gauge theory using a fully programmable trapped-ion quantum simulator. We emulate external static charges and strings via site-dependent magnetic-field control enabled by a dual array of tightly focused laser beams targeting individual ions. First, we study how confinement affects isolated charges, finding that they freely spread without string tension but exhibit localized oscillations when tension is increased. Then, we observe and characterize string-breaking dynamics of a string stretched between two static charges after an abrupt increase in string tension. Charge pairs appear near the string edges and spread into the bulk, revealing a route to dynamical string-breaking distinct from the conventional Schwinger mechanism. Our work demonstrates that analog quantum simulators have achieved the necessary control to explore string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.

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arXiv2024

Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.

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arXiv2024

Thermalization and Criticality on an Analog-Digital Quantum Simulator

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

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arXiv2024

Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon

Simulating fermions coupled to spin degrees of freedom, relevant for a range of quantum field theories, represents a promising application for quantum simulators. Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions, and mapping bosons demands substantial quantum-computational overhead. These features complicate the realization of mixed fermion-boson quantum systems in digital quantum computers. We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon. Specifically, we show how to use a dynamical lattice of coupled nuclear spins and conduction-band electrons to realize a quantum field theory: an extended Jackiw-Rebbi model involving coupled fermions and quantum rotors. We demonstrate the feasibility of observing dynamical mass generation and a confinement-deconfinement quantum phase transition in 1+1 dimensions on this platform, even in the presence of strong long-range Coulomb interactions. Furthermore, we employ finite-temperature Hartree-Fock-Bogoliubov simulations to investigate the dynamics of mass generation in two-dimensional square and honeycomb arrays, showing that this phenomenon can be simulated with realistic experimental parameters. Our findings reveal two distinct phases, and demonstrate robustness against the addition of Coulomb interactions. Finally, we discuss experimental signatures of the phases through transport and local charge sensing in dopant arrays. This study lays the foundation for quantum simulations of quantum field theories exhibiting fermions coupled to spin degrees of freedom using donors in silicon.

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arXiv2023

Observation of a finite-energy phase transition in a one-dimensional quantum simulator

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to $23$ spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.

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arXiv2023

Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers

Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, [Lu, Bañuls and Cirac, PRX Quantum 2, 020321 (2021)] suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.

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arXiv2023

Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $\langle ψ| e^{-i \hat H t}|ψ\rangle$ from initial states $|ψ\rangle$ and a time evolution under the Hamiltonian $\hat H$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.

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arXiv2023

The strongly driven Fermi polaron

Quasiparticles are emergent excitations of matter that underlie much of our understanding of quantum many-body systems. Therefore, the prospect of manipulating their properties with external fields -- or even destroying them -- has both fundamental and practical implications. However, in solid-state materials it is often challenging to understand how quasiparticles are modified by external fields owing to their complex interplay with other collective excitations, such as phonons. Here, we take advantage of the clean setting of homogeneous quantum gases and fast radio-frequency control to manipulate Fermi polarons -- quasiparticles formed by impurities interacting with a non-interacting Fermi gas -- from weak to ultrastrong drives. Exploiting two internal states of the impurity species, we develop a steady-state spectroscopy, from which we extract the energy of the driven polaron. We measure the decay rate and the quasiparticle residue of the driven polaron from the Rabi oscillations between the two internal states. At large drive strengths, the so-extracted quasiparticle residue exceeds unity, raising intriguing questions on the relationship between the Rabi oscillations and the impurity's spectral functions. Our experiment establishes the driven Fermi polaron as a promising platform for studying controllable quasiparticles in strongly driven quantum matter.

cond-mat.quant-gas↗

arXiv2023

Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics

Preparing finite temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu, Banuls and Cirac, PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions.

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arXiv2023

Ultracold plasmas from strongly anti-correlated Rydberg gases in the Kinetic Field Theory formalism

The dynamics of correlated systems is relevant in many fields ranging from cosmology to plasma physics. However, they are challenging to predict and understand even for classical systems due to the typically large numbers of particles involved. Here, we study the evolution of an ultracold, correlated many-body system with repulsive interactions and initial correlations set by the Rydberg blockade using the analytical framework of Kinetic Field Theory (KFT). The KFT formalism is based on the path-integral formulation for classical mechanics and was first developed and successfully used in cosmology to describe structure formation in Dark Matter. The theoretical framework offers a high flexibility regarding the initial configuration and interactions between particles and, in addition, is computationally cheap. More importantly, the analytic approach allows us to gain better insight into the processes which dominate the dynamics. In this work we show that KFT can be applied in a much more general context and study the evolution of a correlated ion plasma. We find good agreement between the analytical KFT results for the evolution of the correlation function and results obtained from numerical simulations. We use the correlation functions obtained with KFT to compute the temperature increase in the ionic system due to disorder-induced heating. For certain choices of parameters we observe that the effect can be reversed, leading to correlation cooling. Due to its numerical efficiency as compared to numerical simulations, a detailed study using KFT can help to constrain parameter spaces where disorder-induced heating is minimal in order to reach the regime of strong coupling.

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arXiv2021

Visualizing spinon Fermi surfaces with time-dependent spectroscopy

Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. In order to probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground state energy at momentum $\mathbf{q} = (π,π)$, where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route towards solving the mystery of the Fermi arcs in the cuprate materials.

cond-mat.quant-gas↗

arXiv2020

Non-local emergent hydrodynamics in a long-range quantum spin system

Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as $r^{-α}$. While diffusion is recovered for $α>1.5$, longer-ranged couplings with $0.5<α\leq 1.5 $ give rise to effective classical Lévy flights; a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<α\leq1.5$ autocorrelations show hydrodynamic tails decaying in time as $t^{-1/(2α-1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.

cond-mat.quant-gas↗

arXiv2020

Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations

The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input. This leaves many of the general assumptions of ETH untested. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH. We discuss and propose protocols to independently measure fluctuations and dissipations as well as higher-order time ordered correlation functions. We first show how the emergence of fluctuation dissipation relations from a nonequilibrium initial state can be observed for the 2D Bose-Hubbard model in superconducting qubits or quantum gas microscopes. Then we focus on the long-range transverse field Ising model (LTFI), which can be realized with trapped ions. The LTFI exhibits rich thermalization phenomena: For strong transverse fields, we observe prethermalization to an effective magnetization-conserving Hamiltonian in the fluctuation dissipation relations. For weak transverse fields, confined excitations lead to non-thermal features resulting in a violation of the fluctuation-dissipation relations up to long times. Moreover, in an integrable region of the LTFI, thermalization to a generalized Gibbs ensemble occurs and the fluctuation-dissipation relations enable an experimental diagonalization of the Hamiltonian. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.

cond-mat.quant-gas↗

arXiv2020

Rydberg Entangling Gates in Silicon

In this paper, we propose a new Rydberg entangling gate scheme which we demonstrate theoretically to have an order of magnitude improvement in fidelities and speed over existing protocols. We find that applying this gate to donors in silicon would help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling. We calculate multivalley Rydberg interactions for several donor species using the Finite Element Method, and show that induced electric dipole and Van der Waals interactions, calculated here for the first time, are important even for low-lying excited states. We show that Rydberg gate operation is possible within the lifetime of donor excited states with 99.9% fidelity for the creation of a Bell state in the presence of decoherence.

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