arXiv subjects

Maicol A. Ochoa

Publications and source records attributed to Maicol A. Ochoa.

At least 19 recordsLinked to original sources

arXiv2025

A semiclassical nonequilibrium Green's Function approach to electron transport in systems exhibiting electron-phonon couplings

We formulate a semiclassical theory for electron transport in open quantum systems with electron-phonon interactions adequate for situations when the system's phonon dynamics is comparable with the electron transport timescale. Starting from the Keldysh non-equilibrium Green's function formalism we obtain equations of motion for the retarded and lesser electronic Green's functions including contributions due to the phonon dynamics up to second order in the electron-phonon coupling strength. The resulting equations assume that the system's phonon follow classical time-local dynamics with delta-correlated noise. We apply our method to the study of the charging/discharging of a periodically driven quantum dot, and a three-level model for a single-electron pump, analyzing the signatures in the transient current, electron population and process performance of the phonon dynamics. For these systems, we adopt the fluctuation-dissipation theorem and consider external harmonic driving of the phonon at frequencies comparable with the electron modulation, and different scenarios, varying electron-phonon coupling strength, coupling to the electron part of the system, and in phase and anti-phase driving. Our results illustrate that our method provides an efficient protocol to describe the effects of nuclear motion in ultrafast transient phenomena.

cond-mat.mes-hall↗

arXiv2025

Atomistic tight-binding Hartree-Fock calculations of multielectron configurations in P-doped silicon devices: wavefunction reshaping

Donor-based quantum devices in silicon are attractive platforms for universal quantum computing and analog quantum simulations. The nearly-atomic precision in dopant placement promises great control over the quantum properties of these devices. We present atomistic calculations and a detailed analysis of many-electron states in a single phosphorus atom and selected phosphorus dimers in silicon. Our self-consistent method involves atomistic calculations of the electron energies utilizing representative tight-binding Hamiltonians, computations of Coulomb and exchange integrals without any reference to an atomic orbital set, and solutions to the associated Hartree-Fock equations. First, we assess the quality of our tight-binding Hartree-Fock protocol against Configuration-Interaction calculations for two electrons in a single phosphorus atom, finding that our formalism provides an accurate estimation of the electron-electron repulsion energy requiring smaller computational boxes and single-electron wavefunctions. Then, we compute charging and binding energies in phosphorus dimers observing their variation as a function of impurity-impurity separation. Our calculations predict an antiferromagnetic ground state for the two-electron system and a weakly bound three-electron state in the range of separations considered. We rationalize these results in terms of the single-electron energies, charging energies, and the wavefunction reshaping.

quant-ph↗

arXiv2024

Lossy anharmonic polaritons under periodic driving

We report on the anharmonic signatures in dissipative polaritons' stationary energy distribution and thermodynamics under external periodic driving. First, we introduce a dynamic model for the dissipative anharmonic Jaynes-Cummings polariton with a generic time-periodic interaction representing modulations of the polariton's energy due to an external force or field. We characterize the stationary state in terms of the exciton, phonon, and interaction energy dependence on the phonon anharmonicity, exciton-phonon coupling strength, and intensity and form of the external field-polariton coupling. Our model also captures the quantum thermodynamics of the driven polariton, which we analyze in connection with the irreversible heat, maximum power, and efficiency of the process. We find considerable differences in energy distribution and thermodynamics between harmonic, moderate, and strongly anharmonic polaritons. Moreover, comparing the external modulations to the phonon and exciton energy, we conclude that the former enhances the polariton's energy storage capacity and is occasionally limited by interference effects and energy saturation at the exciton.

quant-ph↗

arXiv2024

Single-electron states of phosphorus-atom arrays in silicon

We characterize the single-electron energies and the wavefunction structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic tight-binding calculations and analyzing wavefunction overlaps to identify the single-dopant states that hybridize to make the array states. The energy spectrum and wavefunction overlap variation as a function of dopant separation for these arrays shows that hybridization mostly occurs between single-dopant states of the same type, with some cross-hybridization between $A_1$ and $E$ states occurring at short separations. We also observe energy crossings between hybrid states of different types as a function of impurity separation. We then extract tunneling rates for electrons in different dopants by mapping the state energies into hopping Hamiltonians in the site representation. Significantly, we find that diagonal and nearest neighbor tunneling rates are similar in magnitude in a square array. Our analysis also accounts for the shift of the on-site energy at each phosphorus atom resulting from the nuclear potential of the other dopants. This approach constitutes a solid protocol to map the electron energies and wavefunction structure into Fermi-Hubbard Hamiltonians needed to implement and validate analog quantum simulations in these devices.

quant-ph↗

arXiv2023

Quantum thermodynamics of periodically driven polaritonic systems

We investigate the energy distribution and quantum thermodynamics in periodically driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and quantify the energy reorganization between these two systems and their interaction as a function of coupling strength, driving force, and detuning. After deriving the quantum master equation for the polariton density matrix with weak environment interactions, we obtain the dissipative time propagator and the long-time evolution of an equilibrium initial state. This approach provides direct access to the stationary state and overcomes the difficulties found in the numerical evolution of weakly damped quantum systems near resonance, also providing maps on the polariton lineshape. Then, we compute the thermodynamic performance during harmonic modulation and demonstrate that maximum efficiency occurs at resonance. We also provide an expression for the irreversible heat rate and numerically demonstrate that this agrees with the thermodynamic laws.

cond-mat.mes-hall↗

arXiv2021

Coupling, lifetimes and "strong coupling" maps for single molecules at plasmonic interfaces

The interaction between excited states of a molecule and excited states of metal nanostructure (e.g. plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when $2|U|/{\hbarΓ}>1$, where $U$ and $Γ$ are the molecule-plasmon coupling and the spectral width of the optical transition respectively. Because both $U$ and $Γ$ strongly increase with decreasing distance between a molecule and a plasmonic structure it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work we investigate the behavior of $U$ and $Γ$ for several geometries. Surprisingly, we find that if the only contributions to $Γ$ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion $2|U|/{\hbarΓ}>1$ is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.

physics.chem-ph↗

arXiv2020

Metal adsorbate interactions and the convergence of density functional calculations

The adsorption of metal atoms on nanostructures, such as graphene and nanotubes, plays an important role in catalysis, electronic doping, and tuning material properties. Quantum chemical calculations permit the investigation of this process to discover desirable interactions and obtain mechanistic insights into adsorbate behavior, of which the binding strength is a central quantity. However, binding strengths vary widely in the literature, even when using almost identical computational methods. To address this issue, we investigate the adsorption of a variety of metals onto graphene, carbon nanotubes, and boron nitride nanotubes. As is well-known, calculations on periodic structures require a sufficiently large system size to remove interactions between periodic images. Our results indicate that there are both direct and indirect mechanisms for this interaction, where the latter can require even larger system sizes than typically employed. The magnitude and distance of the effect depend on the electronic state of the substrate and the open- or closed-shell nature of the adsorbate. For instance, insulating substrates (e.g., boron nitride nanotubes) show essentially no dependence on system size, whereas metallic or semi-metallic systems can have a substantial effect due to the delocalized nature of the electronic states interacting with the adsorbate. We derive a scaling relation for the length dependence with a representative tight-binding model. These results demonstrate how to extrapolate the binding energies to the isolated-impurity limit.

cond-mat.mes-hall↗

arXiv2020

Optimal in situ electromechanical sensing of molecular species

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors in ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties, provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at fixed bias, and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing.

cond-mat.mes-hall↗

arXiv2019

Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions

Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry.

cond-mat.mes-hall↗

arXiv2018

A universal approach to quantum thermodynamics in the strong coupling regime

We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is positive and is found to be related to the excess work dissipated by friction, at least up to second order in the driving speed. As an example of the present methodology, we reproduce the results for the quantum thermodynamics of the driven resonance level model. We also emphasize that our formalism is quite general and allows for electron-electron interactions, which can give rise to exotic Kondo resonances appearing in thermodynamic quantities.

cond-mat.stat-mech↗

arXiv2017

Quantum Thermodynamics for Driven Dissipative Bosonic Systems

We investigate two prototypical dissipative bosonic systems under slow driving and arbitrary system-bath coupling strength, recovering their dynamic evolution as well as the heat and work rates, and we verify that thermodynamic laws are respected. Specifically, we look at the damped harmonic oscillator and the damped two-level system. For the former, we study independently the slow time- dependent perturbation in the oscillator frequency and in the coupling strength. For the latter, we concentrate on the slow modulation of the energy gap between the two levels. Importantly, we are able to find the entropy production rates for each case without explicitly defining nonequilibrium extensions for the entropy functional. This analysis also permits the definition of phenomenological friction coefficients in terms of structural properties of the system-bath composite.

