Wirtschaft und Informationstechnik Bocholt
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We study the nonequilibrium dynamics of a quantum system under the influence of two noncommuting fluctuation sources, i.e., purely dephasing fluctuations and relaxational fluctuations. We find that increasing purely dephasing fluctuations suppress increasing relaxation in the quantum system. This effect is further enhanced when both fluctuation sources are fully correlated. These effects arise for medium to strong primary fluctuations already when the secondary fluctuations are weak due to their noncommuting coupling to the quantum system. Dephasing, in contrast, is increased by increasing any of the two fluctuations. Fully correlated fluctuations result in overdamping at much lower system-bath coupling than uncorrelated noncommuting fluctuations. In total, we observe that treating subdominant secondary environmental fluctuations perturbatively leads, as neglecting them, to erroneous conclusions.
We study the impact of underdamped intramolecular vibrational modes on the efficiency of the excitation energy transfer in a dimer in which each state is coupled to its own underdamped vibrational mode and, in addition, to a continuous background of environmental modes. For this, we use the numerically exact hierarchy equation of motion approach. We determine the quantum yield and the transfer time in dependence of the vibronic coupling strength, and in dependence of the damping of the incoherent background. Moreover, we tune the vibrational frequencies out of resonance with the excitonic energy gap. We show that the quantum yield is enhanced by up to 10% when the vibrational frequency of the donor is larger than at the acceptor. The vibronic energy eigenstates of the acceptor acquire then an increased density of states, which leads to a higher occupation probability of the acceptor in thermal equilibrium. We can conclude that an underdamped vibrational mode which is weakly coupled to the dimer fuels a faster transfer of excitation energy, illustrating that long-lived vibrations can, in principle, enhance energy transfer, without involving long-lived electronic coherence.
We study a quantum two-level system under the influence of two independent baths, i.e., a sub-Ohmic pure dephasing bath and an Ohmic or sub-Ohmic relaxational bath. We show that cooling such a system invariably polarizes one of the two baths. A polarized relaxational bath creates an effective asymmetry. This asymmetry can be suppressed by additional dephasing noise. This being less effective, the more dominant low frequencies are in the dephasing noise. A polarized dephasing bath generates a large shift in the coherent oscillation frequency of the two-level system. This frequency shift is little affected by additional relaxational noise nor by the frequency distribution of the dephasing noise itself. As our model reflects a typical situation for superconducting phase qubits, our findings can help optimize cooling protocols for future quantum electronic devices.
Ultrafast Energy Transfer in Excitonically Coupled Molecules Induced by a Nonlocal Peierls Phonon
(2019)
Molecular vibration can influence exciton transfer via either a local (intramolecular) Holstein or a nonlocal (intermolecular) Peierls mode. We show that a strong vibronic coupling to a nonlocal mode dramatically speeds up the transfer by opening an additional transfer channel. This Peierls channel is rooted in the formation of a conical intersection of the excitonic potential energy surfaces. For increasing Peierls coupling, the electronically coherent transfer for weak coupling turns into an incoherent transfer of a localized exciton through the intersection for strong coupling. The interpretation in terms of a conical intersection intuitively explains recent experiments of ultrafast energy transfer in photosynthetic and photovoltaic molecular systems.
When a hydrophilic solute in water is suddenly turned into a hydrophobic species, for instance, by photoionization, a layer of hydrated water molecules forms around the solute on a time scale of a few picoseconds. We study the dynamic buildup of the hydration shell around a hydrophobic solute on the basis of a time-dependent dielectric continuum model. Information about the solvent is spectroscopically extracted from the relaxation dynamics of a test dipole inside a static Onsager sphere in the nonequilibrium solvent. The growth process is described phenomenologically within two approaches. First, we consider a time-dependent thickness of the hydration layer that grows from zero to a finite value over a finite time. Second, we assume a time-dependent complex permittivity within a finite layer region around the Onsager sphere. The layer is modeled as a continuous dielectric with a much slower fluctuation dynamics. We find a time-dependent frequency shift down to the blue of the resonant absorption of the dipole, together with a dynamically decreasing line width, as compared to bulk water. The blue shift reflects the work performed against the hydrogen-bonded network of the bulk solvent and is a directly measurable quantity. Our results are in agreement with an experiment on the hydrophobic solvation of iodine in water.
Quantum systems are typically subject to various environmental noise sources. Treating these environmental disturbances with a system-bath approach beyond weak coupling, one must refer to numerical methods as, for example, the numerically exact quasi-adiabatic path integral approach. This approach, however, cannot treat baths which couple to the system via operators, which do not commute. We extend the quasi-adiabatic path integral approach by determining the time discrete influence functional for such non-commuting fluctuations and by modifying the propagation scheme accordingly. We test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent baths via non-commuting operators. We show that the convergent results can be obtained and agreement with the analytical weak coupling results is achieved in the respective limits.
