arXiv subjects

Ignacio Franco

Publications and source records attributed to Ignacio Franco.

At least 19 recordsLinked to original sources

arXiv2026

How NOT to build control-target gates in semiconductor quantum dots and beyond

Universal quantum computation requires single-qubit control together with at least one entangling two-qubit gate. CNOT and CROT gates are two famous examples of such gates, wherein the state of one qubit (control) dictates the transformation applied to the other (target). By using a simple derivation motivated by symmetry, we show that current device architectures of semiconductor-based quantum dot devices prevent efficient implementation of a CNOT and other asymmetric control-target gates via Heisenberg exchange, Coulomb repulsion, or other interaction that is invariant under spin exchange. Guided by this general principle, we propose a heterogeneous blueprint of double quantum dot devices that enables efficient implementation of the CNOT by breaking the spin exchange symmetry. Crucially, our numerical simulations predict that this novel device blueprint can enable a single-pulse fault-tolerant 100-ns CNOT gate in isotopically purified silicon.

cond-mat.mes-hall↗

arXiv2026

TENSO: Software Package for Numerically Exact Open Quantum Dynamics Based on Efficient Tree Tensor Network Decomposition of the Hierarchical Equations of Motion

TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the hierarchical equations of motion (HEOM) that efficiently curbs its curse of dimensionality with bath complexity. As such, TENSO enables exact non-Markovian open quantum dynamics simulations even with complex environments typical of chemistry and quantum information science. TENSO allows for time-dependent drive in the system, and for non-commuting fluctuations. More generally, TENSO efficiently propagates the dynamics for any method with a generator of the dynamics that can be expressed in a sum-of-products form, including the HEOM and multi-layer multiconfigurational time-dependent Hartree methods. TENSO enables simulations using tensor trees and trains of arbitrary order, and implements three propagation strategies for the coupled master equations; two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive rank method with a variable memory footprint controlled by the target level of computational error. In contrast to the accompanying theory and algorithmic paper [J. Chem. Phys. 163, 104109 (2025)] the focus here is on the practical usage and applications of TENSO with underlying theoretical concepts introduced only as needed.

physics.chem-ph↗

arXiv2026

Light-Matter Interactions Beyond the Dipole Approximation in Extended Systems Without Multipole Expansion

We present a general theoretical framework to capture light-matter interactions beyond the electric-dipole approximation (EDA), applicable to extended nano- and microscale materials interacting with spatially structured electric fields without truncation at finite multipolar order. The approach is based on the Power-Zienau-Woolley (PZW) Hamiltonian for light-matter interactions and a representation of the material's Hamiltonian in a basis of maximally localized Wannier functions (MLWFs), obtainable from first-principles calculations. We utilize this approach to clarify the limitations of the ubiquitous dipole approximation. We consider electric fields with both uniform and non-uniform intensities and a range of ratios of system size to the wavelength of light. Through this analysis, we identify the conditions under which the EDA breaks down, leading to significant errors in the light-induced dynamics. Contrary to conventional belief, we find that the EDA is remarkably robust for uniformly illuminated 1-D or 2-D materials when light propagates perpendicular to the material. For 3-D materials or non-perpendicular illumination of lower-dimensional materials, conventional wisdom holds and the EDA begins to break down when the wavelength becomes comparable to the system size. Furthermore, the EDA fails when the material is illuminated partially or non-uniformly. For slowly varying field intensities this failure can be corrected by finite-order multipolar corrections. However, for fields that vary substantially, correcting via multipolar terms becomes computationally impractical. In contrast, our approach captures beyond-dipole light-matter interactions at the computational cost of a standard dipole calculation. This efficiency enables accurate first-principles simulations of spatially structured light-matter dynamics in nanoscale devices, quantum materials, and interfaces.

quant-ph↗

arXiv2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM -- rooted in bath correlation function decompositions -- proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna--Matthews--Olson complex model highlight TTN-HEOM's superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

quant-ph↗

arXiv2025

General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal system-bath couplings

