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Kluwer Academic Publishers eBooks

Preparation of Highly Excited Motional Energy Eigenstates with a Trapped Atom

Sascha Wallentowitz, W. Vogel, P. E. Toschek

Published Dec 19, 2005• 0 citations
Publisher

Abstract

Highly excited eigenstates of the motion of an individual spatially confined atom may be prepared making use of a “trapping” mechanism based on the nonlinearity of the laser-mediated coupling of internal excitation and center-of-mass vibration of the atom. In contrast to micromaser-type trapping states, these states are insensitive to laser-phase fluctuations, and a long sequence of laser pulses may be applied to the atom with little degradation only of the atomic motion. Thus, vibrational number states of high quantum numbers are achievable.

DOI
10.1007/0-306-47097-7_40

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Bulletin of the American Physical Society•May 1, 1993•0 citations
Highly excited eigenstates of the motion of an individual spatially confined atom may be prepared making use of a “trapping” mechanism based on the nonlinearity of the laser-mediated coupling of internal excitation and center-of-mass vibration of the atom. In contrast to micromaser-type trapping states, these states are insensitive to laser-phase fluctuations, and a long sequence of laser pulses may be applied to the atom with little degradation only of the atomic motion. Thus, vibrational number states of high quantum numbers are achievable.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
A scheme is proposed to generate an arbitrary entangled state of the two-dimensional vibrational motion of a trapped ion. In the scheme the ion is excited by a sequence of laser pulses tuned to the appropriate vibrational sidebands. In order to generate a pure state with upper phonon numbers M and N in the X and Y directions, respectively, we require no more than (M+2)(N+1)(M+2)(N+1)(M+2)(N+1) operations.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less