We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher-order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e., even many-body systems.
Recent experimental results showing atypical nonlinear absorption and marked deviations from well known universality in the low temperature acoustic and dielectric losses in amorphous solids prove the need for improving the understanding of the nature of two-level systems (TLSs) in these materials. Here we suggest the study of TLSs focused on their properties which are nonuniversal. Our theoretical analysis shows that the standard tunneling model and the recently suggested two-TLS model provide markedly different predictions for the experimental outcome of these studies. Our results may be directly tested in disordered lattices, e.g KBr:CN, where there is ample theoretical support for the validity of the two-TLS model, as well as in amorphous solids. Verification of our results in the latter will significantly enhance understanding of the nature of TLSs in amorphous solids, and the ability to manipulate them and reduce their destructive effect in various cutting edge applications including superconducting qubits.
Environmental rocking ratchet: Environmental rectification by a harmonically driven avoided crossing
(2017)
We propose a rocking ratchet designed as a symmetric quantum two-state system driven by a single periodic harmonic force and influenced symmetrically by thermal fluctuations. We show that the necessary broken symmetry can dynamically be achieved by a thermal environment that couples to the energy difference between the two states and the tunnel coupling between them. The quantum two-state system is driven by the harmonic periodic drive through its avoided crossing. The correspondingly driven dissipative quantum dynamics results on average in a finite population difference between both states. This then causes directed particle transport.
Environmental noise leads to dephasing and relaxation in a quantum system. Often, a rigorous treatment of multiple noise sources within a system-bath approach is not possible. We discuss the influence of environmental fluctuations on a quantum system whose dynamics is dephasing already due to a phenomenologically treated additional noise source. For this situation, we develop a path-integral approach, which allows us to treat the system-environment coupling in a numerically exact way, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerically exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative.
The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.
Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. Wefind that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect-phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect-phonon coupling. This allows direct experimental determination of the defect-phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.
The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.
We present a scheme for cooling a vibrational mode of a magnetic molecular nanojunction by a spin-polarized charge current upon exploiting the interaction between its magnetic moment and the vibration. The spin-polarized charge current polarizes the magnetic moment of the nanoisland, thereby lowering its energy. A small but finite coupling between the vibration and the magnetic moment permits a direct exchange of energy such that vibrational energy can be transferred into the magnetic state. For positive bias voltages, this generates an effective cooling of the molecular vibrational mode. We determine parameter regimes for the cooling of the vibration to be optimal. Although the flowing charge current inevitably heats up the vibrational mode via Ohmic energy losses, we show that due to the magnetomechanical coupling, the vibrational energy (i.e, the effective phonon temperature) can be lowered below 50% of its initial value, when the two leads are polarized anti-parallel. In contrast to the cooling effect for positive bias voltages, net heating of the vibrational mode occurs for negative bias voltages. The cooling effect is enhanced for a stronger anti-parallel magnetic polarization of the leads, while the heating is stronger for a larger parallel polarization. Yet, dynamical cooling is also possible with parallel lead alignments when the two tunneling barriers are asymmetric.
Commonly, nanosystems are characterized by their response to time-dependent external fields in the presence of inevitable environmental fluctuations. The direct impact of the external driving on the environment is generally neglected. While this approach is satisfactory for macroscopic systems, on the nanoscale, an interaction of external fields with the environment is often unavoidable on principle. We extend the standard linear response theory of quantum dissipative systems to strongly driven baths. Significant modifications are found for two paradigm examples. First, we evaluate the polarizability of a molecule immersed in a strongly polarizable medium that responds to terahertz radiation. We find an increase of the molecular polarizability by about 30%. Second, we determine the response of a semiconductor quantum dot in close proximity to a metallic nanoparticle. Both are placed in a polarizable medium and exposed to electromagnetic irradiation. We show that the response of the quantum dot is qualitatively modified by the driven nanoparticle, including the generation of an additional channel of stimulated emission.
When an open quantum system is driven by an external time-dependent force, the coupling of the driving to the central system is usually included, whereas the impact of the driving field on the bath is neglected. We investigate the effect of a quantum bath of linearly driven harmonic oscillators on the relaxation dynamics of a quantum two-level system which is not directly driven. In particular, we calculate the frequency-dependent response of the system when the bath is subject to Dirac and Gaussian driving pulses. We show that a time-retarded effective force on the system is induced by the driven bath which depends on the full history of the perturbation and the spectral characteristics of the underlying bath. In particular, when a structured Ohmic bath with a pronounced Lorentzian peak is considered, the dynamical response of the system to a driven bath is qualitatively different than that of the undriven bath. Specifically, additional resonances appear which can be directly associated with a Jaynes-Cummings-like effective energy spectrum.
We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.