This paper extends the previously reported theory of dissipation pathways [J. Chem. Phys. 160, 214111 (2024)] to incorporate off-diagonal subsystem-bath coupling, which is often required to model molecular systems where the environment directly influences transitions and couplings between subsystem states. We systematically derive master equations for both population transfer and dissipation into individual bath components, for which we also rigorously prove energy conservation and detailed balance. The approach is based on second-order perturbation theory with respect to the subsystem-bath couplings, whose form is not limited to any specific model. The accuracy of the developed method is tested by applying it to diverse model Hamiltonians involving linearly coupled harmonic oscillator baths and comparing the outcomes against the hierarchical equations of motion (HEOM) method. Overall, our method accurately quantifies the contributions of specific bath components to the overall dissipation while significantly reducing the computational cost compared to numerically exact methods such as HEOM, thus offering a path to examine how vibronic interactions steer non-adiabatic processes in realistic chemical systems.

physics.chem-ph↗

arXiv2025

Dissipation Pathways in a Photosynthetic Complex

Determining how energy flows within and between molecules is crucial for understanding chemical reactions, material properties, and even vital processes such as photosynthesis. While the general principles of energy transfer are well established, elucidating the specific molecular pathways by which energy is funneled remains challenging as it requires tracking energy flow in complex molecular environments. Here, we demonstrate how photon excitation energy is partially dissipated in the light-harvesting Fenna-Matthews-Olson (FMO) complex, mediating the excitation energy transfer from light-harvesting chlorosomes to the photosynthetic reaction center in green sulfur bacteria. Specifically, we isolate the contribution of the protein and specific vibrational modes of the pigment molecules to the energy dynamics. For this, we introduce an efficient computational implementation of a recently proposed theory of dissipation pathways for open quantum systems. Using it and a state-of-the-art FMO model with highly structured and chromophore-specific spectral densities, we demonstrate that energy dissipation is dominated by low-frequency modes ($<$ 800 cm$^{-1}$) as their energy range is near-resonance with the energy gaps between electronic states of the pigments. We identify the most important mode for dissipation to be in-plane breathing modes ($\sim$200 cm$^{-1}$) of the bacteriochlorophylls in the complex. Conversely, far-detuned intramolecular vibrations with higher frequencies ($>$ 800 cm$^{-1}$) play no role in dissipation. Interestingly, the FMO complex first needs to borrow energy from the environment to release excess photonic energy, making the energy dissipation dynamics non-monotonic. Beyond their fundamental value, these insights can guide the development of artificial light-harvesting devices and, more broadly, engineer environments for chemical and quantum control tasks.

cond-mat.other↗

arXiv2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the bexcitonic generalization of the numerically-exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system-bath interaction. These master equations are constructed based on the time-dependent Dirac--Frenkel variational principle which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, Tensor Equations for Non-Markovian Structured Open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: Two fixed-rank methods that require a constant memory footprint during the dynamics, and one adaptive-rank method with variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude--Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable to simulate both dephasing and relaxation dynamics of driven quantum system interacting with structured baths, even those of chemical complexity, with affordable computational cost.

quant-ph↗

arXiv2025

Robust purely optical signatures of Floquet states in laser-dressed crystals

Strong light-matter interactions can create non-equilibrium materials with on-demand novel functionalities. For periodically driven solids, the Floquet theorem provides the natural states to characterize the physical properties of these laser-dressed systems. However, signatures of the Floquet states are needed, as common experimental conditions, such as pulsed laser excitation and dissipative many-body dynamics, can disrupt their formation and survival. Here, we identify a tell-tale signature of Floquet states in the linear optical response of laser-dressed solids that remains prominent even in the presence of strong spectral congestion of bulk matter. To do so, we introduce a computationally efficient strategy based on the Floquet formalism to finally capture the full frequency-dependence in the optical response properties of realistic laser-dressed crystals, and use it investigate the Floquet engineering in a first-principle model for ZnO of full dimensionality. The computations reveal intense, spectrally isolated, laser-controllable, absorption/stimulated emission features at mid-infrared energies present for a wide range of laser-driving conditions that arise due to the hybridization of the Floquet states. As such, these spectral features open a purely optical pathway to investigate the birth and survival of Floquet states while avoiding the experimental challenges of fully reconstructing the band structure.

