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Photonics

Reverse-Engineered Exact Control of Population Transfer in Lossy Nonlinear Three-State Systems

Artur Mikhailovich Ishkhanyan

Published Oct 25, 2024• 2 citations
Publisher

Abstract

We introduce a reverse-engineered scheme for achieving the precise control of population transfer in nonlinear quantum systems characterized by a 1:2 resonance. This scheme involves the use of two resonant laser pulses that transition from initial and final states to an intermediate level exhibiting irreversible losses. In comparison to alternative techniques, our approach offers computational efficiency advantages. Notably, the analytically defined form of the pump pulse enables tailored control strategies, enhancing robustness against decoherence and imperfections. This flexibility extends to choosing dump pulses and designing time evolution scenarios. These features open doors for practical implementation and scalability in quantum technologies, with potential applications in quantum information processing, quantum computing, and quantum communication.

DOI
10.3390/photonics11111007

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We introduce a reverse-engineered scheme for achieving the precise control of population transfer in nonlinear quantum systems characterized by a 1:2 resonance. This scheme involves the use of two resonant laser pulses that transition from initial and final states to an intermediate level exhibiting irreversible losses. In comparison to alternative techniques, our approach offers computational efficiency advantages. Notably, the analytically defined form of the pump pulse enables tailored control strategies, enhancing robustness against decoherence and imperfections. This flexibility extends to choosing dump pulses and designing time evolution scenarios. These features open doors for practical implementation and scalability in quantum technologies, with potential applications in quantum information processing, quantum computing, and quantum communication.
It has long been interest to control the transfer of population between specified quantum states and protect the coherence of the system at the same time. In this paper, we investigate a scheme to improve the strategy of state transfer for open quantum systems using no-knowledge measurement-based feedback control and reverse engineering. In order to ensure that the system can process information effectively, we first design the control pulse in advance from the perspective of population and coherence and then verify it through numerical simulations. The research results show that, based on the designed control pulse, we can indeed drive the system from any initial state to the desired target state, and the coherence of the system can be effectively protected during the state transition.
Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr\"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.
In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.
Shortening the operation time of implementing scheme and reducing the influence of harmful factors have always been the research objectives pursued by people. Based on invariant-based reverse engineering, we present a general scheme for implementing robust population transfer in a three-level system via optimal shortcut to adiabatic passage. The systematic error sensitivity is introduced to measure the robustness of the process. The smooth Rabi frequencies are expressed with some coefficients, which are also related to the systematic error sensitivity and the population of intermediate state. When the amplitude of control field is given, the transfer can be optimized within as small systematic error sensitivity as possible, i.e., the robustness against systematic errors is further improved by choosing suitable correlation coefficient. Additionally, we apply the technique to achieve robust excitation fluctuation transfer between two membranes in an optomechanical system. The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is analysed. Numerical result shows that the fidelity keeps over 0.95 even if the coupling strengths deviates from 20% of the theoretical value. Moreover, comparison with existing literature [Opt. Express29, 7998 (2021)10.1364/OE.417343], the proposed scheme possesses stronger robustness against variations of effective optomechanical coupling strengths and lower population of unwanted states. The idea may provide a promising approach for quantum information processing.
Abstract We propose a scheme to inverse engineer the Hamiltonian of any general driven three-level system by employing a SU(3) transformation. For special cases, the scheme is then introduced to explore nonadiabatic dynamic evolution of systems with two-photon resonance. We demonstrate that, by selecting the control parameters with explicit function forms, both the ideal process and the practical evolution driving with the truncation of pulses, systematic error and decaying can implement fast population transfer with high fidelity. Moreover, the nonadiabatic passages are not reconstructed by the superadiabatic approach.
We apply reverse engineering to find electromagnetic pulses that allow for the control of populations in quantum systems under dephasing and thermal noises. In particular, we discuss two-level systems given their importance in the description of several molecular systems as well as quantum computing. Such an investigation naturally finds applications in a multitude of physical situations involving the control of quantum systems. We present an analytical description of the pulse which solves a constrained dynamics where the initial and final populations are fixed a priori. This constrained dynamics is sometimes impossible, and we precisely spot the conditions for that. One of our results is the presentation of analytical conditions for the establishment of steady states for finite coherence in the presence of noise. This might naturally find applications in quantum memories.