Using feedback for coherent control of quantum systems

Temporally shaped Laguerre-Gaussian femtosecond laser beams

Femtosecond vortex beams with adjustable temporal pulse shapes are generated. These shaped laser pulses are characterized in the spectral domain by determination of the spectral amplitude and phase as well as in the spatial domain by expansion of the beam profile in a superposition of Laguerre-Gaussian transversal laser modes. The experiments demonstrate that the temporal pulse shapes impressed with a pulse shaper based on a programmable liquid-crystal spatial light modulator are basically unaltered by subsequent transmission through a spiral phase plate, while a high-quality optical vortex is imposed. The combination of programmable pulse shapes and optical vortices in femtosecond laser beams opens new possibilities for applications in micromachining, high harmonic generation, and microscopy.

Quantum control study of ultrafast optical responses in semiconductor quantum dot devices

Two quantum control spectroscopic techniques were applied to study InAs quantum dot (QD) devices, which contain different strain-reducing layers. By adaptively control light matter interaction, a delayed resonant response from the InAs QDs was found to be encoded into the optimal phase profile of ultrafast optical pulse used. We verified the delayed resonant response to originate from excitons coupled to acoustic phonons of InAs QDs with two-dimensional coherent spectroscopy. Our study yields valuable dynamical information that can deepen our understanding of the coherent coupling process of exciton in the quantum-confined systems.

Adaptive reshaping of objects in (multiparameter) Hilbert space for enhanced detection and classification: an application of receiver operating curve statistics to laser-based mass spectroscopy

We propose a new approach to the classical detection problem of discrimination of a true signal of interest from an interferent signal, which may be applied to the area of chemical sensing. We show that the detection performance, as quantified by the receiver operating curve (ROC), can be substantially improved when the signal is represented by a multicomponent data set that is actively manipulated by means of a shaped laser probe pulse. In this case, the signal sought (agent) and the interfering signal (interferent) are visualized by vectors in a multidimensional detection space. Separation of these vectors can be achieved by adaptive modification of a probing laser pulse to actively manipulate the Hamiltonian of the agent and interferent. We demonstrate one implementation of the concept of adaptive rotation of signal vectors to chemical agent detection by means of strong-field time-of-flight mass spectrometry.

Local control theory applied to molecular photoassociation

Local control theory (LCT) is employed to achieve molecular photoassociation with shaped laser pulses. Within LCT, the control fields are constructed from the response of the system to the perturbation which makes them accessible to a straightforward interpretation. This is shown regarding the ground-state collision of H+F and H+I atoms. Different objectives are defined, which aim at the formation of vibrational cold or hot associated molecules, respectively. Results are presented for s-wave scattering, where the rotational degree of freedom is ignored and also for full scale calculations including rotations, in order to describe more realistic conditions.

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.

Control Goal Selection through Anticorrelation Analysis in the Detection Space

A statistical method is reported to determine the pairs of fragment ions in a mass spectrum that are most susceptible to control by adaptive optimization of the laser pulse shapes in the strong-field regime. The proposed method is based on covariance analysis of the mass spectral fragmentation patterns generated by a set of randomly shaped pulses. The pairs of fragment ions that have higher negative covariances possess a correspondingly higher degree of controllability in an adaptive control experiment, whereas the pairs that have higher positive covariances possess correspondingly lower controllability.

Optimal control landscapes for quantum observables

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable finite dimensional quantum systems with no constraints placed on the controls, it is shown that there is only a finite number of distinct values for the extrema, dependent on the spectral degeneracy of the initial and target density matrices. The consequences of these findings for the practical discovery of effective quantum controls in the laboratory is discussed.

Local control of the quantum dynamics in multiple potential wells

The driven wave-packet dynamics in potentials exhibiting several potential wells is investigated. Therefore, local-control strategies are employed where the control field is constructed from the system's dynamics at any instant of time. It is shown that particles can be moved successively between various potential minima. Furthermore, results presented indicate that the intuitive local-control scheme allows for the initiation of a clockwise or counterclockwise rotational motion of a model molecular motor.

Local control of molecular fragmentation: The role of orientation

Local control theory, where the instantaneous response of a system to an external field determines the control field, is employed for the purpose of inducing molecular fragmentation processes via infrared excitation. In particular, the effects of the orientational motion are investigated and compared with the idealized case of a frozen rotation. It is shown that the rotational degree of freedom is crucial for the applicability of the employed local control algorithm. The addition of an additional static electric field which induces a molecular preorientation offers an efficient way for the local control. In particular, with increasing static field strength, the fragmentation yield approaches unity so that the idealized rotationless case is recovered. Numerical results are presented for the NaI molecule.

Systematic Control of Nonlinear Optical Processes Using Optimally Shaped Femtosecond Pulses

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.

Instantaneous dynamics and quantum control fields: Principle and numerical applications

The relation between laser pulses serving the purpose of controlling elementary molecular processes and the instantaneous dynamics of the perturbed system is investigated. The application of the conditions assuring a controlled change of the expectation value of an observable directly links the internal motion to the external perturbation. Several numerical applications document that the derived control fields are efficient and can be interpreted clearly on physical grounds.

RYDBERG WAVEPACKETS IN MOLECULES: From Observation to Control

▪ Abstract  Significant advances in laser technology have led to an increasing interest in the time evolution of Rydberg wavepackets as a means to understanding, and ultimately controlling, quantum phenomena. Rydberg wavepackets in molecules are particularly interesting as they possess many of the dynamical complications of large molecules, such as nonadiabatic coupling between the various degrees of freedom, yet they remain tractable experimentally and theoretically. This review explains in detail how the method of interfering wavepackets can be applied to observe and control Rydberg wavepackets in molecules; it discusses the achievements to date and the possibilities for the future.

Use of coherent control methods through scattering biological tissue to achieve functional imaging

We test whether coherent control methods based on ultrashort-pulse phase shaping can be applied when the laser light propagates through biological tissue. Our results demonstrate experimentally that the spectral-phase properties of shaped laser pulses optimized to achieve selective two-photon excitation survive as the laser pulses propagate through tissue. This observation is used to obtain functional images based on selective two-photon excitation of a pH-sensitive chromophore in a sample that is placed behind a slice of biological tissue. Our observation of coherent control through scattering tissue suggests possibilities in multiphoton-based imaging and photodynamic therapy.

Control of trapped-ion quantum states with optical pulses

We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped-ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways--one that makes the system completely uncontrollable and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schrödinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.

Molecular alignment by trains of short laser pulses

We show that a dramatic field-free molecular alignment can be achieved after exciting molecules with proper trains of strong ultrashort laser pulses. Optimal two- and three-pulse excitation schemes are defined, providing an efficient and robust molecular alignment. This opens new prospects for various applications requiring macroscopic ensembles of highly aligned molecules.