physics.optics↗

arXiv2025

First-principle based Floquet engineering of solids in the velocity gauge

We introduce a practical and accurate strategy to capture light-matter interactions using the Floquet formalism in the velocity gauge in combination with realistic first-principle models of solids. The velocity gauge, defined by the linear coupling to the vector potential, is a standard method to capture the light-matter interaction in solids. However, its use with first-principle models has been limited by the challenging fact that it requires a large number of bands for convergence and its incompatibility with non-local pseudopotential plane wave methods. To improve its convergence properties, we explicitly take into account the truncation of Hilbert space in the construction of the Floquet Hamiltonian in the velocity gauge. To avoid the incompatibility with the pseudopotentials, we base our computations on generalized tight-binding Hamiltonians derived from first-principles through maximally-localized Wannier functions. We exemplify the approach by computing the optical absorption spectra of laser-dressed trans-polyacetylene chain using realistic electronic structure. We show that, by proceeding in this way, Floquet consideration involving the truncated Hilbert spaces reproduces the full basis calculations with only a few bands and with significantly reduced computation time. The strategy has been implemented in FloqticS, a general code for the Floquet engineering of the optical properties of materials. Overall, this work introduces a useful theoretical tool to realize Floquet engineering of realistic solids in the velocity gauge.

cond-mat.mtrl-sci↗

arXiv2024

Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond

In this work, we examine how the structure of system-bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath's frequencies. For initially unentangled qubit-bath states Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit-bath interaction strength, and bath correlation time. Initial system-bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. Still, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Further, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic lineshape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system-bath dynamics even when there is no inhomogeneity in the initial conditions.

physics.chem-ph↗

arXiv2024

General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. I. Theoretical Formulation

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is done by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillator or spin baths, and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic bath [J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.

quant-ph↗

arXiv2024

General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost as compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understanding how energy is dissipated in realistic open quantum system dynamics.

quant-ph↗

arXiv2024

High-frequency tails in spectral densities

Recent advances in numerically exact quantum dynamics methods have brought the dream of accurately modeling the dynamics of chemically complex open systems within reach. Path-integral-based methods, hierarchical equations of motion (HEOM) and quantum analog simulators all require the spectral density (SD) of the environment to describe its effect on the system. Here we focus on the decoherence dynamics of electronically excited species in solution in the common case where nonradiative electronic relaxation dominates and is much slower than electronic dephasing. We show that the computed relaxation rate is highly sensitive to the choice of SD representation $\unicode{x2013}$ such as the Drude-Lorentz or Brownian modes $\unicode{x2013}$ or strategy used to capture the main SD features, even when early-times dephasing dynamics remains robust. The key reason is that electronic relaxation is dominated by the resonant contribution from the high-frequency tails of the SD, which are orders of magnitude weaker than the main features of the SD and can vary significantly between strategies. This finding highlights an important, yet overlooked, numerical challenge: obtaining an accurate spectral density requires capturing its structure over several orders of magnitude to ensure correct decoherence dynamics at both early and late times. To address this, we provide a simple transformation that recovers the correct relaxation rates in quantum simulations constrained by algorithmic or physical limitations on the shape of the SD. Our findings enable comparison of different numerically exact simulation methods and expand the capabilities of analog simulations of open quantum dynamics.

physics.chem-ph↗

arXiv2024

Bexcitonics: Quasi-particle approach to open quantum dynamics

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.

