Quantum hysteresis and resonant tunneling in bistable systems

Fast Quantum State Preparation and Bath Dynamics Using Non-Gaussian Variational Ansatz and Quantum Optimal Control

Fast preparation of quantum many-body states is essential for myriad quantum algorithms and metrological applications. Here, we develop a new pathway for fast, nonadiabatic preparation of quantum many-body states that combines quantum optimal control with a variational Ansatz based on non-Gaussian states. We demonstrate our approach on the spin-boson model, a single spin interacting with the bath. We use a multipolaron Ansatz to prepare near-critical ground states. For one mode, we achieve a reduction in infidelity of up to ≈60 (≈10) times compared to linear (optimized local adiabatic) ramps; for many modes, we achieve a reduction in infidelity of up to ≈5 times compared to nonadiabatic linear ramps. Further, we show that the typical control quantity, the leakage from the variational manifold, provides only a loose bound on the state's fidelity. Instead, in analogy to the bond dimension of matrix product states, we suggest a controlled convergence criterion based on the number of polarons. Finally, motivated by the possibility of realizations in trapped ions, we study the dynamics of a system with bath properties going beyond the paradigm of (sub- and/or super-) Ohmic couplings.

Coherent and incoherent theories for photosynthetic energy transfer

There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.

Vibronically coherent speed-up of the excitation energy transfer in the Fenna-Matthews-Olson complex

We show that underdamped molecular vibrations fuel the efficient excitation energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions. By employing an environmental fluctuation spectral function derived from experiments, we obtain numerically exact results for the exciton quantum dynamics in the presence of underdamped vibrationally coherent quantum states. Assuming the prominent 180-cm(-1) vibrational mode to be underdamped, additional coherent transport channels for the excitation energy transfer open up and we observe an increase of the transfer speed towards the reaction center by up to 24%.

Quantification of non-Markovian effects in the Fenna-Matthews-Olson complex

The excitation energy transfer dynamics in the Fenna-Matthews-Olson complex is quantified in terms of a non-Markovianity measure based on the time evolution of the trace distance of two quantum states. We use a system description derived from experiments and different environmental fluctuation spectral functions, which are obtained either from experimental data or from molecular dynamics simulations. These exhibit, in all cases, a nontrivial structure with several peaks attributed to vibrational modes of the pigment-protein complex. Such a structured environmental spectrum can, in principle, give rise to strong non-Markovian effects. We present numerically exact real-time path-integral calculations for the transfer dynamics and find, in all cases, a monotonic decrease of the trace distance with increasing time which renders a Markovian description valid.

Dynamics of the sub-Ohmic spin-boson model: a comparison of three numerical approaches

Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local field. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D(1) ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.

Equilibration and thermalization of the dissipative quantum harmonic oscillator in a nonthermal environment

We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.

Exciton transfer dynamics and quantumness of energy transfer in the Fenna-Matthews-Olson complex

We present numerically exact results for the quantum coherent energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions, including vibrational fluctuations of the protein and the pigments for an experimentally determined fluctuation spectrum. We find coherence times shorter than observed experimentally. Furthermore, we determine the energy transfer current and quantify its "quantumness" as the distance of the density matrix to the classical pointer states for the energy current operator. Most importantly, we find that the energy transfer happens through a "Schrödinger-cat-like" superposition of energy current pointer states.

Multiphonon transitions in the biomolecular energy transfer dynamics

We show that the biomolecular exciton dynamics under the influence of slow polarization fluctuations in the solvent cannot be described by lowest order, one-phonon approaches which are perturbative in the system-bath coupling. Instead, nonperturbative multiphonon transitions induced by the slow bath yield significant contributions. This is shown by comparing results for the decoherence rate of the exciton dynamics of a resumed perturbation theory with numerically exact real-time path-integral data. The exact decoherence rate for realistically slow solvent environments is significantly modified by multiphonon processes even in the weak coupling regime, while a one-phonon description is satisfactory only for fast environmental noise. Slow environments inhibit bath modes that are resonant with the exciton dynamics, thereby suppressing one-phonon transitions and enhancing multiphonon processes, which are typically not captured by lowest order perturbative treatments, such as Redfield or Lindblad approaches, even in more refined variants.

Switching mechanism in periodically driven quantum systems with dissipation

We introduce a switching mechanism in the asymptotic occupations of quantum states induced by the combined effects of a periodic driving and a weak coupling to a heat bath. It exploits one of the ubiquitous avoided crossings in driven systems and works even if both involved Floquet states have small occupations. It is independent of the initial state and the duration of the driving. As a specific example of this general switching mechanism we show how an asymmetric double well potential can be switched between the lower and upper well by a periodic driving that is much weaker than the asymmetry.

Numerical study on dynamical behavior in oscillatory driven quantum double-well systems

We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.

Quantifying stochastic resonance: theory versus experiment

We discuss different quantifiers of stochastic resonance (SR) and how far they are mathematically related with each other. Specifically, we address bona fide SR in terms of the areas of the hysteresis loops and of the first peaks in the residence time distributions. We demonstrate a surprisingly good agreement of these two SR quantifiers experimentally for colloidal particles in periodically modulated laser traps. A simple theoretical model is established, which reproduces the experimental observations very well.

Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum-mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path-integral algorithm. We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.

Strong coupling theory for driven tunneling and vibrational relaxation

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled non-Markovian master equations. We present analytical treatments that describe the dynamics in the regime of strong system-bath coupling. Our findings are corroborated by "ab initio" real-time path integral calculations.

Stochastic resonance and nonlinear response using NMR spectroscopy

We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced relaxation dynamics can be characterized via a single relaxation time scale. The picture is validated by a simple nuclear magnetic resonance experiment on water.

Quantum stochastic resonance in symmetric systems

We investigate the low-temperature quantum stochastic resonance (QSR) phenomenon in a two-level system (TLS) which is coupled to an Ohmic heat bath. In contrast to common belief we find that QSR occurs also for symmetric (i.e., unbiased) TLS's if the viscous friction parameter alpha exceeds a critical value: We demonstrate that with respect to the spectral power amplification measure QSR always occurs for alpha>1; in contrast, the output signal-to-noise ratio exhibits an amplification only for alpha>3/2.