Off-diagonal Coupling Research Articles

Airy structure inO16+C14nuclear rainbow scattering

The Airy structure in $^{16}$O+$^{14}$C rainbow scattering is studied with an extended double folding (EDF) model that describes all the diagonal and off-diagonal coupling potentials derived from the microscopic realistic wave functions for $^{16}$O using a density-dependent nucleon-nucleon force. The experimental angular distributions at $E_L$=132, 281 and 382.2 MeV are well reproduced by the calculations. By studying the energy evolution of the Airy structure, the Airy minimum at around $\theta$=76$^\circ$ in the angular distribution at $E_L$=132 MeV is assigned as the second order Airy minimum $A2$ in contrast to the recent literature which assigns it as the third order $A3$. The Airy minima in the 90$^\circ$ excitation function is investigated in comparison with well-known $^{16}$O+$^{16}$O and $^{12}$C+$^{12}$C systems. Evolution of the Airy structure into the molecular resonances with the $^{16}$O+$^{14}$C cluster structure in the low energy region around $E_{c.m.}$=30 MeV is discussed. It is predicted theoretically for the first time for a non-$4N$ $^{16}$O+$^{14}$C system that Airy elephants in the 90$^\circ$ excitation function are present.

Polaron dynamics with a multitude of Davydov D2 trial states.

We propose an extension to the Davydov D2 Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D2 Ansatz" is a linear combination of Davydov D2 trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D1 and D2 Ansätze. With an increase in the number of the Davydov D2 trial states in the multi-D2 Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.

Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties

A generalized trial wave function termed as the "multi-D1 Ansatz" has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties including the energy and the spin polarization are investigated, and the results are consistent with those from the exact diagonalization and density matrix renormalization group approaches for the cases involving two oscillators and two baths described by a continuous spectral density function. Breakdown of the rotational and parity symmetries along the continuous quantum phase transition separating the localized phase from the critical phase has been uncovered. Moreover, the phase boundary is determined accurately with the corresponding symmetry parameters of the rotational and parity symmetries. A critical value of the spectral exponent s* = 0.49(1) is predicted in the weak coupling limit, which is in agreement with the mean-field prediction of 1/2, but much smaller than the earlier literature estimate of 0.75(1).

Ground-state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling

By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as symmetry and mean-field analyses, the ground state properties of the two-bath spin boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A novel quantum phase transition from a doubly degenerate "localized phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the multi-D1 ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG and exact diagonalization. An effective spatial dimension $d_{eff} = 2.37(6)$ is then estimated, which is found to be compatible with the mean-field prediction. Furthermore, the quantum phase transition is inferred to be of first order for the baths described by a continuous spectral density function. In the case of single mode, however, the transition is softened.

Fluorescent triphenylamine derivative: Theoretical design based on reduced vibronic coupling

A triphenylamine derivative containing monocarborane was designed to exhibit fluorescence by considering vibronic couplings in the non-fluorescent parent compound. Off-diagonal vibronic coupling constants, which govern the rate constant of non-radiative transitions, were reduced. Based on analysis of vibronic coupling densities, this reduction was attributed to the fact that the highest occupied molecular orbital (HOMO), which is localized on the unsubstituted triphenylamine, became partly delocalized to monocarborane in the derivative, while the lowest unoccupied molecular orbital (LUMO) was strongly localized on triphenylamine. This suggests a design principle for the suppression of non-radiative decay in light-emitting materials.

Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits

We apply the quantum optimal control theory based on the Krotov method to implement single-qubit $X$ and $Z$ gates and two-qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme shares an advantage with other direct-coupling schemes in that it requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal coherence points and the gate operation times (less than 1 ns for single-qubit gates and $\ensuremath{\sim}2$ ns for cnotgates) are much shorter than the corresponding qubit decoherence time. A cnot gate or other general quantum gates can be implemented in a single run of the pulse sequence rather than being decomposed into several single-qubit and several entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high fidelity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two-qubit interaction as well as all other time-dependent magnetic-field-induced single-qubit interactions and two-qubit couplings. The effect of leakage to higher-energy-level states and the effect of qubit decoherence on the quantum-gate operations are also discussed.

Communication: Spin-boson model with diagonal and off-diagonal coupling to two independent baths: Ground-state phase transition in the deep sub-Ohmic regime

We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual types for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.

