Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory

Quantum thermodynamics and open-systems modeling

A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.

Control aspects of quantum computing using pure and mixed states

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

SELECTIVE EXCITATION OF HIGH VIBRATIONAL STATES OF HYDROGEN FLUORIDE IN A THERMAL ENVIRONMENT BY ULTRAFAST INFRARED LASER PULSES

The selective excitation of the high ground vibrational state of rotationless HF in an unobserved quasi-resonant thermal environment under the control of a single pulse and pulse train is studied using the reduced density matrix theory. It is shown that the pulse train can enhance the population transfer probability. The numerical results reveal that the vibrational relaxation process is affected by the distribution of the environment frequency and the molecule–environment coupling intensity. The effects of the molecule–environment coupling parameter and the overlapping pulses on the population of the target state of HF are also discussed.

PERFECT POPULATION TRANSFER IN PULSE-DRIVEN QUANTUM CHAINS

The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.

Optimal control of open quantum systems: cooperative effects of driving and dissipation

We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative algorithm, with no need for Markovian or rotating-wave approximations. The application to a harmonic degree of freedom reveals cooperative effects of driving and dissipation that a standard Markovian treatment cannot capture. Remarkably, control can modify the open-system dynamics to the point where the entropy change turns negative, thus achieving cooling of translational motion without any reliance on internal degrees of freedom.

Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory

Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.

Cooperating or fighting with decoherence in the optimal control of quantum dynamics

This paper explores the use of laboratory closed-loop learning control to either fight or cooperate with decoherence in the optimal manipulation of quantum dynamics. Simulations of the processes are performed in a Lindblad formulation on multilevel quantum systems strongly interacting with the environment without spontaneous emission. When seeking a high control yield it is possible to find fields that successfully fight with decoherence while attaining a good quality yield. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with decoherence and thereby drive the dynamics more efficiently. In the latter regime when the control field and the decoherence strength are both weak, a theoretical foundation is established to describe how they cooperate with each other. In general, the results indicate that the population transfer objectives can be effectively met by appropriately either fighting or cooperating with decoherence.

Optimal dynamic discrimination of similara quantum systems in the presence of decoherence

Optimal dynamic discrimination (ODD) of a mixture of similar quantum systems with time series signals enables the extraction of the associated concentrations with reasonable levels of laser-pulse noise, signal detection errors, and imperfect signal detector resolution [Li et al., J. Chem. Phys. 122, 154103 (2005)]. The ODD paradigm is reexpressed in the density-matrix formulation to allow for the consideration of environmental decoherence on the quality of the extracted concentrations, along with the above listed factors. Simulations show that although starting in a thermally mixed state along with decoherence can be detrimental to discrimination, these effects can be counteracted by seeking a suitable optimal control pulse. Additional sampling of the temporal data also aids in extracting more information to better implement ODD.

Laser Control of Desorption through Selective Surface Excitation

We review recent developments in controlling photoinduced desorption processes of alkali halides. We focus primarily on hyperthermal desorption of halogen atoms and show that the yield, electronic state, and velocity distributions of desorbed atoms can be selected using tunable laser excitation. We demonstrate that the observed control is due to preferential excitation of surface excitons. This approach takes advantage of energetic differences between surface and bulk exciton states and probes the surface exciton directly. We demonstrate that desorption of these materials leads to controlled modification of their surface geometric and electronic structures. We then extend the exciton mechanism of desorption, developed for alkali halides, to metal oxide surfaces, in particular magnesium oxide. In addition, these results demonstrate that laser desorption can serve as a solid-state source of halogen and oxygen atoms, in well-defined electronic and velocity states, for studying chemical processes in the gas phase and at surfaces.

QUANTUM MECHANICS OF DISSIPATIVE SYSTEMS

Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions. Discrimination is made in favor of an unconventional formulation that in a sense combines the merits of both the conventional time-local and memory-kernel prescriptions, where the latter is least favorite in terms of the applicability range of parameters for system-bath coupling, non-Markovian, and temperature. Also highlighted is the importance of correlated driving and dissipation effects, not only on the dynamics under strong external field driving, but also in the calculation of field-free correlation and response functions.

Optimal dynamic discrimination of similar quantum systems with time series data

Optimal dynamic discrimination (ODD) was proposed [Li et al., J. Phys. Chem. B 106, 8125 (2002)] as a paradigm for discriminating noninteracting similar quantum systems in a mixture. This paper extends the ODD concept to optimize a laser control pulse for guiding similar quantum systems such that each exhibits a distinct time series signal for maximum discrimination. The use of temporal data addresses various experimental difficulties, including noise in the laser pulse, signal detection errors, and finite time resolution in the signal. Simulations of ODD with time series data are presented to explore these effects. It is found that the use of an optimally chosen control pulse can significantly enhance the discrimination quality. The ODD technique is also adapted to the case where the sample contains an unknown background species.

Correlation and response functions with non-Markovian dissipation: A reduced Liouville-space theory

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.

Coherence spectroscopy in dissipative media: A Liouville space pathway approach

We address the possibility of using coherent control tools to extract useful information about the interaction of a system with a dissipative environment. To that end we extend previous work, which developed a coherence spectroscopy based on two-pathway excitation phase control, from the isolated molecule limit to dense media. Specifically, we explore the properties of the channel phase, an observable of energy-domain two-pathway excitation experiments that was shown in the isolated molecule limit to carry information about the phase properties of the material system. Our analysis is based on the combination of steady state and time-dependent analytical perturbative approaches within the density matrix formalism, complemented by nonperturbative numerical simulations. We find that the channel phase carries significantly richer information in the presence of decoherence mechanisms than in their absence. In particular, rescattering events in the structured continuum introduce new features in the channel phase spectrum, whose structure conveys information about both the molecular continuum and the system bath interaction.

Optimal laser control of ultrafast photodissociation of I[sub 2][sup −] in water: Mixed quantum/classical molecular dynamics simulation

A linearized optimal control method in combination with mixed quantum/classical molecular dynamics simulation is used for numerically investigating the possibility of controlling photodissociation wave packets of I(2)(-) in water. Optimal pulses are designed using an ensemble of photodissociation samples, aiming at the creation of localized dissociation wave packets. Numerical results clearly show the effectiveness of the control although the control achievement is reduced with an increase in the internuclear distance associated with a target region. We introduce effective optimal pulses that are designed using a statistically averaged effective dissociation potential, and show that they semiquantitatively reproduce the control achievements calculated by using optimal pulses. The control mechanisms are interpreted from the time- and frequency-resolved spectra of the effective optimal pulses.