arXiv subjects

Ludwig Mathey

Publications and source records attributed to Ludwig Mathey.

At least 19 recordsLinked to original sources

arXiv2026

Pulse engineering via projection of response functions at infinite nonlinear order

Optimal control problems arise in a wide range of scientific disciplines, but the corresponding optimization algorithms often display a strong dependence on hyperparameters that significantly influence performance and convergence. For the optimal implementation of quantum algorithms, these challenges are further amplified by high-dimensional control landscapes and the need for high-fidelity operations. Here, we propose an algorithm for optimal control problems in quantum computing to efficiently generate high-fidelity control protocols for multi-qubit systems in a hyperparameter and gradient free manner. The method, referred to as Pulse Engineering via Projection of response functions at infinite nonlinear order (PEPRino), leverages the framework of response theory to navigate the control landscape to find high-fidelity implementations. This is achieved by determining the control landscape via response functions to infinite order, efficiently evaluated by resummation in terms of the first and second order response function. To demonstrate the approach, we apply it to quantum systems consisting of two and three qubits for the optimal implementation of the Quantum Fourier Transform (QFT). We benchmark the proposed algorithm against the Chopped Random Basis (CRAB) algorithm utilizing the Nelder-Mead method, focusing on the 2-qubit scenario. The results indicate faster convergence regarding iteration steps and computational time, highlighting the advantages of our approach.

quant-ph↗

arXiv2026

Fermionic Hamiltonian engineering with local control

Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible target Hamiltonians from a fixed system Hamiltonian defined by the hardware. We introduce a new framework for fermionic Hamiltonian engineering based on conjugating free evolution under the system Hamiltonian with sequences of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently via a linear program. By interleaving system evolution with these local unitaries, our method realizes effective time evolution under a broad class of target Hamiltonians, with intrinsic robustness to finite-pulse-time errors. In particular, we demonstrate that arbitrary complex tunnelling coefficients can be realized, constrained only by the connectivity of the underlying system Hamiltonian. We illustrate this capability by engineering the dynamics of the non-interacting Harper-Hofstadter model on a 1088-mode lattice and an interacting Fermi-Hubbard chain with complex tunnelling coefficients. By construction, our approach avoids the continuous energy absorption inherent to Floquet engineering.

quant-ph↗

arXiv2026

Time crystals in cavity-BEC systems

The understanding of light-induced dynamical states continues to be a challenging and fruitful pursuit of science. This pursuit is supported by quantum simulation of dynamical phenomena, e.g., in ultracold atom systems. Typically, ultracold atom dynamics are read out destructively, via time-of-flight imaging, limiting a detailed analysis. However, atom-cavity systems provide a real-time readout of the photonic state via photon emission from the cavity, making the system ideally suited for the simulation of dynamical phenomena. Here, we review three distinct time crystalline states, predicted and realized in a cavity-BEC system. We give an example for each of them, based on minimal few-mode models. We characterize the time crystalline states via correlation functions of the cavity mode, and characteristic momentum modes of the condensate. This supports a clear distinction between these time crystals. More generally, the sequence of studies reviewed here, serves as a blueprint for setting up minimal models and their characterization, for dynamical phenomena.

cond-mat.quant-gas↗

arXiv2026

Phase-resolved multichannel quantum escape between limit cycles

Driven-dissipative quantum systems can recover stable dynamical attractors in the semiclassical limit, including coexisting limit cycles. At finite fluctuation strength, this classical coexistence becomes quantum metastability: the corresponding oscillatory states undergo rare fluctuation-induced transitions. We demonstrate phase-resolved quantum escape between two such states in a driven optomechanical resonator. Unlike escape from fixed points, switching between extended attractors occurs across a periodic basin boundary and depends on the phase at which fluctuations approach it. Using quantum-jump trajectories across a controlled quantum-to-classical crossover, we reconstruct the escape geometry directly from switching events. Escape from the small-amplitude cycle proceeds through a single radial corridor and exhibits near-Arrhenius scaling, whereas escape from the large-amplitude cycle involves competing phase-localized corridors with distinct effective activation scales. The resulting curvature in the switching-rate scaling, together with event-conditioned phase distributions, identifies finite-fluctuation multichannel quantum escape between extended attractors.

