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arXiv:2211.08214 · Lobachevskii Journal of Mathematics

Laser and Diffusion Driven Optimal Discrimination of Similar Quantum Systems in Resonator

Konstantin Andreevich Lyakhov, Alexander Nikolaevich Pechen

Published Jul 1, 2022• 1 citation
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Abstract

Abstract In this work, a method for solving the problem of efficient population transfer from the ground to some excited state by available technical means (varying resonator length) is proposed. We consider a mixture of similar quantum systems distributed in a stationary gas flow in the resonator with variable resonator length, which implements tailored laser field close to the optimal one. In difference from previous works, in this work piezoelectric transducer (PZT; or actuator) is used as mean of control to manipulate variable resonator length. The external actions are optimized to selectively prepare different stationary states of different species which are then separated using their diffusion with rates which differ due to different masses. This system provides an example of the general problem of optimizing states of distributed systems with stationary gas flow with diffusion.

DOI
10.1134/s1995080222100249

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Abstract This paper proposes a numerical approach to the problem of inverse quantum control with a focus on the automated formation of external laser control fields that ensure high-precision and controlled population transfer in multilevel quantum systems. The method is based on optimizing the parameters of control pulses using gradient algorithms in combination with automatic differentiation, which allows for effective control of the physical characteristics of laser fields and increases the stability of the transfer process. The obtained results provide a foundation for the development of more general quantum control methods focused on experimental implementation on real physical platforms.
A paradigm for discriminating similar quantum systems in the laboratory is presented based on optimal control principles with the aid of closed loop learning algorithms. The optimal dynamic discrimination (ODD) process is simulated for a noninteracting mixture of up to three similar finite-dimensional quantum systems. The optimal control field giving rise to species discrimination, that considers the presence of field and observation noise, is deduced with a genetic algorithm (GA). The similar quantum systems yield distinct dynamics and detection signals, although influenced by the same control laser pulse. The ODD process is shown to operate by drawing on constructive and destructive interference effects to simultaneously maximize or minimize the signals from each of the species in the mixture. The ODD technique may have applications to the analysis and separation of possibly even complex chemical species.
Similar molecules or materials have comparable composition, structure, and other properties thus making them difficult to discriminate for purposes of detection. Although the species may be spectrally similar, they each could have significantly different (quantum) dynamical behavior for detection. Optimal dynamic discrimination (ODD) aims to maximally draw out the differences among similar species by manipulating their molecular dynamics with optimized radiation resources. The highest degrees of discrimination arise upon exploiting control of the quantum dynamics of the species. Theoretical analysis shows that quantum systems differing even infinitesimally in character may be distinguished by means of their dynamics when acted upon by a suitably shaped control field. Simulations have demonstrated the capabilities of optimal discrimination in the presence of laser-pulse noise, signal detection errors, and imperfect signal detection resolution. Recent experiments have demonstrated the feasibility of ODD.
State-selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules, or quantum dots is the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology, and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum system is presented.
This paper considers the optimal control of quantum systems. The controlled quantum systems are described by the probability-density-matrix-based Liouville–von Neumann equation. Using projection operators, the states of the quantum system are decomposed into two sub-spaces, namely the 'main state' space and the 'remaining state' space. Since the control energy is limited, a solution for optimizing the external control force is proposed in which the main state is brought to the desired main state at a certain target time, while the population of the remaining state is simultaneously suppressed in order to diminish its effects on the final population of the main state. The optimization problem is formulated by maximizing a general cost functional of states and control force. An efficient algorithm is developed to solve the optimization problem. Finally, using the hydrogen fluoride (HF) molecular population transfer problem as an illustrative example, the effectiveness of the proposed scheme for a quantum system initially in a mixed state or in a pure state is investigated through numerical simulations.
A theoretical study is presented concerning the ability to dynamically discriminate between members of a set of different (but possibly similar) quantum systems. This discrimination is analysed in terms of independently and simultaneously steering about the wavefunction of each component system to a target state of interest using a tailored control (i.e. laser) field. Controllability criteria are revealed and their applicability is demonstrated in simple cases. Discussion is also presented in some uncontrollable cases.