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Physical Review A

Quantum-state information retrieval in a Rydberg-atom data register

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

Published Aug 27, 2002• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.022312

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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.
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.
The field of coherent control has today been seeing significant progress, in a wide array of physical systems. One such system is the Rydberg atom. The long lifetime, strong dipole interactions, multiple degrees of freedom, and simple atomic structure make Rydberg atoms particularly appealing for experiments involving coherent control. The same properties have led to the exploration of Rydberg atoms as candidates for quantum information storage, processing and retrieval. Quantum information processing is a particular application of coherent control. Rather than being disparate subjects of study, coherent control of Rydberg atoms and processing of information stored as phase in different Rydberg levels are two sides of the same coin. In this dissertation, we experimentally characterize the effect of a half-cycle pulse on the phases of the states of a Rydberg wave packet and their mutual coherence. This has bearing both on our ability to control the states of the atom and on our ability to measure the information stored as quantum phase. We observe delay dependent phase shifts and losses of coherence. Despite a loss of information due to transfer of quantum amplitude to states outside the data register, we demonstrate partial retrieval of that information by the application of a second half cycle pulse. We also present an essential states model of the interaction, and we compare results from the model to experimental features observed. Although the particulars may vary, the concepts involved are quite general and may be applied to multilevel systems other than Rydberg atoms.
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.
We demonstrate an information hiding and retrieval scheme with the relative phases between states in a Rydberg wave packet acting as the bits of a data register. We use a terahertz half-cycle pulse (HCP) to transfer phase-encoded information from an optically accessible angular momentum manifold to another manifold which is not directly accessed by our laser pulses, effectively hiding the information from our optical interferometric measurement techniques. A subsequent HCP acting on these wave packets reintroduces the information back into the optically accessible data register manifold which can then be read out.