Sub-Ohmic spin-boson model with off-diagonal coupling: Ground state properties

We have carried out analytical and numerical studies of the spin-boson model in the sub-ohmic regime with the influence of both the diagonal and the off-diagonal coupling accounted for, via the Davydov D1 variational ansatz. While a second-order phase transition is known to be exhibited by this model in the presence of diagonal coupling only, we demonstrate the emergence of a discontinuous first order phase transition upon incorporation of the off-diagonal coupling. A plot of the ground state energy versus magnetization highlights the discontinuous nature of the transition between the isotropic (zero magnetization) state and nematic (finite magnetization) phases. We have also calculated the entanglement entropy and a discontinuity found at a critical coupling strength further supports the discontinuous crossover in the spin-boson model in the presence of off-diagonal coupling. It is further revealed via a canonical transformation approach that for the special case of identical exponents for the spectral densities of the diagonal and the off-diagonal coupling, there exists a continuous crossover from a single localized phase to doubly degenerate localized phase with differing magnetizations.

A finite element method perturbation expansion for a coupled structural-acoustic system: two dimensional case

The structural acoustic coupled vibration problem is very important in many engineering applications such as quality control of vehicles. Formulating the problem using the finite element method leads to a nonsymmetric generalized eigenvalue problem. We show that the problem can be reformulated into uncoupled structural and acoustic problems by introducing a coupling strength parameter \({\varepsilon}\) as a multiplier applied to the off-diagonal coupling terms. The discretized uncoupled problems then lead to a pair of symmetric generalized eigenvalue problems which can be efficiently and independently solved. The solutions of the uncoupled problems are then used to compute the coupled solution using the perturbation method and the introduced coupling strength parameter. We confirm the adequacy of the method by investigating numerical examples for a two dimensional uniform mesh, whose exact solution is known, as well as arbitrary meshes for a car-like example.

Multi-chimera states in FitzHugh-Nagumo oscillators

Chimera states are spatio-temporal patterns of synchrony and disorder observed in homogeneous oscillatory media with nonlocal coupling. They are characterized by coexistence of distinct spatial regions with regular synchronized and irregular incoherent motion. Initially discovered for phase oscillators, chimera states have been also found in systems of nonlocally coupled discrete maps [1], time-continuous chaotic systems [2] and have been recently realized in experiments [3]. We demonstrate the existence of chimera states for neural oscillators [4]. In detail, we investigate the cooperative dynamics of nonlocally coupled neural populations modeled by FitzHugh-Nagumo systems, where each individual system displays oscillatory local dynamics described by a fast activator and slow inhibitor variable. Applying a phase-reduction technique we show that off-diagonal nonlocal coupling is a crucial factor for the appearance of chimera states. In the considered configuration, this off-diagonal coupling is realized by a rotational coupling matrix that mixes input of the activator and inhibitor and that is conveniently described by the coupling phase as a single control parameter. We analyze the stability of chimera states in the parameter space of the system and discuss mechanisms of transitions between different chimera types. Surprisingly, we find that for increasing coupling strength classical chimera states undergo transitions from one to multiple domains of incoherence. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multi-chimeras arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

Electric in-plane polarization in multiferroic CoFe2O4/BaTiO3 nanocomposite tuned by magnetic fields

Ferrimagnetic CoFe2O4 nanopillars embedded in a ferroelectric BaTiO3 matrix are an example for a two-phase magnetoelectrically coupled system. They operate at room temperature and are free of any resource-critical rare-earth element, which makes them interesting for potential applications. Prior studies succeeded in showing strain-mediated coupling between the two subsystems. In particular, the electric properties can be tuned by magnetic fields and the magnetic properties by electric fields. Here we take the analysis of the coupling to a new level utilizing soft X-ray absorption spectroscopy and its associated linear dichroism. We demonstrate that an in-plane magnetic field breaks the tetragonal symmetry of the (1,3)-type CoFe2O4/BaTiO3 structures and discuss it in terms of off-diagonal magnetostrictive-piezoelectric coupling. This coupling creates staggered in-plane components of the electric polarization, which are stable even at magnetic remanence due to hysteretic behaviour of structural changes in the BaTiO3 matrix. The competing mechanisms of clamping and relaxation effects are discussed in detail.