quant-ph↗

arXiv2023

Stark Control of Electrons Across the Molecule-Semiconductor Interface

Controlling matter at the level of electrons using ultrafast laser sources represents an important challenge for science and technology. Recently we introduced a general laser control scheme (the Stark Control of Electrons at Interfaces or SCELI) based on the Stark effect that uses the subcycle structure of light to manipulate electron dynamics at semiconductor interfaces [{Phys. Rev. B \textbf{98}, 121305 (2018)}]. Here, we demonstrate that SCELI is also of general applicability in molecule-semiconductor interfaces. We do so by following the quantum dynamics induced by non-resonant few-cycle laser pulses of intermediate intensity (non-perturbative but non-ionizing) across model molecule-semiconductor interfaces of varying level alignments. We show that SCELI induces interfacial charge transfer regardless of the energy level alignment of the interface and even in situations where charge exchange is forbidden via resonant photoexcitation. We further show that the SCELI rate of charge transfer is faster than those offered by resonant photoexcitation routes as it is controlled by the subcycle structure of light. The results underscore the general applicability of SCELI to manipulate electron dynamics at interfaces on ultrafast timescales.

physics.chem-ph↗

arXiv2023

Mapping Electronic Decoherence Pathways in Molecules

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in ~ 30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.

physics.chem-ph↗

arXiv2023

Floquet theory and computational method for the optical absorption of laser-dressed solids

Recent advances in laser technology now enable engineering the electronic structure of matter through strong light-matter interactions. However, the effective physicochemical properties of these laser-dressed nonequilibrium materials are not well understood. Here we develop a general theory that now enables modeling and interpreting the linear optical absorption of solids that are dressed by light of arbitrary strength and photon energy. The theory applies to any crystalline solid and quantum materials. In the theory, the dressing of Bloch electrons by the driving laser is treated exactly using Floquet theory. The effective optical properties of this laser-dressed material are probed through a weak laser whose effects are captured to first order in perturbation theory. Remarkably, in this nonequilibrium system the time- and space-periodic Floquet-Bloch modes play the role of the pristine eigenstates of matter as the optical absorption is seen to emerge from transitions among them. We implement the theoretical framework into a code FloqticS: Floquet optics in Solids) available through Github. To isolate the emergent phenomenology, we performed computations in a model solid with a cosine-shaped lattice potential driven by strong nonresonant light. The computations recover the dynamical Franz-Keldysh effect and identify novel dramatic changes in the optical absorption upon increasing the amplitude of the driving laser. The Floquet replicas open absorption sidebands separated by integer multiples of the drive photon energy. The hybridization of the Floquet-Bloch modes, create intense low-frequency absorption and stimulated emissions, and dips in the absorption spectrum. We assign these emerging effects as purely-optical tell-tale signatures of the Floquet-Bloch modes. These advances can be used to model, control and characterize the response properties of laser-dressed materials.

physics.optics↗

arXiv2023

Microscopic Theory, Analysis, and Interpretation of Conductance Histograms in Molecular Junctions

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here, we develop a theory for the conductance histogram, which accurately fits experimental data and augments the information content that can be extracted, by merging the theory of force-spectroscopy with molecular conductance. Specifically, we propose a microscopic model of the junction evolution under the modulation of external mechanical forces and combine it with the non-equilibrium stochastic features of junction rupture and formation. Our formulation captures contributions to the conductance dispersion that emerge due to changes in the conductance during the mechanical elongation inherent to the experiments. The final histogram shape is determined by the statistics of junction rupture and formation. The procedure yields analytical equations for the conductance histogram in terms of parameters that describe the free-energy profile of the junction, its mechanical manipulation, and the ability of the molecule to transport charge. All physical parameters that define our microscopic model can be obtained from separate conductance and rupture force measurements on molecular junctions. Further, the predicted behavior with respect to physical parameters can be used to test the range of validity of the microscopic model, understand the conductance histograms, and design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

physics.chem-ph↗