arXiv subjects

Ian Mondragon-Shem

Publications and source records attributed to Ian Mondragon-Shem.

At least 19 recordsLinked to original sources

arXiv2026

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

quant-ph↗

arXiv2025

Exceeding the Parametric Drive Strength Threshold in Nonlinear Circuits

Superconducting quantum circuits rely on strong drives to implement fast gates, high-fidelity readout, and state stabilization. However, these drives can induce uncontrolled excitations, so-called "ionization", that compromise the fidelity of these operations. While now well-characterized in the context of qubit readout, it remains unclear how general this limitation is across the more general setting of parametric control. Here, we demonstrate that a nonlinear coupler, exemplified by a transmon, undergoes ionization under strong parametric driving, leading to a breakdown of coherent control and thereby limiting the accessible gate speeds. Through experiments and numerical simulations, we associate this behavior with the emergence of drive-induced chaotic dynamics, which we characterize quantitatively using the instantaneous Floquet spectrum. Our results reveal that the Floquet spectrum provides a unifying framework for understanding strong-drive limitations across a wide range of operations on superconducting quantum circuits. This insight establishes fundamental constraints on parametric control and offers design principles for mitigating drive-induced decoherence in next-generation quantum processors.

quant-ph↗

arXiv2022

Local imaging of diamagnetism in proximity coupled niobium nano-island arrays on gold thin films

In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low local applied magnetic fields, is well described by this junction network model, and we discuss these results as they relate to inhomogeneous two-dimensional (2D) superconductors. Our model of the static magnetic response of the arrays does not fully capture the onset of nonlinearity and dissipation with increasing applied field, as these effects are associated with vortex motion due to the dynamic nature of the scanning SQUID susceptometry measurement. This work demonstrates a model 2D superconducting system with engineered disorder and highlights the impact of dissipation on the local magnetic properties of 2D superconductors and Josephson junction arrays.

cond-mat.supr-con↗

arXiv2022

Computer-aided quantization and numerical analysis of superconducting circuits

The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at the lumped-element level, starting from a circuit network and culminating in a Hamiltonian appropriately describing the quantum properties of the circuit, is a well-established procedure, yet cumbersome to carry out manually for larger circuits. We present work utilizing symbolic computer algebra and numerical diagonalization routines versatile enough to tackle a variety of circuits. Results from this work are accessible through a newly released module of the scqubits package.

quant-ph↗

arXiv2021

Imaging and controlling vortex dynamics in mesoscopic superconductor-normal-metal-superconductor arrays

Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, we obtain a variety of striking spatial patterns that encode information about the energy landscape for vortices in the system. We interpret these patterns in terms of local vortex dynamics and extract the relative strengths of the characteristic energy scales in the system, such as the vortex-magnetic field and vortex-vortex interaction strengths, as well as the vortex chemical potential. We also demonstrate that the relative strengths of the interactions can be tuned and show how these interactions shift with an applied bias. The high degree of tunability and local nature of such vortex imaging and control not only enable new understanding of vortex interactions, but also have potential applications in more complex systems such as those relevant to quantum computing.

cond-mat.supr-con↗

arXiv2020

The fate of quantum many-body scars in the presence of disorder

Experiments performed on strongly interacting Rydberg atoms have revealed surprising persistent oscillations of local observables. These oscillations have been attributed to a special set of non-ergodic states, referred to as quantum many-body scars. Although a significant amount of research has been invested to understand these special states, it has remained unclear how stable scar states are against disorder. We address this question by studying numerically and analytically the magnetization and spatio-temporal correlators of a model of interacting Rydberg atoms in the presence of disorder. While the oscillation amplitudes of these observables decay with time as the disorder strength is increased, their oscillation frequency remains remarkably constant. We show that this stability stems from resonances in the disordered spectrum that are approximately centered at the same scar energies of the clean system. We also find that multiple additional sets of scar resonances become accessible due to the presence of disorder and further enhance the oscillation amplitudes. Our results show the robustness of non-ergodic dynamics in scar systems, and opens the door to understanding the behavior of experimentally realistic systems.

cond-mat.quant-gas↗

arXiv2019

Robust topological invariants of topological crystalline phases in the presence of impurities