quant-ph↗

arXiv2026

Critical behavior of the thermal phase transition of U(1) lattice gauge systems

We model the phase transition of a superconductor as a U(1) lattice gauge system, and determine its critical behavior. For this, we perform Monte Carlo simulations, treating the order parameter field and the gauge field on equal footing, without additional approximations. As the defining correlation function, we determine the order parameter correlation function including a gauge string, thus achieving a gauge-invariant characterization of the long-range behavior explicitly. We obtain a critical exponent $\beta$ that is consistent with the exponent of the U(1) transition of neutral bosons, i.e. of Bose-Einstein condensation. We further extract the anomalous dimension $\eta$ for our parameter sets which is significantly smaller than the U(1) anomalous dimension. We determine the critical behavior of the heat capacity, which displays a temperature depends consistent with an XY transition. These results clarify the universality class of the phase transition of this system.

cond-mat.supr-con↗

arXiv2026

Deterministic Quantum Jump (DQJ) Method for Weakly Dissipative Systems

Physical quantum systems are generically coupled to an environment, resulting in open system dynamics. A typical approach to simulating this dynamics is to propagate the density matrix of the system via the Lindblad master equation. This approach is numerically challenging due to the size of the density matrix, which has led to the development of quantum jump methods, which unravel the density matrix into an ensemble of state vectors. These methods utilize a stochastic sampling of the quantum jump times, which becomes inefficent for weakly dissipative dynamics, in which jumps are rare events. Here, we propose the deterministic quantum jump (DQJ) method, which we show to outperform standard quantum jump methods in the weakly dissipative regime, by removing the error of stochastic sampling. We describe the methodology at the single-jump and two-jump level, reconstructing the density matrix at the corresponding level. We demonstrate the performance of the method for two examples, the dissipative transverse-field Ising model, and the dissipative Kerr oscillator. Given that quantum technologies such as quantum computing have weakly dissipative quantum dynamics as their central focus, we propose this method to be utilized in that context, for exploring and understanding quantum technology platforms.

quant-ph↗

arXiv2026

First-order transition into a topological superfluid state in an atom-cavity system

We propose to combine Bose-Einstein condensation in higher Bloch bands and a driven-dissipative cavity-BEC system into a hybrid light-matter platform. Specifically, the condensate is trapped in a bipartite $s$-$p_x$-$p_y$-lattice, with a tunable energy offset. This enables a controlled population transfer from the $s$-orbital to the nearly degenerate $p_x$ and $p_y$ orbitals. The system forms a chiral ground state with $p_x \pm i p_y$ symmetry, with staggered orbital currents. By increasing the transverse pump strength, we drive the system into the superradiant phase, resulting in a self-organized, density checkerboard, which rectifies the staggered chiral order into a topological superfluid state. Using truncated Wigner simulations and complementary mean-field analysis, we determine the phase transition into this state as first order. Our results show that higher-band condensates coupled to a cavity provide a promising platform for engineering non-trivial orbital order and topological superfluid phases in quantum optical many-body systems.

cond-mat.quant-gas↗

arXiv2026

Quantum Deep Learning: A Comprehensive Review

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

quant-ph↗

arXiv2025

Fluctuation amplification engineering in multimode Raman-cavity systems

Parametric amplification is a key ingredient of a wide range of phenomena, from the classical to the quantum domain. Although such phenomena have been demonstrated in non-equilibrium settings, their use for fluctuation engineering has been put forth in Raman-cavity hybrids only recently. In this work, we generalize fluctuation engineering to a multi-mode scenario in which multiple Raman-active modes interact nonlinearly with multiple cavity modes. We demonstrate the emergence of resonant and non-resonant collective fluctuations that can be non-reciprocally controlled by engineering the band dispersion of photons and phonons. As an example we show how Raman fluctuations can be selectively attenuated by tuning the photonic bandgap or even nonresonantly amplified, in marked contrast to the single-mode scenario. We also identify a regime in which the amplification of cavity fluctuations in a specific mode is boosted, surpassing a $\sqrt{N}$ scaling with increasing number of $N$ Raman and cavity modes. Our study reveals the key role of multi-mode interactions on fluctuations in nonlinear cavity-matter hybrids. Noise engineering through different photon and phonon dispersions, as demonstrated here, could be leveraged for the design of novel quantum sensing platforms and advanced spectroscopy in the THz regime.

