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Physical Review A

Maxwell-Schrödinger hybrid simulation for optically controlling quantum states: A scheme for designing control pulses

Takashi Takeuchi, Shinichiro Ohnuki, Tokuei Sako

Published Mar 3, 2015• 39 citations
Publisher

Abstract

A scheme of designing laser pulses for controlling discrete quantum states has been proposed, relying on the recently developed highly accurate Maxwell-Schr\"odinger hybrid simulation. A single electron confined in a quasi-one-dimensional nanoscale potential well has been used as an illustrative example and a control pulse transferring completely the probability density from the ground state to the first excited state has been designed by the present Maxwell-Schr\"odinger hybrid scheme and by the conventional one that solves the time-dependent Schr\"odinger equation only without accounting for feedback from the electron system to the external electromagnetic field. The resultant pulses obtained by these two methods can be different largely owing to the modification of the laser field by the locally strong radiation from the excited electron. The present study demonstrates that light control pulses designed by the conventional method may need to be rectified for practical implementation in experiments.

DOI
10.1103/physreva.91.033401

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A scheme of designing laser pulses for controlling discrete quantum states has been proposed, relying on the recently developed highly accurate Maxwell-Schr"odinger hybrid simulation. A single electron confined in a quasi-one-dimensional nanoscale potential well has been used as an illustrative example and a control pulse transferring completely the probability density from the ground state to the first excited state has been designed by the present Maxwell-Schr"odinger hybrid scheme and by the conventional one that solves the time-dependent Schr"odinger equation only without accounting for feedback from the electron system to the external electromagnetic field. The resultant pulses obtained by these two methods can be different largely owing to the modification of the laser field by the locally strong radiation from the excited electron. The present study demonstrates that light control pulses designed by the conventional method may need to be rectified for practical implementation in experiments.
The control and readout of a transmon qubit through applied microwave pulses is a key capability in operating many quantum technologies. Currently, the design of microwave pulses for these purposes is done through simple theoretical or numerical models that do not account for how the transmon modifies the applied microwave field. In this work, we present the formulation and discretization of a self-consistent semiclassical model that solves the Schrödinger equation describing qubit dynamics in tandem with a one-dimensional wave equation describing transmission line dynamics. Numerical results are presented using this Maxwell-Schrödinger method to characterize the control and readout of a transmon qubit. We show that our method matches simple theoretical predictions in relevant operating regimes and also look at situations where simplified models break down. In the future, our method can be used to explore these broader operating regimes to search for more effective control and readout protocols.
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.
Control of quantum phenomena has grown from a dream to a burgeoning field encompassing wide-ranging experimental and theoretical activities. Theoretical research in this area primarily concerns identification of the principles for controlling quantum phenomena, the exploration of new experimental applications and the development of associated operational algorithms to guide such experiments. Recent experiments with adaptive feedback control span many applications including selective excitation, wave packet engineering and control in the presence of complex environments. Practical procedures are also being developed to execute real-time feedback control considering the resultant back action on the quantum system. This focus issue includes papers covering many of the latest advances in the field. Focus on Quantum Control Contents Control of quantum phenomena: past, present and future Constantin Brif, Raj Chakrabarti and Herschel Rabitz Biologically inspired molecular machines driven by light. Optimal control of a unidirectional rotor Guillermo Pérez-Hernández, Adam Pelzer, Leticia González and Tamar Seideman Simulating quantum search algorithm using vibronic states of I2 manipulated by optimally designed gate pulses Yukiyoshi