cond-mat.mes-hall↗

arXiv2017

Simultaneous weak measurement of non-commuting observables

In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A full description of such measurement should describe the measurement protocol and provide an explicit form of the measurement operator that transform the quantum state to its post measurement form. A simultaneous measurement of non-commuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator often used to model a weak measurement of a single observable is obtained by projecting a naïve extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.

quant-ph↗

arXiv2017

Quantum mechanics in a metric sheaf: a model theoretic approach

We study model-theoretical structures for prototypical physical systems. First, a summary of the model theory of sheaves, adapted to the metric case, is presented. In particular, we provide conditions for a generalization of the generic model theorem to metric sheaves. The essentials of the model theory of metric sheaves appeared in the form of Conference Proceedings. We provide a version of those results, for the sake of completeness, and then build metric sheaves for physical systems in the second part of the paper. Specifically, metric sheaves for quantum mechanical systems with pure point and continuous spectra are constructed. In the former case, every fiber is a finite projective Hilbert space determined by the family of invariant subspaces of a given operator with pure point spectrum, and we also consider unitary transformations in a finite-dimensional space. For an operator with continuous spectrum, every fiber is a two sorted structure of subsets of the Schwartz space of rapidly decreasing functions that includes imperfect representations of position and momentum states. The imperfection character is parametrically determined by the elements on the base space and refined in the generic model. Position and momentum operators find a simple representation in every fiber as well as their corresponding unitary operators. These results follow after recasting the algebraic properties of the integral transformations frequently invoked in the description of quantum mechanical systems with continuous spectra. Finally, we illustrate how this construction permits the calculation of the quantum mechanical propagator for a free particle.

math.LO↗

arXiv2016

Nonequilibrium diagrammatic technique for Hubbard Green functions

We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular junctions. Within the technique intra-system interactions are taken into account exactly, while molecular coupling to contacts is used as a small parameter in perturbative expansion. We demonstrate the viability of the approach with numerical simulations for a generic junction model of quantum dot coupled to two electron reservoirs.

cond-mat.mes-hall↗

arXiv2016

Energy distribution and local fluctuations in strongly coupled open quantum systems: The extended resonant level model

We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B {\bf 89}, 161306 (2014), Phys. Rev. B {\bf 93}, 115318 (2016)] have found, for a resonant electronic level interacting with a thermal free electron wide-band bath, that the expectation value for the energy of the interacting subsystem can be correctly calculated by considering a symmetric splitting of the interaction Hamiltonian between the subsystem and the bath. However, the general implications of this approach were questioned [Phys. Rev. B {\bf 92}, 235440 (2015)]. Here we show that already at equilibrium, such splitting fails to describe the energy fluctuations, as measured here by the second and third central moments (namely width and skewness) of the energy distribution. Furthermore, we find that when the wide-band approximation does not hold, no splitting of the system-bath interaction can describe the system thermodynamics. We conclude that in general no proper division subsystem of the Hamiltonian of the composite system can account for the energy distribution of the subsystem. This also implies that the thermodynamic effects due to local changes in the subsystem cannot in general be described by such splitting.

cond-mat.mes-hall↗

arXiv2015

On the nature of heat in strongly coupled open quantum systems

We study heat transfers in a single level quantum dot strongly coupled to fermionic reservoirs and subjected to a time-dependent protocol modulating the dot energy as well as the dot-reservoir coupling strength. The dynamics is described using nonequilibrium Greens functions (NEGFs) evaluated to first order beyond quasi-static driving. We show that any heat definition expressed as an energy change in the reservoir energy plus any fraction of the system-reservoir interaction is not an exact differential when evaluated along reversible isothermal transformations, except when that fraction is zero. However, even in that latter case the reversible heat divided by temperature, namely the entropy, does not satisfy the third law of thermodynamics and diverges in the low temperature limit. Our results cast doubts on the possibility to define a thermodynamically consistent notion of heat expressed as the expectation value of some Hamiltonian terms.

cond-mat.stat-mech↗

arXiv2015

Efficiency fluctuations in quantum thermoelectric devices

We present a method, based on characterizing efficiency fluctuations, to asses the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the latter for a variety of simple models where our method is exact. By analyzing the discrepancies with the semi-classical prediction of a quantum master equation (QME) approach, we emphasize the quantum nature of efficiency fluctuations for realistic junction parameters. We finally propose an approximate Gaussian method to express efficiency fluctuations in terms of nonequilibrium currents and noises which are experimentally measurable in molecular junctions.

cond-mat.mes-hall↗

arXiv2015

Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green functions (NEGF). The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

cond-mat.stat-mech↗