Coupling Hamiltonian Research Articles

Entropy production of quantum reset models

We analyze the entropy production of Quantum Reset Models (QRMs) corresponding to quantum dynamical semigroups driven by Lindbladians motivated by a probabilistic description of dissipation in an external environment. We investigate the strict positivity of entropy production for Lindbladians given as sums of QRMs, when the Hamiltonian of the total Lindbladian is split as an affine combination of Hamiltonians of the individual QRMs. In this setup, we derive conditions on the coefficients of the combination and on the reset states ensuring either positive or zero entropy production. Second, we deal with a tri-partite system subject at its ends to two independent QRMs and a weak coupling Hamiltonian. The latter is split as an affine combination of individual Hamiltonians, and we provide necessary and sufficient conditions ensuring strict positivity of the entropy production to leading order, with the possible exception of one affine combination. We apply these results to a physically motivated model and exhibit explicit expressions for the leading orders steady-state solution, entropy production and entropy fluxes. Moreover, these approximations are numerically shown to hold beyond the expected regimes.

Internal Conversion Cascade in a Carbon Nanobelt: A Multiconfigurational Quantum Dynamical Study.

Carbon nanobelts feature intriguing photophysical properties, due to their high symmetry and structural rigidity. Here, we consider a (6,6) armchair carbon nanobelt, i.e., the very first carbon nanobelt to be synthesized [Povie et al., Science 2017, 356, 172] and characterize the internal conversion dynamics using multiconfigurational quantum dynamics via the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) method. A symmetry-adapted linear vibronic coupling Hamiltonian for 26 electronic states and 210 vibrational modes is employed. Electronic excitations are found to decay through a dense manifold of excited states, which interact via multiple conical intersections, while inducing minimal geometry change. It is shown that a rapid coherent decay, exhibiting a nonvanishing quantum flux on a time scale of less than 50 fs, transitions toward a slower, decoherent decay at longer times. As previously suggested in the literature, electronic relaxation is hindered by phonon bottlenecks such that a stepwise internal conversion cascade is observed. The computed vibronic absorption spectrum is shown to be in good agreement with the experimental spectrum.

First-principles study of electronic and magnetic properties of Fe atoms on Cu2N/Cu(100)

Abstract First-principles calculations were conducted to investigate the structural, electronic, and magnetic properties of single Fe atoms and Fe dimers on Cu2N/Cu(100). Upon adsorption of an Fe atom onto Cu2N/Cu(100), robust Fe–N bonds form, resulting in the incorporation of both single Fe atoms and Fe dimers within the surface Cu2N layer. The partial occupancy of Fe-3d orbitals lead to large spin moments on the Fe atoms. Interestingly, both single Fe atoms and Fe dimers exhibit in-plane magnetic anisotropy, with the magnetic anisotropy energy (MAE) of an Fe dimer exceeding twice that of a single Fe atom. This magnetic anisotropy can be attributed to the predominant contribution of the component along the x direction of the spin–orbital coupling Hamiltonian. Additionally, the formation of Fe–Cu dimers may further boost the magnetic anisotropy, as the energy levels of the Fe-3d orbitals are remarkably influenced by the presence of Cu atoms. Our study manifests the significance of uncovering the origin of magnetic anisotropy in engineering the magnetic properties of magnetic nanostructures.

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

Vibronic coupling and ultrafast relaxation dynamics in the first five excited singlet electronic states of bithiophene.

The vibronic structure and nuclear dynamics in the first five excited singlet electronic states of bithiophene (2T) are investigated here. Specifically, considerations are given to comprehend the first two structureless and broad electronic absorption bands and the role of nonadiabatic coupling in the excited state relaxation mechanism of 2T in the gas phase. Associated potential energy surfaces (PESs) are established by constructing a model vibronic coupling Hamiltonian using 18 vibrational degrees of freedom and extensive abinitio electronic structure calculations. The topographies of these PESs are critically examined, and multiple conical intersections are established. The nuclear dynamics calculations are performed by propagating wave packets on the coupled electronic manifold. The present theoretical results are in good agreement with the experimental observations. It is found that strong nonadiabatic coupling between the S1-S4 and S1-S5 states along totally symmetric modes is predominantly responsible for the structureless and broad first absorption band, and overlapping S2, S3, S4, and S5 states form the second absorption band. Photorelaxation from the highly excited S5 to the lowest S1 state takes place through a cascade of diabatic population transfers among the S1-S4-S5 electronic manifold within the first ∼100fs. Totally symmetric C=C stretching, C-S stretching, C-H wagging, ring puckering, and inter-ring bending modes collectively drive such relaxation dynamics.

