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arXiv:quant-ph/0605012 · Physical Review A

Information hiding and retrieval in Rydberg wave packets using half-cycle pulses

Joel M. Murray, S. N. Pisharody, Haidan Wen, Chitra Rangan, P. H. Bucksbaum

Published Oct 4, 2006• 2 citations
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Abstract

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.

DOI
10.1103/physreva.74.043402

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•Jan 1, 2006•0 citations
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.
Summary form only given. Optical pulse shaping and wave-packet holography have been used to store information in the phase of an atomic Rydberg wave-packet. We present a new method of retrieving this phase information by using a terahertz domain half-cycle pulse (HCP) to coherently redistribute the Rydberg population. We use programmed optical pulses to create radial wave-packets in a beam of atomic Cs centered at n = 26p with one state phase-reversed from the others. An impulse model for this atom-HCP interaction is employed to qualitatively explain this flipped-state amplification.
A kick from a unipolar half-cycle pulse (HCP) can redistribute population and shift the relative phase between states in a radial Rydberg wave packet. We have measured the quantum coherence properties following the kick, and show that selected coherences can be destroyed by applying a HCP at specific times. Quantum mechanical simulations show that this is due to redistribution of the angular momentum in the presence of noise. These results have implications for the storage and retrieval of quantum information in the wave packet.
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.
Recent advances in the study of Rydberg atoms have focused on the control, manipulation and detection of Rydberg wave packets using novel external fields such as half-cycle pulses. The radial degree of freedom has been controlled and used to process information encoded in Rydberg states. However, these previous experiments make use of only a single degree of freedom, restricting the potential of other degrees of freedom for quantum computing in Rydberg atoms. In this dissertation, we explore the control and detection of other degrees of freedom in an electron wave packet, such as the angular momentum quantum number ℓ, the magnetic quantum number m and the electron spin; so that the full range of quantum numbers can participate in information processing. We first propose an interferometric control of the population of angular momentum states using two time-delayed phase-locked ultrafast laser pulses. The population of arbitrary angular momentum states can be greatly enhanced by optimizing the time delay and the relative phases between two laser pulses. We then qualitatively measure the evolution of angular momentum components in Stark wave packets by a weak half-cycle pulse (HCP). This measurement utilizes a time-delayed HCP and is proved to be effective for detecting various aspects of wave packet dynamics, particularly, the evolution of non-stationary states. The technique relies on the fact that the HCP redistributes the eigenstate populations and induced the population variation which reflects the evolution of eigenstate phases. Finally, we find that the dynamics of m-states could be highly correlated with the internal degree of freedom of the electron, the spin. We study the effect of spin-orbit coupling on the wave packet dynamics and observe the angular precession of a Rydberg wave packet. The population redistribution from p to s states is highly sensitive to the polarization of the HCP and changes with the precession of the electron orbit. We obtain the selection rules and give an intuitive classical interpretation of angular momentum redistribution by an HCP. In short, new dynamics involving multiple degrees of freedom of an electron wave packet are discovered, observed and understood.