Topological crystalline phases (TCPs) are topological states protected by spatial symmetries. A broad range of TCPs have been conventionally studied by formulating topological invariants (symmetry indicators) at invariant momenta in the Brillouin zone, which leaves open the question of their stability in the absence of translational invariance. In this work, we show that robust basis-independent topological invariants can be generically constructed for TCPs using projected symmetry operators. Remarkably we show that the real-space topological markers of these invariants are exponentially localized to the fixed points of the spatial symmetry. As a result, this real-space structure protects them against the presence of impurities that are located away from the fixed points. By considering all possible symmetry centers in a crystalline system we can generate a mesh of real-space topological markers that can provide a local topological distinction for TCPs. We illustrate the robustness of this mesh of invariants with 1D and 2D TCPs protected by inversion, rotational and mirror symmetries. Finally, we find that the boundary modes of these TCPs can also exhibit robust topological invariants with localized markers on the edges. We illustrate this with the gapless Majorana boundary modes of mirror-symmetric topological superconductors, and relate their integer topological edge invariant with a quantized effective edge polarization.

cond-mat.dis-nn↗

arXiv2019

Quantized frequency-domain polarization of driven phases of matter

Periodically driven quantum systems can realize novel phases of matter that do not exist in static settings. We study signatures of these drive-induced phases on the $(d+1)$-dimensional Floquet lattice, comprised of $d$ spatial dimensions plus the frequency domain. The average position of Floquet eigenstates along the frequency axis can be written in terms of a non-adiabatic Berry phase, which we interpret as frequency-domain polarization. We argue that whenever this polarization is quantized to a nontrivial value, the phase of matter cannot be continuously connected to a time-independent state and, as a consequence, it captures robust properties of its dynamics. We illustrate this in driven topological phases, such as superconducting wires and the anomalous Floquet Anderson insulator; as well as in driven symmetry-broken phases, such as time crystals. We further introduce a new dynamical phase of matter that we construct by imposing quantization conditions on its frequency-domain polarization. This illustrates the potential for using this kind of polarization as a tool to search for new driven phases of matter.

cond-mat.mes-hall↗

arXiv2017

Observation of domain wall motion in a polycrystalline vortex lattice

We present measurements showing how disorder determines the dynamics of a vortex lattice. Using superconductor-normal-superconductor (SNS) arrays placed in finite magnetic fields, disorder is introduced by shifting the field away from values where the vortex lattice is commensurate with the SNS array. By applying a current to drive vortex motion, we observe a two-step transition at incommensurate fields: first from pinned vortices to lattice defect motion, and then from individual defect to bulk vortex lattice flow. This behavior is consistent with a polycrystalline vortex structure where defects form on the edges of crystalline domains. This demonstrates that a disordered, interacting vortex system can favor interface physics rather than a quasiperiodic regime.

cond-mat.supr-con↗

arXiv2016

History-dependent dissipative vortex dynamics in superconducting arrays

We perform current(I)-voltage(V) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex de-pinning current, and a broad linear I-V region with an extrapolated I intercept equal to the de-pinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history dependent dissipative force. This approach has not been considered previously, yet is crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.

cond-mat.supr-con↗

arXiv2015

Many-body mobility edge due to symmetry-constrained dynamics and strong interactions

We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and anti-ferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.

cond-mat.dis-nn↗

arXiv2014

Entanglement of a 3D generalization of the Kitaev model on the diamond lattice

We study the entanglement properties of a three dimensional generalization of the Kitaev honeycomb model proposed by Ryu [Phys. Rev. B 79, 075124, (2009)]. The entanglement entropy in this model separates into a contribution from a $Z_2$ gauge field and that of a system of hopping Majorana fermions, similar to what occurs in the Kitaev model. This separation enables the systematic study of the entanglement of this 3D interacting bosonic model by using the tools of non-interacting fermions. In this way, we find that the topological entanglement entropy comes exclusively from the $Z_2$ gauge field, and that it is the same for all of the phases of the system. There are differences, however, in the entanglement spectrum of the Majorana fermions that distinguish between the topologically distinct phases of the model. We further point out that the effect of introducing vortex lines in the $Z_2$ gauge field will only change the entanglement contribution of the Majorana fermions. We evaluate this contribution to the entanglement which arises due to gapless Majorana modes that are trapped by the vortex lines.

