arXiv subjects

Hsing-Ta Chen

Publications and source records attributed to Hsing-Ta Chen.

34 records · Page 2Linked to original sources

arXiv2019

Quasiclassical Modeling of Cavity Quantum Electrodynamics

We model a collection of $N$ two-level systems (TLSs) coupled to a multimode cavity via Meyer-Miller-Stock-Thoss (MMST) dynamics, sampling both electronic and photonic zero-point energies (ZPEs) and propagating independent trajectories in Wigner phase space. By investigating the ground state stability of a single TLS, we use MMST dynamics to separately study both electronic ZPE effects (which would naively lead to the breakdown of the electronic ground state) as well as photonic ZPE effects (which would naively lead to spontaneous absorption). By contrast, including both effects (i.e., sampling both electronic and photonic ZPEs) leads to the dynamical stability of the electronic ground state. Therefore, MMST dynamics provide a practical way to identify the contributions of self-interaction and vacuum fluctuations. More importantly, we find that MMST dynamics can predict accurate quantum dynamics for both electronic populations and electromagnetic field intensity in the high saturation limit. For a single TLS in a cavity, MMST dynamics correctly predict the initial exponential decay of spontaneous emission, Poincaré recurrences, and the positional dependence of a spontaneous emission rate. For an array of $N$ equally spaced TLSs with only one TLS excited initially, MMST dynamics correctly predict the modification of spontaneous emission rate as a function of the spacing between TLSs. Finally, MMST dynamics also correctly model Dicke's superradiance and subradiance (i.e., the dynamics when all TLSs are excited initially) including the correct quantum statistics for the delay time (as found by counting trajectories, for which a full quantum simulation is hard to achieve). Therefore, this work raises the possibility of simulating large-scale collective light-matter interactions with methods beyond mean-field theory.

quant-ph↗

arXiv2019

Non-adiabatic Dynamics in a Laser Field with Floquet Fewest Switches Surface Hopping: The Need for An Accurate Treatment of Coherence and Decoherence Remains

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between Floquet states. Our results should be of interest to all those interested in laser induced molecular dynamics.

physics.chem-ph↗

arXiv2019

Understanding the Nature of Mean-Field Semiclassical Light-Matter Dynamics: An Investigation of Energy Transfer, Electron-Electron Correlations, External Driving and Long-Time Detailed Balance

Semiclassical electrodynamics is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting different molecules plus a classical transverse E-field; we will call this Hamiltonian #I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body E-field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian #II. Moreover, one can also mix these two Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a pair of identical two-level systems (TLSs) undergoing either resonance energy transfer (RET) or collectively driven dynamics. While all approaches perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions. Each method has its own distinct problems: Hamiltonian #I performs best for RET but behaves in a complicated manner for driven dynamics. Hamiltonian #II is always stable, but obviously fails for RET at short distances. One key finding is that, under externally driving, a full configuration interaction description of Hamiltonian #I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field treatment.

physics.chem-ph↗

arXiv2019

Predictive Semiclassical Model for Coherent and Incoherent Emission in the Strong Field Regime: The Mollow Triplet Revisited

We re-investigate the famous Mollow triplet and show that most of the well-known quantum characteristics of the Mollow triplet--including incoherent emission and a non-standard dependence of the sidebands on detuning--can be recovered quantitatively using semiclassical dynamics with a classical light field. In fact, by not relying on the rotating wave approximation, a semiclassical model predicts some quantum effects beyond the quantum optical Bloch equation, including higher order scattering and asymmetric sideband features. This letter highlights the fact that, with strong intensities, many putatively quantum features of light-matter interactions arise from a simple balance of mean-field electrodynamics and elementary spontaneous emission which requires minimal computational cost. Our results suggest that the application of semiclassical electrodynamics to problems with strong light-matter coupling in the fields of nanophotonics and superradiance are likely to yield a plethora of new information.

physics.chem-ph↗

arXiv2019

Understanding Detailed Balance for an Electron-Radiation System Through Mixed Quantum-Classical Electrodynamics

We investigate detailed balance for a quantum system interacting with thermal radiation within mixed quantum-classical theory. For a two-level system coupled to classical radiation fields, three semiclassical methods are benchmarked: (1) Ehrenfest dynamics over-estimate the excited state population at equilibrium due to the failure of capturing vacuum fluctuations. (2) The coupled Maxwell-Bloch equations, which supplement Ehrenfest dynamics by damping at the full golden rule rate, under-estimate the excited state population due to double-counting of the self-interaction effect. (3) Ehrenfest+R dynamics recover detailed balance and the correct thermal equilibrium by enforcing the correct balance between the optical excitation and spontaneous emission of the quantum system. These results highlight the fact that, when properly designed, mixed quantum-classical electrodynamics can simulate thermal equilibrium in the field of nanoplasmonics.

physics.chem-ph↗

arXiv2019

A Comparison of Different Classical, Semiclassical and Quantum Treatments of Light-Matter Interactions: Understanding Energy Conservation

The optical response of an electronic two-level system (TLS) coupled to an incident continuous wave (cw) electromagnetic (EM) field is simulated explicitly in one dimension by the following five approaches: (i) the coupled Maxwell-Bloch equations, (ii) the optical Bloch equation (OBE), (iii) Ehrenfest dynamics, (iv) the Ehrenfest+R approach and (v) classical dielectric theory (CDT). Our findings are as follows: (i) standard Ehrenfest dynamics predict the correct optical signals only in the linear response regime where vacuum fluctuations are not important; (ii) both the coupled Maxwell-Bloch equations and CDT predict incorrect features for the optical signals in the linear response regime due to a double-counting of self-interaction; (iii) by exactly balancing the effects of self-interaction versus the effects of quantum fluctuations (and insisting on energy conservation), the Ehrenfest+R approach generates the correct optical signals in the linear regime and slightly beyond, yielding, e.g., the correct ratio between the coherent and incoherent scattering EM fields. As such, Ehrenfest+R dynamics agree with dynamics from the quantum OBE, but whereas the latter is easily applicable only for a single TLS in vacuum, the former should be applicable to large systems in environments with arbitrary dielectrics. Thus, this benchmark study suggests that the Ehrenfest+R approach may be very advantageous for simulating light-matter interactions semiclassically.

physics.optics↗

arXiv2018

A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?

