Dissipative Quantum Dynamics Research Articles

Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-Schrödinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems

In linear control, balanced truncation is known as a powerful technique to reduce the state-space dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. This work deals with a first application of balanced truncation to the control of open quantum systems which are modeled by the Liouville-von Neumann equation within the Lindblad formalism. Generalization of the linear theory has been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system. As an example we choose the dissipative quantum dynamics of a particle in an asymmetric double well potential driven by an external control field, monitoring population transfer between the potential wells as a control target. The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system. The dimension of the model system can be reduced very efficiently where the degree of reduction depends on temperature and relaxation rate.

Quantum dynamics of a two-level system in a structured environment: Numerical study beyond perturbation theory

The dissipative quantum dynamics of a two-level system interacting with a structured reservoir consisting of a damped harmonic mode is investigated by means of the numerically exact path integral Monte Carlo method. This approach provides benchmark results in a broad range of parameter space, in particular, in those domains which are not accessible by approximate methods and alternative numerical schemes, that is, strong coupling between system and harmonic mode and from low to high temperatures. For low temperatures the numerical data are quantitatively in agreement with the noninteracting blip approximation only in the regimes of very weak and very strong coupling. It turns out that the entangled dynamics of the two-level system and the harmonic mode is relatively robust so that its signatures are observable up to relatively strong friction and high temperatures. Nonequilibrium initial preparations of the reservoir with respect to the initial state of the system give rise, for strong interactions, to a stepwise decay of the population, thus displaying coherent dynamics of the bath. The impact of an additional Ohmic bath coupled directly to the two-level system is studied as well, including the case where both reservoirs carry different temperatures.

Real-time path integrals for quantum dots: Quantum dissipative dynamics with superohmic environment coupling

Real-time path integrals for quantum dots: Quantum dissipative dynamics with superohmic environment coupling

The effect of correlated bath fluctuations on exciton transfer.

Excitation dynamics of various light harvesting systems have been investigated with many theoretical methods including various non-Markovian descriptions of dissipative quantum dynamics. It is typically assumed that each excited state is coupled to an independent thermal environment, i.e., that fluctuations in different environments are uncorrelated. Here the assumption is dropped and the effect of correlated bath fluctuations on excitation transfer is investigated. Using the hierarchy equations of motion for dissipative quantum dynamics it is shown for models of the B850 bacteriochlorophylls of LH2 that correlated bath fluctuations have a significant effect on the LH2→LH2 excitation transfer rate. It is also demonstrated that inclusion of static disorder is crucial for an accurate description of transfer dynamics.

Communication: Universal Markovian reduction of Brownian particle dynamics

Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density J(0), we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by J(0) and defines a sequence {J(n)}(n∈N) of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple one-term recurrence relation for this sequence and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of J(0), convergence is fast enough to be useful in practice for an effective Ohmic reduction of the dissipative dynamics.

Vibrational relaxation and dephasing of Rb2 attached to helium nanodroplets

The vibrational wave-packet dynamics of diatomic rubidium molecules (Rb(2)) in triplet states formed on the surface of superfluid helium nanodroplets is investigated both experimentally and theoretically. Detailed comparison of experimental femtosecond pump-probe spectra with dissipative quantum dynamics simulations reveals that vibrational relaxation is the main source of dephasing. The rate constant for vibrational relaxation in the first excited triplet state 1(3)Σ(g)+ is found to be constant γ ≈ 0.5 ns(-1) for the lowest vibrational levels v ≲ 15 and to increase sharply when exciting to higher energies.

Quantum Dynamics of a Harmonic Oscillator in a Deformed Bath

The dissipative quantum dynamics of a harmonic oscillator in the presence of a deformed bath is investigated. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The transition probabilities between energy levels of the oscillator are obtained perturbatively and discussed.