quant-ph↗

arXiv2025

Controlled generation of 3D vortices in driven atomic Josephson junctions

We propose an ac-driven atomic Josephson junction as a clean and tunable source of three dimensional (3D) solitary waves in quantum fluids. Depending on the height of the junction barrier, the emitted excitations appear as vortex rings at low velocity or vorticity-free rarefaction pulses near the sound velocity, thus spanning the complete Jones-Roberts family of solitons. The Shapiro-step phenomenon renders the emission deterministic: on the first, second, third Shapiro steps, the junction ejects one, two, and three solitary excitations per drive cycle. This enables controlled generation of single- and multi-excitation configurations, allowing detailed studies of the full crossover between vortex rings and rarefaction pulses and their interaction dynamics. In particular, deterministic multi-ring emission provides insights into leapfrogging dynamics of two and three coaxial rings and their decay via boundary-assisted, sound-mediated processes. This ac-driven protocol establishes a compact and reproducible platform for generating, classifying, and controlling 3D solitonic excitations, paving the way for precision studies of nonlinear vortex dynamics, dissipation, and quantum turbulence in trapped superfluids.

cond-mat.quant-gas↗

arXiv2025

Coupling-induced universal dynamics in bilayer two-dimensional Bose gases

The emergence of order in many-body systems and the associated self-similar dynamics governed by dynamical scaling laws is a hallmark of universality far from equilibrium. Measuring and classifying such nontrivial behavior for novel symmetry classes remains challenging. Here, we realize a well-controlled interlayer coupling quench in a tunable bilayer two-dimensional Bose gas, driving the system to an ordered phase. We observe robust self-similar dynamics and a universal critical exponent consistent with diffusion-like coarsening, driven by vortex and antivortex annihilation induced by the interlayer coupling. Our results extend the understanding of universal dynamics in many-body systems and provide a robust foundation for quantitative tests of nonequilibrium effective field theories.

cond-mat.quant-gas↗

arXiv2025

Coherent Optical Control of Electron Dynamics in Patterned Graphene Nanoribbons

The field of coherent electronics aims to advance electronic functionalities by utilizing quantum coherence. Here, we demonstrate a viable and versatile methodology for controlling electron dynamics optically in graphene nanoribbons. In particular, we propose to flatten the band structure of armchair graphene nanoribbons via control electrodes, arranged periodically along the extended direction of the nanoribbon. This addresses a key mechanism for dephasing in solids, which derives from the momentum dependence of the energy gap between the valence and the conduction band. We design an optimal driving field pulse to produce collective Rabi oscillations between these bands, in their flattened configuration. As an example for coherent control, we show that these optimized pulses can be used to invert the entire electronic band population by a $\pi$ pulse in a reversible fashion, and to create a superposition state via a $\pi/2$ pulse, which generates an alternating photocurrent. Our proposal consists of a platform and methodological approach to optically control the electron dynamics of graphene nanoribbons, paving the way toward novel coherent electronic and quantum information processing devices in solid-state materials.

cond-mat.mes-hall↗

arXiv2025

Weak-link to tunneling crossover in an atomic Josephson junction

We present a unified, quantitative description of transport across the crossover between hydrodynamic weak-link flow and tunneling-dominated Josephson dynamics in a three-dimensional quantum fluid. Using an atomic Josephson junction realized in a Bose-Einstein condensate, we continuously tune the barrier strength to access both regimes within a single, well-controlled system. Measurements of the critical current and Josephson oscillations are in quantitative agreement with numerical simulations and analytical modeling, enabling a consistent inference of the microscopic mechanisms governing dissipation. In the weak-link regime, dissipative transport is consistent with vortex-ring-mediated phase slips, whereas in the tunneling regime it is consistent with rarefaction-pulse excitations. The crossover is further reflected in a transition from a multi-harmonic to a predominantly single-harmonic current-phase relation, signaling the emergence of tunneling-dominated transport. These results establish a general framework linking nonlinear excitations to coherent quantum transport across distinct dynamical regimes. More broadly, they provide insight into the microscopic origin of dissipation in driven quantum fluids, a problem that remains difficult to access in conventional solid-state systems.