cond-mat.stat-mech↗

arXiv2014

Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions

We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and internal degrees of freedom of fermions are affected by the presence of disorder in such cases. We develop entanglement tools that reveal the existence of metallic states in the presence of disorder and further show clear signatures of the corresponding localization transition even in the presence of interactions. In systems where the internal degrees of freedom are coupled with the motion of the electrons, topological phases develop. We subject a topological insulator model to different types of disorder and discuss how the topological aspects of the system can be captured through entanglement, even at strong disorder.

cond-mat.dis-nn↗

arXiv2013

Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder

The chiral AIII symmetry class in the periodic table of topological insulators contains topological phases classified by a winding number $ν$ for each odd space-dimension. An open problem for this class is the characterization of the phases and phase-boundaries in the presence of strong disorder. In this work, we derive a covariant real-space formula for $ν$ and, using an explicit 1-dimensional disordered topological model, we show that $ν$ remains quantized and non-fluctuating when disorder is turned on, even though the bulk energy-spectrum is completely localized. Furthermore, $ν$ remains robust even after the insulating gap is filled with localized states, but when the disorder is increased even further, an abrupt change of $ν$ to a trivial value is observed. Using exact analytic calculations, we show that this marks a critical point where the localization length diverges. As such, in the presence of disorder, the AIII class displays a markedly different physics from everything known to date, with robust invariants being carried entirely by localized states and bulk extended states emerging from an absolutely localized spectrum. Detailed maps and a clear physical description of the phases and phase boundaries are presented based on numerical and exact analytic calculations.

cond-mat.dis-nn↗

arXiv2012

Characterizing disordered fermion systems using the momentum-space entanglement spectrum

The use of quantum entanglement to study condensed matter systems has been flourishing in critical systems and topological phases. Additionally, using real-space entanglement entropies and entanglement spectra one can characterize localized and delocalized phases of disordered fermion systems. Here we instead propose the momentum-space entanglement spectrum as a means of characterizing disordered models. We show that localization in 1D arises from the momentum space entanglement between left and right movers and illustrate our methods using explicit models with spatially correlated disorder that exhibit phases which avoid complete Anderson localization. The momentum space entanglement spectrum clearly reveals the location of delocalized states in the energy spectrum and can be used as a signature of the phase transition between a delocalized and localized phase.

cond-mat.mes-hall↗

arXiv2011

Unconventional Bose-Einstein condensations from spin-orbit coupling

According to the "no-node" theorem, many-body ground state wavefunctions of conventional Bose-Einstein condensations (BEC) are positive-definite, thus time-reversal symmetry cannot be spontaneously broken. We find that multi-component bosons with spin-orbit coupling provide an unconventional type of BECs beyond this paradigm. We focus on the subtle case of isotropic Rashba spin-orbit coupling and the spin-independent interaction. In the limit of the weak confining potential, the condensate wavefunctions are frustrated at the Hartree-Fock level due to the degeneracy of the Rashba ring. Quantum zero-point energy selects the spin-spiral type condensate through the "order-from-disorder" mechanism. In a strong harmonic confining trap, the condensate spontaneously generates a half-quantum vortex combined with the skyrmion type of spin texture. In both cases, time-reversal symmetry is spontaneously broken. These phenomena can be realized in both cold atom systems with artificial spin-orbit couplings generated from atom-laser interactions and exciton condensates in semi-conductor systems.

cond-mat.supr-con↗

arXiv2009

Ultracold atoms in optical lattices induced by photonic crystals

We propose a way of generating optical lattices embedded in photonic crystals. By setting up extended modes in photonic crystals, ultracold atoms can be mounted in different types of field intensity distributions. This novel way of constructing optical lattices can be used to produce more elaborate periodic potentials by manufacturing appropriate geometries of photonic crystals. We exemplify this with a square lattice and comment on the possibility of using geometries with defects.

cond-mat.quant-gas↗

arXiv2009

Coulomb matrix elements of bilayers of confined charge carriers with arbitrary spatial separation

We describe a practical procedure to calculate the Coulomb matrix elements of 2D spatially separated and confined charge carriers, which are needed for detailed theoretical descriptions of important condensed matter finite systems. We derive an analytical expression, for arbitrary separations, in terms of a single infinite series and apply a u-type Levin transform in order to accelerate the resulting infinite series. This procedure has proven to be efficient and accurate. Direct consequences concerning the functional dependence of the matrix elements on the separation distance, transition amplitudes and the diagonalization of a single electron-hole pair in vertically stacked parabolic quantum dots are presented.

cond-mat.mes-hall↗