Energy transfer dynamics in an RC–LH1–PufX tubular photosynthetic membrane

Light absorption and the subsequent transfer of excitation energy are the first two steps in the photosynthetic process, carried out by protein-bound pigments, mainly bacteriochlorophylls (BChls), in photosynthetic bacteria. BChls are anchored in light-harvesting (LH) complexes, such as light-harvesting complex I (LH1), which directly associates with the reaction center (RC), forming the RC–LH1 core complex. In Rhodobacter sphaeroides, RC–LH1 core complexes contain an additional protein, PufX, and assemble into dimeric RC–LH1–PufX core complexes. In the absence of LH complex II (LH2), the former complexes can aggregate into a helically ordered tubular photosynthetic membrane. We have examined the excitation transfer dynamics in a single RC–LH1–PufX core complex dimer using the hierarchical equations of motion for dissipative quantum dynamics that accurately, yet in a computationally costly manner, treat the coupling between BChls and their protein environment. A widely employed description, the generalized Förster (GF) theory, was also used to calculate the transfer rates of the same excitonic system in order to verify the accuracy of this computationally cheap method. Additionally, in light of the structural uncertainties in the Rba. sphaeroides RC–LH1–PufX core complex, geometrical alterations were introduced into the BChl organization. It is shown that the energy transfer dynamics are not affected by the considered changes in the BChl organization and that the GF theory provides accurate transfer rates. An all-atom model for a tubular photosynthetic membrane is then constructed on the basis of electron microscopy data, and the overall energy transfer properties of this membrane are computed.

Dissipative quantum systems and the heat capacity

We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behaviors of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit (t-->infinity) is taken seems to assume significance.

Dissipative vibrational wave packet dynamics of alkali dimers attached to helium nanodroplets

Femtosecond pump–probe spectroscopy has been used to study vibrational dynamics of potassium dimers attached to superfluid helium nanodroplets. Comparing the measured data with theoretical results based on dissipative quantum dynamics we propose that the most important effect of the helium environment is a general damping of the vibrational dynamics. The calculations allow us to explain crucial experimental findings that are unobserved in gas phase measurements. Remarkably, wave packet velocities of such alkali dimer vibrations are just about in the range of the Landau critical velocity of superfluid helium. We therefore also discuss a possible influence of superfluidity on the induced wave packet dynamics.

Analysis of the continuous-configuration time-dependent self-consistent field method applied to system-bath dynamics

We have implemented and studied the continuous-configuration time-dependent self-consistent field scheme, a variation of the multiconfiguration time-dependent Hartree method, which aims to get around the latter's exponential scaling problem, especially with regard to system-bath dynamics. We present applications to quantum dissipative dynamics and an analysis of the computational effort. Namely, propagation times within this scheme scale linearly with the number of bath modes.

Semiclassical non-Markovian Brownian motion in anharmonic potentials

The combination of an exact stochastic decomposition of non-Markovian dissipative quantum dynamics with the semiclassical initial value formalism is applied to Brownian motion in a Morse potential. The unified sampling of the stochastic noise and the semiclassical phase space distribution introduced in Koch et al. [W. Koch, F. Grossmann, J.T. Stockburger, J. Ankerhold, Non-Markovian semiclassical dynamics, Phys. Rev. Lett. 100 (2008) 230402] is laid out here in detail. By comparing our numerical results to those obtained by using the Caldeira–Leggett master equation, we show that even in the challenging regime of moderate friction and at low temperatures, where reservoir fluctuations are clearly non-Markovian, this approach allows for the accurate description of dissipative dynamics over many oscillation periods until thermalization is reached.

Exact quantum dissipative dynamics under external time-dependent driving fields

An exact and nonperturbative quantum master equation can be constructed via the calculus on the path integral. It results in hierarchical equations of motion for the reduced density operator. Involved also are a set of well-defined auxiliary density operators that resolve not just the system–bath coupling strength but also memory. In this work, we scale these auxiliary operators individually to achieve a uniform error tolerance, as set by the reduced density operator. An efficient propagator is then proposed to the hierarchical Liouville-space dynamics of quantum dissipation. Numerically exact studies are carried out on the dephasing effect on population transfer in the simple stimulated Raman adiabatic passage scheme. We also make assessments on several perturbative theories for their applicabilities in the present system of study.