Spin-Vibronic Intersystem Crossing and Molecular Packing Effects in Heavy Atom Free Organic Phosphor.

We present a detailed investigation into the excited state properties of a planar D3h symmetric azatriangulenetrione, HTANGO, which has received significant interest due to its high solid-state phosphorescence quantum yield and therefore potential as an organic room temperature phosphorescent (ORTP) dye. Using a model linear vibronic coupling Hamiltonian in combination with quantum dynamics simulations, we observe that intersystem crossing (ISC) in HTANGO occurs with a rate of ∼1010 s-1, comparable to benzophenone, an archetypal molecule for fast ISC in heavy metal free molecules. Our simulations demonstrate that the mechanism for fast ISC is associated with the high density of excited triplet states which lie in close proximity to the lowest singlet states, offering multiple channels into the triplet manifold facilitating rapid population transfer. Finally, to rationalize the solid-state emission properties, we use quantum chemistry to investigate the excited state surfaces of the HTANGO dimer, highlighting the influence and importance of the rotational alignment between the two HTANGO molecules in the solid state and how this contributes to high phosphorescence quantum yield.

Polarization mixing, bound states in a continuum, and exciton-polaritons in photonic crystal slabs by a guided-mode expansion approach

Photonic crystal (PhC) slabs, or patterned multilayer waveguides, are known to support truly guided modes with no losses, as well as quasi-guided modes that lie in the continuum of far-field radiation. In this contribution, we present a guided-mode expansion approach – and the corresponding free software named legume – that allows calculating a number of features of PhC slabs: (a) symmetry properties and the issue of polarization mixing in coupling to far-field radiation; (b) the occurence of bound states in a continuum, which have infinite Q-factor and give rise to topological singularities of the far-field polarization; (c) the description of active two-dimensional layers through a suitably formulated light-matter coupling Hamiltonian, allowing to describe the regime of strong coupling leading to photonic crystal polaritons. Comparison with rigorous coupled-wave analysis, and the insurgence of non-hermitian features in the optical properties, are also addressed.

Intersystem crossing as vibronically induced phonon emission and absorption processes: a unified view of nonradiative transitions in a molecule

Abstract An analytical expression for the nonradiative rate constant is derived based on Fermi's golden rule within the mixed-spin crude adiabatic (CA) approximation. The mixed-spin CA basis is defined by a set of eigenstates for the electronic Hamiltonian that comprises the nonrelativistic electronic Hamiltonian and spin-orbit coupling clumped at the reference nuclear configuration. The mixed-spin basis differs from the pure-spin basis defined by a set of eigenstates for the nonrelativistic electronic Hamiltonian. The mixed-spin CA representation provides a unified view of the nonradiative transitions; both internal conversion and intersystem crossing (ISC) are regarded as vibronically induced phonon emission and absorption processes. The analytical expression enables us to determine important vibrational modes that are responsible for phonon emission/absorption (promoting modes) and accepting excitation energy (accepting modes) according to the selection rule of vibronic coupling. An advantage of the CA representation is that the spatial distribution of vibronic coupling is elucidated based on its density form, i.e. vibronic coupling density, which can be applied to theoretical molecular designs with controlled nonradiative processes. The calculated ISC rate constant for tetracene reproduces the experimental result well.

Exceptional Point in a Microwave Plasmonic Dipole Resonator for Sub‐Microliter Solution Sensing

AbstractMicrowave resonance sensing has attracted significant interest due to its promising potential in developing ultracompact integrated sensors. For biomedical sensing applications, it is required to realize high sensitivity to tiny volumes of solution using such long microwave wavelengths. Here, a chiral microwave plasmonic resonator, which can induce exceptional point (EP) state based on the coalescence of non‐Hermitian dipole eigenmodes, is proposed. The intrinsically geometric asymmetry leads to strong asymmetry of non‐Hermitian Hamiltonian and strong coupling between the two non‐degenerate dipoles, hence resulting in significantly enhanced frequency splitting signals. Benefiting from the subwavelength dipole resonances, the proposed resonator has advantages of the EP state's high sensitivity to tiny targets and strong plasmonic wavelength compression. Its sensing performance is experimentally validated by metal scatterer detection and glucose solution measurement. The minimum detectable metal scatterer features a diameter of λ0/280 and a volume of 2.9 × 10−9 λ03 (λ0 is free‐space wavelength). The solution volume under detection features a volume of 4.4 × 10−7 λ03 and the reporting limit for glucose reaches 0.26 µmol. These results envision a feasible route for trace‐amount biomedical sensing at the microwave frequencies.