Ohtsuki Efficient coherent control by sequences of pulses of finite duration Götz S Uhrig and Stefano Pasini Control by decoherence: weak field control of an excited state objective Gil Katz, Mark A Ratner and Ronnie Kosloff Multi-qubit compensation sequences Y Tomita, J T Merrill and K R Brown Environment-invariant measure of distance between evolutions of an open quantum system Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif and Herschel Rabitz Simplified quantum process tomography M P A Branderhorst, J Nunn, I A Walmsley and R L Kosut Achieving 'perfect' molecular discrimination via coherent control and stimulated emission Stephen D Clow, Uvo C Holscher and Thomas C Weinacht A convenient method to simulate and visually represent two-photon power spectra of arbitrarily and adaptively shaped broadband laser pulses M A Montgomery and N H Damrauer Accurate and efficient implementation of the von Neumann representation for laser pulses with discrete and finite spectra Frank Dimler, Susanne Fechner, Alexander Rodenberg, Tobias Brixner and David J Tannor Coherent strong-field control of multiple states by a single chirped femtosecond laser pulse M Krug, T Bayer, M Wollenhaupt, C Sarpe-Tudoran, T Baumert, S S Ivanov and N V Vitanov Quantum-state measurement of ionic Rydberg wavepackets X Zhang and R R Jones On the paradigm of coherent control: the phase-dependent light-matter interaction in the shaping window Tiago Buckup, Jurgen Hauer and Marcus Motzkus Use of the spatial phase of a focused laser beam to yield mechanistic information about photo-induced chemical reactions V J Barge, Z Hu and R J Gordon Coherent control of multiple vibrational excitations for optimal detection S D McGrane, R J Scharff, M Greenfield and D S Moore Mode selectivity with polarization shaping in the mid-IR David B Strasfeld, Chris T Middleton and Martin T Zanni Laser-guided relativistic quantum dynamics Chengpu Liu, Markus C Kohler, Karen Z Hatsagortsyan, Carsten Muller and Christoph H Keitel Continuous quantum error correction as classical hybrid control Hideo Mabuchi Quantum filter reduction for measurement-feedback control via unsupervised manifold learning Anne E B Nielsen, Asa S Hopkins and Hideo Mabuchi Control of the temporal profile of the local electromagnetic field near metallic nanostructures Ilya Grigorenko and Anatoly Efimov Laser-assisted molecular orientation in gaseous media: new possibilities and applications Dmitry V Zhdanov and Victor N Zadkov Optimization of laser field-free orientation of a state-selected NO molecular sample Arnaud Rouzee, Arjan Gijsbertsen, Omair Ghafur, Ofer M Shir, Thomas Back, Steven Stolte and Marc J J Vrakking Controlling the sense of molecular rotation Sharly Fleischer, Yuri Khodorkovsky, Yehiam Prior and Ilya Sh Averbukh Optimal control of interacting particles: a multi-configuration time-dependent Hartree-Fock approach Michael Mundt and David J Tannor Exact quantum dissipative dynamics under external time-dependent driving fields Jian Xu, Rui-Xue Xu and Yi Jing Yan Pulse trains in molecular dynamics and coherent spectroscopy: a theoretical study J Voll and R de Vivie-Riedle Quantum control of electron localization in molecules driven by trains of half-cycle pulses Emil Persson, Joachim Burgdorfer and Stefanie Grafe Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling Jean-Michel Coron, Andreea Grigoriu, Catalin Lefter and Gabriel Turinici Sliding mode control of quantum systems Daoyi Dong and Ian R Petersen Implementation of fault-tolerant quantum logic gates via optimal control R Nigmatullin and S G Schirmer Generalized filtering of laser fields in optimal control theory: application to symmetry filtering of quantum gate operations Markus Schroder and Alex Brown
Based on the Maxwell–Schrödinger system, a novel numerical scheme for controlling the quantum states of a single electron is proposed in this paper. The key ingredient of the scheme is to employ the electromagnetic potentials instead of the conventional fields for avoiding extra steps of the simulation. The relevant perfect matched layer is given to simulate seemingly infinite regions. And with the help of precise transfer between the objective and the start state, a control pulse can be designed to accurately excite the particle into the objective state. The proposed scheme can perform an ideal quantum state switching while of a simple numerical process.
We use analytic (current) density-potential maps of time-dependent (current) density-functional theory [TD(C)DFT] to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schr\"odinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time-dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum not gate.