Free-time and fixed end-point optimal control theory in dissipative media: Application to entanglement generation and maintenance

We develop monotonically convergent free-time and fixed end-point optimal control theory (OCT) in the density-matrix representation to deal with quantum systems showing dissipation. Our theory is more general and flexible for tailoring optimal laser pulses in order to control quantum dynamics with dissipation than the conventional fixed-time and fixed end-point OCT in that the optimal temporal duration of laser pulses can also be optimized exactly. To show the usefulness of our theory, it is applied to the generation and maintenance of the vibrational entanglement of carbon monoxide adsorbed on the copper (100) surface, CO/Cu(100). We demonstrate the numerical results and clarify how to combat vibrational decoherence as much as possible by the tailored shapes of the optimal laser pulses. It is expected that our theory will be general enough to be applied to a variety of dissipative quantum dynamics systems because the decoherence is one of the quantum phenomena sensitive to the temporal duration of the quantum dynamics.

Semiclassical formulation of non-Markovian quantum Brownian motion

Recently it was shown [W. Koch, F. Grossmann, J.T. Stockburger, J. Ankerhold, Phys. Rev. Lett. 100 (2008) 230402] that a combination of an exact stochastic decomposition of non-Markovian dissipative quantum dynamics with the time-dependent semiclassical initial value formalism offers a powerful tool to describe quantum Brownian motion in domains of parameter space where other approaches fail. In particular, low temperatures, stronger friction, a wide range of spectral bath densities, and continuous nonlinear systems can be treated. Details of this formulation including its numerical implementation and the impact of non-Markovian phenomena are discussed for the exactly solvable case of a harmonic oscillator.

Salt-marshes as emergent novelties in the Venice Lagoon

It has been observed in Venice Lagoon that salt-marshes have appeared and developed as a consequence of the presence of artificial or biological confinements, maintaining separation domains in the hydrodynamic wave and tidal flow field. This surprising result is analysed in terms of a recently developed point of view on the emergence of self-organization in liquid water near interfaces with walls. This self-organization emerges through the combined action of quantum coherence and dissipative dynamics.

A finite-difference implementation of the Caldeira–Leggett master equation

The Caldeira-Leggett master equation for dissipative quantum dynamics has predominantly been implemented in phase space, where it plays the role of a quantum Fokker-Planck equation. Here we demonstrate the feasibility of a pure coordinate space implementation in the case of intermediate damping strength and temperature, for times long enough to observe thermal equilibration. After a thorough numerical investigation of the analytically solvable harmonic oscillator case, a Morse oscillator model is studied. This is a case in which a quantal phase space approach would be difficult to implement and we show how analytical results for thermal averages are reproduced to a surprisingly high degree.

Dissipative quantum dynamics in low-energy collisions of complex nuclei

Model calculations that include the effects of irreversible, environmental couplings on top of a coupled-channels dynamical description of the collision of two complex nuclei are presented. The Liouville-von Neumann equation for the time evolution of the density matrix of a dissipative system is solved numerically providing a consistent transition from coherent to decoherent (and dissipative) dynamics during the collision. Quantum decoherence and dissipation are clearly manifested in the model calculations. Energy dissipation, due to the irreversible decay of giant-dipole vibrational states of the colliding nuclei, is shown to result in a hindrance of quantum tunneling and fusion.

On the Jarzynski relation for dissipative quantum dynamics

In this paper, we will discuss how to compactly express the Jarzynski identity for an openquantum system with dissipative dynamics. In quantum dynamics we must avoid explicitlymeasuring the work directly, which is tantamount to continuously monitoring the state ofthe system, and instead measure the heat flow from the environment. These measurementscan be concisely represented with Hermitian map superoperators, which provide convenientand compact representations of correlation functions and sequential measurements ofquantum systems.