The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.

https://iopscience.iop.org/article/10.1088/0953-8984/28/21/213001/pdf

Controlling open quantum systems: tools, achievements, and limitations.

We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type of control problem is typically solved using derivative-based methods in a high-dimensional control space such as gradient-ascent pulse engineering (GRAPE) and Krotov's method or derivative-free methods in a reduced control space such as Nelder-Mead with a chopped random basis (CRAB). We discuss how these methods can be combined in gradient optimization using parametrization (GROUP) including the finite bandwidth of the control electronics. We compare these methods and find that GROUP converges much faster than Nelder-Mead with CRAB and achieves better results than GRAPE and Krotov's method on the control problem presented here.

Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates

http://absimage.aps.org/image/MAR15/MWS_MAR15-2014-000562.pdf

Controlling open quantum systems: Tools, achievements, limitations

We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization. The package is being developed at this https URL

/pdf/krotov-a-python-implementation-of-krotov-s-method-for-458sx84jpq.pdf

Krotov: A Python implementation of Krotov's method for quantum optimal control

Metasurfaces are subwavelength spatial variations in geometry and material where the structures are of negligible thickness compared to the wavelength of light and are optimized for far-field applications, such as controlling the wavefronts of electromagnetic waves Here, we investigate the potential of the metasurface near-field profile, generated by an incident few-cycle pulse laser, to facilitate the generation of high-frequency light from free electrons In particular, the metasurface near-field contains higher-order spatial harmonics that can be leveraged to generate multiple higher-harmonic X-ray frequency peaks We show that the X-ray spectral profile can be arbitrarily shaped by controlling the metasurface geometry, the electron energy, and the incidence angle of the laser input Using ab initio simulations, we predict bright and monoenergetic X-rays, achieving energies of 30 keV (with harmonics spaced by 3 keV) from 5-MeV electrons using 34-eV plasmon polaritons on a metasurface with a period of 85 nm As an example, we present the design of a four-color X-ray source, a potential candidate for tabletop multicolor hard X-ray spectroscopy Our developments could help pave the way for compact multi-harmonic sources of high-energy photons, which have potential applications in industry, medicine, and the fundamental sciences

/pdf/metasurface-based-multi-harmonic-free-electron-light-source-l84opwfbyr.pdf

Metasurface-based multi-harmonic free-electron light source

We demonstrate coherent control over the photoelectron circular dichroism in randomly oriented chiral molecules, based on quantum interference between multiple photoionization pathways. To significantly enhance the chiral signature, we use a finite manifold of indistinguishable (1+1^{'}) resonantly enhanced multiphoton ionization pathways interfering at a common photoelectron energy but probing different intermediate states. We show that this coherent control mechanism maximizes the number of molecular states that constructively contribute to the dichroism at an optimal photoelectron energy and thus outperforms other schemes, including interference between opposite-parity pathways driven by bichromatic (ω, 2ω) fields as well as sequential pump-probe ionization.

Quantum Control of Photoelectron Circular Dichroism.

Krotov's optimal control method is adapted to studies of multiphoton ionization by strong XUV fields; it is demonstrated that fine-grained control of photoelectron distributions with laser pulse shaping can be achieved systematically by applying the proposed algorithm.

/pdf/quantum-optimal-control-of-photoelectron-spectra-and-angular-3joapfcadz.pdf

Quantum optimal control of photoelectron spectra and angular distributions

Photoionization with attosecond pulses populates hole states in the photoion. Superpositions of hole states represent ideal candidates for time-dependent spectroscopy, for example via pump-probe studies. The challenge consists in identifying pulses that create coherent superpositions of hole states while satisfying practical constraints. Here, we employ quantum optimal control to maximize the degree of coherence between these hole states. To this end, we introduce a derivative-free optimization method with sequential parametrization update (SPA optimization). We demonstrate the versatility and computational efficiency of SPA optimization for photoionization in argon by maximizing the coherence between the $3s$ and $3{p}_{0}$ hole states using shaped attosecond pulses. We show that it is possible to maximize the hole coherence while simultaneously prescribing the ratio of the final hole state populations.

Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update

We report two schemes to generate perfect anisotropy in the photoelectron angular distribution of a randomly oriented ensemble of polyatomic molecules. In order to exert full control over the anisotropy of photoelectron emission, we exploit interferences between single-photon pathways and a manifold of resonantly enhanced two-photon pathways. These are shown to outperform nonsequential (ω, 2ω) bichromatic phase control for the example of CHFClBr molecules. We are able to optimize pulses that yield anisotropic photoelectron emission thanks to a very efficient calculation of photoelectron momentum distributions. This is accomplished by combining elements of quantum chemistry, variational scattering theory, and time-dependent perturbation theory.

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping

We report two schemes to generate perfect anisotropy in the photoelectron angular distribution of a randomly oriented ensemble of polyatomic molecules. In order to exert full control over the anisotropy of photoelectron emission, we exploit interferences between single-photon pathways and a manifold of resonantly-enhanced two-photon pathways. These are shown to outperform non-sequential $(\omega,2\omega)$ bichromatic phase control for the example of CHFClBr molecules. We are able to optimize pulses that yield anisotropic photoelectron emission thanks to a very efficient calculation of photoelectron momentum distributions. This is accomplished by combining elements of quantum chemistry, variational scattering theory, and time-dependent perturbation theory.

R. Esteban Goetz

Papers

Quantum Control of Photoelectron Circular Dichroism.

Quantum optimal control of photoelectron spectra and angular distributions

Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping