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Physical Review A

Theory of detection of angular momentum states in Rydberg atoms using half-cycle pulses

Chitra Rangan, R. J. A. Murray

Published Nov 17, 2005• 4 citations
Publisher

Abstract

The creation and detection of specific angular momentum states in Rydberg atoms is a significant advance in quantum-information processing. Detection of high angular momentum states in alkali-metal atoms is difficult because they are nearly-degenerate in energy. We present theoretical results on the detection of such states using terahertz-frequency half-cycle pulses (HCPs). Calculations are done for $n=15,\ensuremath{\ell}=0,\dots{},14$ states in hydrogen and cesium using a grid-based pseudopotential method. Our results indicate that HCP redistribution is a reliable method of distinguishing angular momentum Rydberg states.

DOI
10.1103/physreva.72.053409

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Theory of detection of angular momentum states in Rydberg atoms using half-cycle pulses

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The creation and detection of specific angular momentum states in Rydberg atoms is a significant advance in quantum-information processing. Detection of high angular momentum states in alkali-metal atoms is difficult because they are nearly-degenerate in energy. We present theoretical results on the detection of such states using terahertz-frequency half-cycle pulses (HCPs). Calculations are done for n=15,=0,...,14 states in hydrogen and cesium using a grid-based pseudopotential method. Our results indicate that HCP redistribution is a reliable method of distinguishing angular momentum Rydberg states.

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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.

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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.

arXiv:quant-ph/0605012•Physical Review A•Oct 4, 2006•2 citations
The creation and detection of specific angular momentum states in Rydberg atoms is a significant advance in quantum-information processing. Detection of high angular momentum states in alkali-metal atoms is difficult because they are nearly-degenerate in energy. We present theoretical results on the detection of such states using terahertz-frequency half-cycle pulses (HCPs). Calculations are done for n=15,\ensuremathℓ=0,…,14n=15,\ensuremath{\ell}=0,\dots{},14n=15,\ensuremathℓ=0,…,14 states in hydrogen and cesium using a grid-based pseudopotential method. Our results indicate that HCP redistribution is a reliable method of distinguishing angular momentum Rydberg states.
The creation and detection of specific angular momentum states in Rydberg atoms is a significant advance in quantum-information processing. Detection of high angular momentum states in alkali-metal atoms is difficult because they are nearly-degenerate in energy. We present theoretical results on the detection of such states using terahertz-frequency half-cycle pulses (HCPs). Calculations are done for n=15,=0,...,14 states in hydrogen and cesium using a grid-based pseudopotential method. Our results indicate that HCP redistribution is a reliable method of distinguishing angular momentum Rydberg states.
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.
We present the technique and results of our study of the redistribution of Rydberg states in barium by a half cycle pulse (HCP). A survey of previous research concerning the interaction of half cycle pulses with Rydberg atoms reveals a lack of experimental data in the area of state redistribution. This is primarily due to an inability to identify the redistributed states accurately using the currently available tool: selective field ionization (SFI). We present the limitations of SFI as a state identification tool. We then present a survey of isolated core excitation as a state identification tool, along with its limitations in dealing with a mixture of states. Combining SFI and ICE overcomes these limitations and allows for the accurate characterization of a mixture of Rydberg states, as found in HCP redistribution. We present our results for the HCP redistribution of a series of ns and nd initial states, for n from 30 to 40, at various HCP intensities. These results primarily involved single photon transitions, confining us to the linear regime. Analyzing the results of these redistributions with respect to the energy difference between initial and final states yielded information about the frequency structure, after transmission to the interaction region, of the HCP. This led us to postulate on the effects of diffraction on the HCP. We conclude with several suggestions for the improvement of the experimental system, as well as a direction for future research.
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.
We study the dynamics of highly excited (Rydberg) atoms in laboratory-scale magnetic fields via their ionization by THz half-cycle pulses (HCPs). A half-cycle pulse is a unipolar electromagnetic pulse that can probe an atomic electron at all points along its orbit around the atomic core. The dynamical evolution of diamagnetic Zeeman states subjected to an ultrashort (picosecond) HCP is calculated for both hydrogen and sodium atoms. Diamagnetic Zeeman states are localized parallel and perpendicular to the magnetic field. We use a grid-based pseudo-potential method to determine these eigenstates of the combined Coulomb-diamagnetic potential. We study states with principal quantum number n between 15--30 in the ℓ-mixing regime at magnetic fields of 1--6T. These initial states are subjected to the electric field of an HCP and their subsequent time evolution is calculated by solving the time-dependent Schrodinger equation. The HCP width is varied between the short pulse (impulsive) and the long pulse limit, keeping the total momentum transferred a constant. We calculate the total ionized fraction, and also the spectrum of the ionized photoelectrons. We find that, in the impulsive limit, where the width of the pulse is much smaller than typical time scales in the system, the calculated amount of ionization and the photoelectron spectra are different depending on the localization of the initial state. These differences are shown to be due to the different initial momentum distributions of the parallel and perpendicular states. As the duration of the HCP is made longer, we find that ionization is suppressed as compared with the impulsive limit. The states localized perpendicular to the magnetic field are found to be much more sensitive to the HCP width than the parallel states, reflecting the fact that the two classes of states interact with different parts of the Coulomb-diamagnetic potential during the HCP. The ionization characteristics are shown to scale classically with the principal quantum number. The results are presented in such a manner that they can be verified by experiment.
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.