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Modern Physics Letters B

PARTICLE TRAPPING BY OSCILLATING FIELDS: CONNECTING SQUEEZING WITH COOLING

B. Baseia, Reeta Vyas, Vanderlei Salvador Bagnato

Published Jun 20, 1996• 1 citation
Publisher

Abstract

The first observation of the squeezing effect outside the optical domain was reported very recently for trapped atoms [D. M. Meekhof et al., Phys. Rev. Lett.76, 1796 (1996)]. Pursuing this line and a sequel of previous works of ours we employ a model by Glauber and a method of invariants by Lewis and Riesenfeld to establish a connection between the squeezing and the cooling effects in the system. From this connection the occurrence of squeezing could be detected through the measurement of the dispersion in the variable [Formula: see text] and of the temperature.

DOI
10.1142/s0217984996000730

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The first observation of the squeezing effect outside the optical domain was reported very recently for trapped atoms [D. M. Meekhof et al., Phys. Rev. Lett.76, 1796 (1996)]. Pursuing this line and a sequel of previous works of ours we employ a model by Glauber and a method of invariants by Lewis and Riesenfeld to establish a connection between the squeezing and the cooling effects in the system. From this connection the occurrence of squeezing could be detected through the measurement of the dispersion in the variable [Formula: see text] and of the temperature.
By making use of the Lewis-Riesenfeld invariant theory, the solution of the Schrödinger equation for the time-dependent linear potential corresponding to the quadratic-form Lewis-Riesenfeld invariant Iq(t)I_{\rm q}(t)Iq​(t) is obtained in the present paper. It is emphasized that in order to obtain the general solutions of the time-dependent Schrödinger equation, one should first find the complete set of Lewis-Riesenfeld invariants. For the present quantum system with a time-dependent linear potential, the linear Il(t)I_{\rm l}(t)Il​(t) and quadratic Iq(t)I_{\rm q}(t)Iq​(t) (where the latter Iq(t)I_{\rm q}(t)Iq​(t) cannot be written as the squared of the former Il(t)I_{\rm l}(t)Il​(t), {\it i.e.}, the relation Iq(t)=cIl2(t)I_{\rm q}(t)= cI_{\rm l}^{2}(t)Iq​(t)=cIl2​(t) does not hold true always) will form a complete set of Lewis-Riesenfeld invariants. It is also shown that the solution obtained by Bekkar {\it et al.} more recently is the one corresponding to the linear Il(t)I_{\rm l}(t)Il​(t), one of the invariants that form the complete set. In addition, we discuss some related topics regarding the comment [Phys. Rev. A {\bf 68}, 016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63}, 034102 (2001)] and Guedes's corresponding reply [Phys. Rev. A {\bf 68}, 016102 (2003)].
We demonstrate that the recently observed damping of Rabi oscillations of a trapped 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ion initially cooled to its motional ground state [Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] is caused by quantum jumps to an auxiliary electronic state. This mechanism also predicts an asymmetric decay of the electronic-state population that is found to be in good agreement with the measured data.