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Journal of Modern Optics

Control of Rydberg atoms to perform Grover's search algorithm

C. Rangan, Jaewook Ahn, D. N. Hutchinson, P. H. Bucksbaum

Published Nov 1, 2002• 10 citations
Publisher

Abstract

It is shown that Grover's search algorithm can be implemented on a Rydberg atom data register using a short terahertz half-cycle pulse. Using optimal control theory, a shaped terahertz pulse is designed that can perform the search algorithm better than an unshaped half-cycle pulse. Starting from an initial wave packet, it is shown that it is possible to use the search algorithm to synthesize single-energy eigenstates.

DOI
10.1080/0950034021000011365

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 18, 2011•0 citations
It is shown that Grover's search algorithm can be implemented on a Rydberg atom data register using a short terahertz half-cycle pulse. Using optimal control theory, a shaped terahertz pulse is designed that can perform the search algorithm better than an unshaped half-cycle pulse. Starting from an initial wave packet, it is shown that it is possible to use the search algorithm to synthesize single-energy eigenstates.
We employ optimal control theory to discover an efficient information-retrieval algorithm that can be performed on a Rydberg-atom data register using a shaped terahertz pulse. The register is a Rydberg wave packet with one consituent orbital phase reversed from the others (the ``marked bit''). The terahertz pulse that performs the decoding algorithm does so by driving electron probability density into the marked orbital. Its shape is calculated by modifying the target of an optimal-control problem so that it represents the direct product of all correct solutions to the algorithm.
Quantum computation has experienced a steady growth in interest in recent years. With the rapid development of quantum technologies, the quantum mechanical nature of physical systems is becoming an increasingly important part of future industrial technology. The Rydberg atom is one of the best test tubes in which to attempt programmable coherent control because of our in-depth understanding of both atomic physics and ultrafast optics. We demonstrate the use of Rydberg atoms for processing quantum information and implementing quantum algorithms. We adopted N Rydberg energy levels of Cesium atom to store information. The phases of the energy states were each programmed and coherently evolve in time with the encoded information. A coherent manipulation then transferred the information contained in the phases to state amplitudes. The programming and the converting of the information in the data register were both performed by ultrafast optical pulses. We implemented an N-state Rydberg atom data register, with N = 6 and 8. Using half-cycle pulses (HCP), we devised methods which perform unitary operations on this data register. Application of the HCP, or terahertz short pulse, to wave packets prepared with one energy state phase-reversed with respect to the others yields a much simpler wave packet. This interaction forced multi-mode interference which constructively interfered only for the phase-flipped state. An impulsive model calculation as well as direct integration of the time-dependent Schrodinger equation showed good agreement with the experimental data. Related to the quantum algorithms, the pseudo-unitary operation implemented by the HCP had a similar structural form to the Grover's inversion-about-average operation. For the same reasons that lead to the Grover's quantum state amplification, the state amplitude of the energy state whose phase was reversed robbed atomic population from all other states. Our implementation of the Grover's inversion-about-average operation has accomplished most of Grover's search protocol. In order to improve upon our implementation and to attempt other quantum algorithms, we conclude that a sophisticated shaping of terahertz pulses is required.
We analyze a quantum search protocol to retrieve phase information from a Rydberg-atom data register using a subpicosecond half-cycle electric field pulse. Calculations show that the half-cycle pulse can perform the phase retrieval only within a range of peak field values. By varying the phases of the constituent orbitals of the Rydberg wave packet register, we demonstrate coherent control of the phase retrieval process. By specially programming the phases of the orbitals comprising the initial wave packet, we show that it is possible to use the search method as a way to synthesize single energy eigenstates.
In this paper, ultrashort, unipolar electric-field (terahertz) pulses have been used to coherently control population transfer between Rydberg states in lithium atom. Our numerical results show that populations of lithium atoms can be driven to lower or higher n levels with a train of half-cycle pulses, and the the transition rate is sensitive to the static-electric-field strength, the main laser frequency, the optical pulse profile, and the chirp of the laser pulse. If the paramerters of the half-cycle pulses is optimized appropriately, the population can be transferred to the target state completely.