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Physical Review Letters

Manipulation of Motional Quantum States of Neutral Atoms

M. Morinaga, Isabelle Bouchoule, J.‐C. Karam, Ch Salomon

Published Nov 15, 1999• 102 citations
Publisher

Abstract

Cold Cs atoms are cooled into the ground state ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) of a far detuned 1D optical lattice. From this state, we prepare and detect several quantum states of motion. First, we produce squeezed states of $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ (and $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$) and record the time evolution of the velocity distribution of these states. A velocity distribution compressed by a factor of 4 compared to that of the ground state is obtained. Second, we prepare a linear superposition of $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and observe its time evolution.

DOI
10.1103/physrevlett.83.4037

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Cold Cs atoms are cooled into the ground state ( n=0n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0n=0) of a far detuned 1D optical lattice. From this state, we prepare and detect several quantum states of motion. First, we produce squeezed states of n=0n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0n=0 (and n=1n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1n=1) and record the time evolution of the velocity distribution of these states. A velocity distribution compressed by a factor of 4 compared to that of the ground state is obtained. Second, we prepare a linear superposition of n=0n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0n=0 and n=1n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1n=1 and observe its time evolution.
In the experiment presented in this thesis, Cesium atoms were trapped in a non-dissipative, intensity lattice produced by two Nd:YAG laser beams. Vertically, atoms are confined in independent micro-planes at each intensity maximum. The gaussian shape of the beams provides the horizontal confinement. Thanks to the strong vertical confinement, we could develop an optical sideband cooling method which accumulates about 95\% of the atoms in the ground state of the vertical motion. From this state, which is almost pure, we prepared other pure quantum states and, using an absoption imaging technique, we visualized directly their velocity distribution. First, we produced the first excited state of motion whose velocity distribution is zero for v=0v=0v=0. We also produced non stationary states and visualized the temporal evolution of their velocity distribution. In this way, the evolution of a superposition of the first two vibrationnal states and that of squeezed states have been recorded. Squeezed states are, as the ground state, minimum uncertainty states (ΔpΔz=ℏ/2\Delta p \Delta z=\hbar/2ΔpΔz=ℏ/2), but their velocity distribution is narrower than that of the ground state. A compression of the velocity distribution by a factor 4 has been obtained. By applying the cooling of the vertical motion for a long time, thanks to the energy transfer from the horizontal to the vertical direction provided by the collisions, we cooled the movement in all three directions. In this way, we obtained a temperature T≃3 μT \simeq 3\,\muT≃3μK for which 80\% of the atoms are in the ground state of the vertical movement. The gas thus realized is pratically a two-dimensionnal gas. Finally, the study of thermalization showed that the scattering resonnance at zero energy of Cesium is not affected by the strong vertical confinement.
We describe the preparation of Fock states of motion of cesium atoms trapped in potential wells of a far detuned optical lattice. Direct observation of the velocity distribution of the ∣n=0〉|n=0〉∣n=0〉 and ∣n=1〉|n=1〉∣n=1〉 Fock states is obtained by an absorption imaging technique.
Experimental techniques of laser cooling and trapping, along with other cooling techniques, have produced gaseous samples of atoms so cold that they are, for many practical purposes, in the quantum ground state of their centre-of-mass motion. Such low velocities have virtually eliminated effects such as Doppler shifts, relativistic time dilation and observation-time broadening that previously limited the performance of atomic frequency standards. Today, the best laser-cooled, caesium atomic fountain, microwave frequency standards realize the International System of Units (SI) definition of the second to a relative accuracy of ≈3×10(-16). Optical frequency standards, which do not realize the SI second, have even better performance: cold neutral atoms trapped in optical lattices now yield relative systematic uncertainties of ≈1×10(-16), whereas cold-trapped ions have systematic uncertainties of 9×10(-18). We will discuss the current limitations in the performance of neutral atom atomic frequency standards and prospects for the future.