Delocalized Davydov D1 Ansatz for the Holstein polaron

An efficient, yet very accurate trial wave function, constructed from projecting the well-known Davydov D1 Ansatz onto momentum eigenstates, is employed to study the ground state properties of the generalized Holstein Hamiltonian with simultaneous diagonal and off-diagonal coupling. Ground-state energies have been obtained with a precision matching that of the computationally much more demanding density-matrix renormalization group method. The delocalized D1 Ansatz lowers the ground-state energies at the Brillouin zone boundary significantly compared with the Toyozawa and Global-Local Ansätze in the weak coupling regime, while considerable improvement is demonstrated to have been achieved over the entire Brillouin zone in the strong coupling regime. Unique solutions are obtained with the delocalized D1 for different initial conditions when the transfer integral is 20 times the phonon frequency at the zone center, implying the absence of any self-trapping discontinuity. The scaled correlation variance is found to fit satisfactorily well with the predictions of the perturbation theories.

Vibrational signatures of Watson–Crick base pairing in adenine–thymine mimics

The vibrational fingerprints of hydrogen-bonding associated with the adenine-thymine (A-T) Watson-Crick (WC) base pair have been identified in an infrared study of the A-T mimics 4-aminopyrimidine-1-methylthymine (4APM-1MT) and 4-aminopyrimidine-6-methyl-4-pyrimidinone (4APM-M4PMN) in the gas-phase. The IR vibrational spectra were measured via a double resonance scheme utilizing femtosecond multiphoton ionization. The changes in the molecular structure, anharmonic vibrational parameters, and the assignment of the observed vibrational spectra in the NH/CH stretch region were investigated by carrying out high-level theoretical calculations of the anharmonic spectra. The experimental observations and theoretical calculations indicate that the hydrogen bonds associated with WC base-pairing are relatively stronger than those associated with reverse WC (rWC) base pairing. This is manifested in a more pronounced red-shift of the H-bonded vibrational modes associated with the WC as compared with the rWC base-pairing. An analysis of the factors contributing to the anharmonicity of the vibrational modes associated with H-bonding reveals that the magnitude of the off-diagonal anharmonic coupling of the H-bonded -NH2 stretch and the -NH2 bend is much smaller in WC base-pairing than in the corresponding rWC base-pairing. The chemical and biological implications of these results, especially in the context of using vibrational spectroscopy as a tool for identifying the signatures of nucleotide base vibrations is addressed.

Dynamics of a Holstein polaron with off-diagonal coupling

Dynamics of a one-dimensional Holstein polaron with off-diagonal exciton-phonon coupling is studied by employing the Dirac-Frenkel time-dependent variational principle. The trial state used is the Davydov D(2) Ansatz with two sets of variational parameters, one for each constituting particle in the linearly coupled exciton-phonon system. Validity of the approach is carefully checked by quantifying how faithfully the trial state follows the Schrödinger equation. A close examination of variational outputs reveals fine details of polaron dynamics and intricacies of dynamic exciton-phonon correlations. In the absence of diagonal coupling, the change in the polaron effective mass hinges on the sign of the transfer integral due to the antisymmetric nature of the off-diagonal coupling. The role of the off-diagonal coupling switches from being an agent of transport at moderate coupling strengths to that of localization at large coupling strengths. Increasing the phonon bandwidth leads to a reduced polaron effective mass at the zone center and an overall lowering of the polaron band.

Polaronic discontinuities induced by off-diagonal coupling

In this paper, we study a form of the Holstein molecular crystal model in which the influence of lattice vibrations on the transfers of electronic excitations between neighboring sites (off-diagonal coupling) is taken into account. Using the Toyozawa Ansatz and the Lanczos algorithm, the Holstein Hamiltonian with two types of off-diagonal coupling is studied focusing on a number of analyticity issues in the ground state. For finite-sized lattices and antisymmetric coupling, a sequence of discontinuities are found in the polaron energy dispersion, the size of the ground-state phonon cloud, and the linearized von Neumann entropy used to quantify the quantum entanglement between the exciton and the phonons in the ground state. Such behavior is accompanied by a shift of the ground-state crystal momentum from zero to nonzero values as the coupling strength is increased. In the thermodynamic limit, all discontinuities associated with antisymmetric coupling vanish except the one corresponding to the initial departure of the ground-state wavevector from the Brillouin zone center. For the case of symmetric off-diagonal coupling, a smooth crossover is found to exist in all parameters regimes.