A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. As performance criteria, such settings employ quadratic (or more complicated) cost functionals of the system and field variables to be minimized over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

The electron-phonon ($e$-ph) coupling system often has a large number of phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. To solve this problem, we propose a new and practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global $U(1)$ fermion symmetry, which maps $2^{N_p}$ bosonic degrees of freedom onto $N_p$ pseudosites, each with two states. This approach can handle arbitrary $e$-ph coupling Hamiltonians where pseudosite DMRG performs efficiently. We use this method to study the spectral functions of the doped extended Hubbard-Holstein model in a regime of strong Coulomb repulsion, which has not been studied extensively before. Key features of the excitation spectra are captured at a modest computational cost. Our results show that weak extended $e$-ph couplings can increase the spectral weight of the holon-folding branch at low phonon frequencies, in agreement with angle-resolved photoemission observations on one-dimensional (1D) cuprates.

Photoelectron spectroscopy and dissociative photoionization of fulminic acid, HCNO.

We report a joint experimental and computational study of the photoelectron spectroscopy and the dissociative photoionization of fulminic acid, HCNO. The molecule is of interest to astrochemistry and astrobiology as a potential precursor of prebiotic molecules. Synchrotron radiation was used as the photon source. Dispersive photoelectron spectra were recorded from 10 to 22eV, covering four band systems in the HCNO cation, and an ionization energy of 10.83eV was determined. Transitions into the Renner-Teller distorted X+2Π state of the cation were simulated using wavepacket dynamics based on a vibronic coupling Hamiltonian. Very good agreement between experiment and theory is obtained. While the first excited state of the cation shows only a broad and unstructured spectrum, the next two higher states exhibit a well-resolved vibrational progression. Transitions into the excited electronic states of HCNO+ were not simulated due to the large number of electronic states that contribute to these transitions. Nevertheless, a qualitative assignment is given, based on the character of the orbitals involved in the transitions. The dissociative photoionization was investigated by photoelectron-photoion coincidence spectroscopy. The breakdown diagram shows evidence for isomerization from HCNO+ to HNCO+ on the cationic potential energy surface. Zero Kelvin appearance energies for the daughter ions HCO+ and NCO+ have been derived.

Spin current and internal Zeeman field in spin-orbit coupled rings

We investigate the one-dimensional quantum ring constructed by the spin-orbit coupled material, in which the quantum spin-Hall Bernevig-Zhang (BZ) Hamiltonian and Rashba-Dirac (RD) type spin-orbit coupling are taken into account (called RD-BZ Hamiltonian in this paper). It is known that the curvature of the ring generates an out-of-plane effective magnetic field, acting as an internal Zeeman field. We find that only the BZ coupling can change the strength of the internal Zeeman field, which enables us to detect the effect of the internal Zeeman field. Furthermore, we find that the total angular momentum is conserved in the RD-BZ Hamiltonian, and the energy eigenvalue and wave function must be modified to fit the conserved quantity, which are ignored in the previous studies. The conductance without leads is discussed. Different from the previous results, we find that the conductance behaves like a beat phenomenon resulting from the interplay between the magnetic flux and Aharonov-Casher (AC) phase, and thus, it can oscillate without passing through the insulating state in some regimes of magnetic flux or AC phase. Importantly, we find that the conductance with integer and half-integer magnetic flux provides us a method to measure the AC phase. The cancellation of the internal Zeeman field due to the BZ coupling can be detected by using specific fractional magnetic flux. In the ring with nonvanishing RD and BZ couplings, the conductance can exhibit a quasiplateau near the small RD coupling. The increase in the strength of BZ coupling would result in wider quasiplateau in conductance, which implies that the ring could remain insulating state (or conducting state) regardless of the small change in RD coupling. The thermal average of spin and charge currents are calculated at low temperatures without impurities. Importantly, we find that the persistent spin and charge currents as a function of the magnetic flux exhibit nodelike lines, which amazingly are perpendicular to each other. As a consequence, the persistent spin current could be nonzero even when the charge current vanishes at nonzero magnetic flux. The result suggests a pure spin current in quantum rings, and its direction can be reversed by changing the magnetic flux. The increase in the BZ coupling would exhibit the plateaulike pure spin current.

Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions.

We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S2 which exhibits a sub-100-fs nonadiabatic decay to a dark state S1. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.

On-site interaction induced peak-dip-hump feature in the APRES spectra of cuprate superconductors

For decades, the difficulty of tackling a strong coupling model with a perturbative approach remained despite numerous inquiries. In this work, a typical mean field theory procedure transforms a strong coupling Hamiltonian into a weak one, which can be solved with a perturbative approach. The Hamiltonian of two-dimensional free electron gas with Hubbard on-site interaction is calculated as a test of the new procedure. Consequently, the spectral characteristics of the cuprates “peak-dip-hump” are reproduced. The result is compared with the past theoretical investigations, e.g., quantum Monte Carlo method, density matrix renormalization group, tensor network methods, etc. which agree well with the spectral curve.

Non-Gaussian superradiant transition via three-body ultrastrong coupling

We introduce a class of quantum optical Hamiltonians characterized by three-body couplings and propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model. Unlike two-body light-matter interactions, this three-body coupling Hamiltonian is exclusively composed of terms which do not conserve the particle number. We explore the three-body ultrastrong-coupling regime, showing the emergence of a superradiant phase transition which is of first order, is characterized by the breaking of ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, and has a strongly non-Gaussian nature. Indeed, in contrast to what is observed in any two-body-coupling model, in proximity of the transition the ground state exhibits a divergent coskewness, i.e., quantum correlations that cannot be captured within semiclassical and Gaussian approximations. Furthermore, we demonstrate the robustness of our findings by including dissipative processes in the model, showing that the steady state of the system inherits from the ground states the most prominent features of the transition.

Optimal local work extraction from bipartite quantum systems in the presence of Hamiltonian couplings

We investigate the problem of finding the local analogue of the ergotropy, that is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and give analytic lower bounds and semidefinite programming upper bounds for the general case. As non-trivial examples of application, we compute the local ergotropy for a atom in an electromagnetic cavity with Jaynes-Cummings coupling, and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with an unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation.

Mind the GAP: quantifying the breakdown of the linear vibronic coupling Hamiltonian.

Excited state dynamics play a critical role across a broad range of scientific fields. Importantly, the highly non-equilibrium nature of the states generated by photoexcitation means that excited state simulations should usually include an accurate description of the coupled electronic-nuclear motion, which often requires solving the time-dependent Schrödinger equation (TDSE). One of the biggest challenges for these simulations is the requirement to calculate the PES over which the nuclei evolve. An effective approach for addressing this challenge is to use the approximate linear vibronic coupling (LVC) Hamiltonian, which enables a model potential to be parameterised using relatively few quantum chemistry calculations. However, this approach is only valid provided there are no large amplitude motions in the excited state dynamics. In this paper we introduce and deploy a metric, the global anharmonicity parameter (GAP), which can be used to assess the accuracy of an LVC potential. Following its derivation, we illustrate its utility by applying it to three molecules exhibiting different rigidity in their excited states.

Effect of the Thermal Fluctuations of the Photophysics of GC and CG DNA Steps: A Computational Dynamical Study

Here we refine and assess two computational procedures aimed to include the effect of thermal fluctuations on the electronic spectra and the ultrafast excited state dynamics of multichromophore systems, focusing on DNA duplexes. Our approach is based on a fragment diabatization procedure that, from a given Quantum Mechanical (QM) reference method, can provide the parameters (energy and coupling) of the reference diabatic states on the basis of the isolated fragments, either for a purely electronic excitonic Hamiltonian (FrDEx) or a linear vibronic coupling Hamiltonian (FrD-LVC). After having defined the most cost-effective procedure for DNA duplexes on two smaller fragments, FrDEx is used to simulate the absorption and Electronic Circular Dichroism (ECD) spectra of (GC)5 sequences, including the coupling with the Charge Transfer (CT) states, on a number of structures extracted from classical Molecular Dynamics (MD) simulations. The computed spectra are close to the reference TD-DFT calculations and fully consistent with the experimental ones. We then couple MD simulations and FrD-LVC to simulate the interplay between local excitations and CT transitions, both intrastrand and interstrand, in GC and CG steps when included in a oligoGC or in oligoAT DNA sequence. We predict that for both sequences a substantial part of the photoexcited population on G and C decays, within 50-100 fs, to the corresponding intrastrand CT states. This transfer is more effective for GC steps that, on average, are more closely stacked than CG ones.