cond-mat.quant-gas↗

arXiv2025

Realizing an Atomtronic AQUID in a Rotating-Box Potential

Atomtronic devices are matter-wave circuits designed to emulate the functional behavior of their electronic counterparts. Motivated by superconducting quantum interference devices (SQUIDs), atomic quantum interference devices (AQUIDs) have been developed using Bose-Einstein condensates (BECs) confined in toroidal geometries. Here, we propose and numerically investigate an alternative implementation of an AQUID based on a BEC confined in a rotating box potential. A ring-like topology is established by introducing a central depletion region via a repulsive potential barrier. We observe the hallmark AQUID feature -- quantized phase winding that increases in discrete steps with angular velocity. Centrifugal effects induced by rotation degrade phase coherence and impair AQUID performance, which we mitigate by applying a counteracting harmonic confinement. Phase slips are found to be mediated by a vortex propagating from the central depletion zone to the edge of the condensate. To characterize the voltage response, we induce a bias current by translating the box along its long axis while keeping the central barrier fixed. This generates a density imbalance between the two reservoirs, exhibiting a periodic dependence on angular velocity -- analogous to the voltage-flux relation in electronic SQUIDs. Our results demonstrate that rotating box geometries provide a viable and flexible platform for realizing atomtronic AQUIDs with controllable dynamics and well-defined response characteristics.

cond-mat.quant-gas↗

arXiv2025

Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities

Nonlinear classical mechanics has established rich phenomena. These include limit tori defined by toroidal attractors supporting quasiperiodic motion with incommensurate frequencies. We study the fate of such structures in open quantum systems using two coupled driven-dissipative Kerr cavities modeled via the Lindblad master equation. Combining Liouvillian spectral theory with the truncated Wigner approximation, we characterize the quantum-to-classical crossover. In the classical limit, two pairs of purely imaginary Liouvillian eigenvalues signal persistent quasiperiodic modes. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes and leading to the quantum melting of the torus. The associated Liouvillian gaps vanish algebraically in the classical limit, indicating a dynamical critical crossover with spontaneous breaking of time-translational symmetry. Quantum trajectory analysis reveals that this melting is driven by fluctuation-induced dephasing. Using a circular-variance-based order parameter, we uncover universal scaling in system size and time. These results establish quantum melting of limit tori as a distinct and robust non-equilibrium critical phenomenon, with clear experimental signatures in trapped ions and superconducting circuits.

quant-ph↗

arXiv2025

Lamb-Dicke Dynamics of Interacting Rydberg Atoms Coupled to the Motion of an Optical Tweezer Array

Neutral Rydberg atoms trapped in optical tweezer arrays provide a platform for quantum simulation and computation. In this work, we investigate the Lamb-Dicke dynamics of coupled Rydberg atoms for different trapping frequencies. We model the atomic motion by both internal and motional degrees of freedom, in which the motional states arise due to the oscillation of each atom in optical tweezer traps due to the light-atom interaction. In this setup, the internal states are coupled to a laser light with a Rabi frequency, while each internal state of each atom is also harmonically trapped with a trap frequency that depends on the internal state. The impact of the coherent motion of the optical tweezers on the collective dynamics of the many-body Rydberg atoms is explored for varying Lamb-Dicke parameters and with different trap frequencies. We see the occurrence of dynamical phases e.g., Rabi oscillations in the decoupled limit, the limit torus phase for magic trapping, and the limit cycle phase as the trap frequency is further increased.

quant-ph↗

arXiv2025

Atomic Josephson Parametric Amplifier

We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is encoded in a specific microscopic pattern of density waves and phase excitations that can be addressed within the experimental cold atoms capabilities. This work paves the way for tunable amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing. At the same time, our analysis provides the microscopic explanation of the general notion of parametric amplification occurring in nonlinear coherent devices.

cond-mat.quant-gas↗

arXiv2025

Eigen-SNAP gate for photonic qubits in a cavity-transmon system

In the pursuit of robust quantum computing, we put forth a platform based on photonic qubits in a circuit-QED environment. Specifically, we propose a versatile two-qubit gate based on two cavities coupled via a transmon, constituting a selective number-dependent phase gate operating on the in-phase eigenmodes of the two cavities, the Eigen-SNAP gate. This gate natively operates in the dispersive coupling regime of the cavities and the transmon, and operates by driving the transmon externally, to imprint desired phases on the number states. As an example for the utility of the Eigen-SNAP gate, we implement a $\sqrt{\text{SWAP}}$ gate on a system of two logical bosonic qubits encoded in the cavities. Further, we use numerical optimization to determine the optimal implementation of the $\sqrt{\text{SWAP}}$. We find that the fidelities of these optimal protocols are only limited by the coherence times of the system's components. These findings pave the way to continuous variable quantum computing in cavity-transmon systems.

quant-ph↗