Multimode Charge-Transfer Dynamics of 4-(Dimethylamino)benzonitrile Probed with Ultraviolet Femtosecond Stimulated Raman Spectroscopy

4-(Dimethylamino)benzonitrile (DMABN) has been one of the most studied photoinduced charge-transfer (CT) compounds for over 50 years, but due to the complexity of its excited electronic states and the importance of both intramolecular and solvent reorganization, the detailed microscopic mechanism of the CT is still debated. In this work, we have probed the ultrafast intramolecular CT process of DMABN in methanol using broad-band transient absorption spectroscopy from 280 to 620 nm and ultraviolet femtosecond stimulated Raman spectroscopy (FSRS) incorporating a 330 nm Raman pump pulse. Global analysis of the transient absorption kinetics revealed dynamics occurring with three distinct time constants: relaxation from the Franck-Condon L(a) state to the lower locally excited (LE) L(b) state in 0.3 ps, internal conversion in 2-2.4 ps that produces a vibrationally hot CT state, and vibrational relaxation within the CT state occurring in 6 ps. The 330 nm FSRS spectra established the dynamics along three vibrational coordinates: the ring-breathing stretch, ν(ph), at 764 cm(-1) in the CT state; the quinoidal C═C stretch, ν(CC), at 1582 cm(-1) in the CT state; and the nitrile stretch, ν(CN), at 2096 cm(-1) in the CT state. FSRS spectra collected with a 400 nm Raman pump probed the dynamics of the 1174 cm(-1) CH bending vibration, δ(CH). Spectral shifts of each of these modes occur on the 2-20 ps time scale and were analyzed in terms of the vibrational anharmonicity of the CT state, calculated using density functional theory. The frequencies of the δ(CH) and ν(CC) modes upshift with a 6-7 ps time constant, consistent with their off-diagonal anharmonic coupling to other modes that act as receiving modes during the CT process and then cool in 6-7 ps. It was found that the spectral down-shifts of the δ(CH) and ν(CN) modes are inconsistent with vibrational anharmonicity and are instead due to changes in molecular structure and hydrogen bonding that occur as the molecule relaxes within the CT state potential energy surface.

Origin of Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in SN2 Reactions

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment.

Resonant energy transfer assisted by off-diagonal coupling

Dynamics of resonant energy transfer of a single excitation in a molecular dimer system are studied in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. It is found that, at given temperatures, the off-diagonal coupling can enhance both the coherence of the resonant energy transfer and the net quantity of energy transferred from an initially excited monomer to the other. Also studied is the dynamics of entanglement between the dimer system and the phonon bath as measured by the von Neumann entanglement entropy, and the inter-monomer entanglement dynamics for the excitonic system.

Off-diagonal carrier-phonon coupling and polaron transport

A method extending the Munn-Silbey approach has been applied to obtain the temperature dependence of transport properties of a generalized Holstein model incorporating simultaneous diagonal and off-diagonal carrier-phonon coupling. The Hamiltonian is partially diagonalized by a canonical transformation, and optimal transformation coefficients are determined in a self-consistent manner. Effects of off-diagonal coupling on the optimal transformation coefficients and diffusion coefficients have been discussed in details. The off-diagonal coupling has been revealed as a localization factor as well as a transport mechanism. Moreover, momentum-space variation of the transformation coefficients are found to be responsible for enhanced transport due to off-diagonal coupling.

Excitonic Aharonov-Bohm effect: Unstrained versus strained type-I semiconductor nanorings

We study how mechanical strain affects the magnetic field dependence of the exciton states in type-I semiconductor nanorings. Strain spatially separates the electron and hole in (In,Ga)As/GaAs nanorings which is beneficial for the occurrence of the excitonic Aharonov-Bohm (AB) effect. In narrow strained (In,Ga)As/GaAs nanorings the AB oscillations in the exciton ground-state energy are due to anticrossings with the first excited state. No such AB oscillations are found in unstrained GaAs/(Al,Ga)As nanorings irrespective of the ring width. Our results are obtained within an exact numerical diagonalization scheme and are shown to be accurately described by a two-level model with off-diagonal coupling $t$. The later transfer integral expresses the Coulomb coupling between states of electron-hole pairs. We also found that the oscillator strength for exciton recombination in (In,Ga)As/GaAs nanorings exhibits AB oscillations, which are superimposed on a linear increase with magnetic field. Our results agree qualitatively with recent experiments on the excitonic Aharonov-Bohm effect in type-I (In,Ga)As/GaAs nanorings.