We investigate two key representative semiclassical approaches for propagating resonant energy transfer between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum-classical mismatch leads to a violation of causality, i.e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with Förster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short range interactions or long range causality? Apparently, one cannot have one's cake and eat it too.

physics.chem-ph↗

arXiv2018

Ehrenfest+R Dynamics I: A Mixed Quantum-Classical Electrodynamics Simulation of Spontaneous Emission

The dynamics of an electronic system interacting with an electromagnetic field is investigated within mixed quantum-classical theory. Beyond the classical path approximation (where we ignore all feedback from the electronic system on the photon field), we consider all electron-photon interactions explicitly according to Ehrenfest (i.e. mean-field) dynamics and a set of coupled Maxwell-Liouville equations. Because Ehrenfest dynamics cannot capture certain quantum features of the photon field correctly, we propose a new Ehrenfest+R method that can recover (by construction) spontaneous emission while also distinguishing between electromagnetic fluctuations and coherent emission.

physics.chem-ph↗

arXiv2018

Ehrenfest+R Dynamics II: A Semiclassical QED Framework for Raman Scattering

In a previous paper, we introduced Ehrenfest+R dynamics for a two-level system and showed how spontaneous emission can be heuristically included such that, after averaging over an ensemble of Ehrenfest+R trajectories, one can recover both coherent and incoherent electromagnetic fields. In the present paper, we now show that Ehrenfest+R dynamics can also correctly describe Raman scattering, whose features are completely absent from standard Ehrenfest dynamics. Ehrenfest+R dynamics appear to be quantitatively accurate both for resonant and off-resonant Raman signals, as compared with Kramers-Heisenberg-Dirac (KHD) theory.

physics.chem-ph↗

arXiv2018

Mixed Quantum-Classical Electrodynamics: Understanding Spontaneous Decay and Zero Point Energy

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one and three dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: the classical path approximation (CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics. The CPA fails to recover a consistent description of spontaneous emission. A consistent "spontaneous" emission can be obtained from Ehrenfest dynamics--provided that one starts in an electronic superposition state. Spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by W. Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights new possibilities for studying light-matter interactions with semiclassical mechanics.

physics.optics↗

arXiv2017

Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms

In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.

physics.chem-ph↗

arXiv2017

Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods

In this second paper of a two part series, we present extensive benchmark results for two different inchworm Monte Carlo expansions for the spin-boson model. Our results are compared to previously developed numerically exact approaches for this problem. A detailed discussion of convergence and error propagation is presented. Our results and analysis allow for an understanding of the benefits and drawbacks of inchworm Monte Carlo compared to other approaches for exact real-time non-adiabatic quantum dynamics.

physics.chem-ph↗

arXiv2016

On the accuracy of the Pade-resummed master equation approach to dissipative quantum dynamics

Well--defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé--resummed master equations with numerically exact results in the context of the spin--boson model demonstrate that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.

cond-mat.mes-hall↗

arXiv2016

The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation

The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. Both the particle-hole symmetric and the more generic particle-hole asymmetric cases are studied. The treatment is based on two complementary non-crossing approximations, the first of which is constructed around the weak-coupling limit and the second around the polaron limit. In general, the two methods disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The frameworks used here can form the starting point for numerically exact methods based on bold-line continuous-time quantum Monte Carlo algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

cond-mat.str-el↗

arXiv2016

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

We perform extensive benchmark comparisons of surface hopping dynamics with numerically exact calculations for the spin-boson model over a wide range of energetic and coupling parameters as well as temperature. We find that deviations from golden-rule scaling in the Marcus regime are generally small and depend sensitively on the energetic bias between electronic states. Fewest switched surface hopping (FSSH) is found to be surprisingly accurate over a large swath of parameter space. The inclusion of decoherence corrections via the augmented FSSH (A-FSSH) algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic, at least for the case of an environment modeled with the commonly used Debye spectral density.

cond-mat.mes-hall↗

arXiv2010

Exploration of the memory effect on the photon-assisted tunneling via a single quantum dot: A generalized Floquet theoretical approach

The generalized Floquet approach is developed to study memory effect on electron transport phenomena through a periodically driven single quantum dot in an electrode-multi-level dot-electrode nanoscale quantum device. The memory effect is treated using a multi-function Lorentzian spectral density (LSD) model that mimics the spectral density of each electrode in terms of multiple Lorentzian functions. For the symmetric single-function LSD model involving a single-level dot, the underlying single-particle propagator is shown to be related to a 2 x 2 effective time-dependent Hamiltonian that includes both the periodic external field and the electrode memory effect. By invoking the generalized Van Vleck (GVV) nearly degenerate perturbation theory, an analytical Tien-Gordon-like expression is derived for arbitrary order multi- photon resonance d.c. tunneling current. Numerically converged simulations and the GVV analytical results are in good agreement, revealing the origin of multi- photon coherent destruction of tunneling and accounting for the suppression of the staircase jumps of d.c. current due to the memory effect. Specially, a novel blockade phenomenon is observed, showing distinctive oscillations in the field-induced current in the large bias voltage limit.

cond-mat.mes-hall↗