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Physical Review A

Schrödinger-cat states in Paul traps

Octavio Castaños, Rocío Jáuregui, Ramón López–Peña, J. Récamier, Vladimir I. Man’ko

Published Feb 1, 1997• 14 citations
Publisher

Abstract

We study the evolution of coherent and Schr\"odinger cat states in radio-frequency traps, which were used to bound ${\mathrm{Hg}}^{+}$ ions. The quantum confinement is determined by evaluating the expectation values and dispersions of the position and momentum operators, together with the probability densities in coordinate and momenta representations. Also the Wigner functions associated to this nonstationary quantum system, a parametric oscillator, are constructed.

DOI
10.1103/physreva.55.1208

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Abstract : We report the creation and full determination of several quantum states of motion of a 9Be ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.
We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.
We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.
The time-dependent Schrödinger equation of an ion moving in an asymmetric Penning trap is solved. Properties of the evolution of squeezed and Schrödinger cat states in the trap are studied. Analytic expressions for the energy expectation values, dispersions and correlations of the position and momentum operators of different macroscopic states, solutions of the time-dependent Schrödinger equation of the trap, are obtained. The probability densities in coordinate and momentum representations are also given. As an example, the behaviour of Schrödinger cat states of a proton moving in the trap is described numerically.
Since their introduction by Glauber in 1963 [1], coherent states have been deeply studied [2] due to the fact that, in some sense, the statistical properties related to the first momenta of their Fock distribution exhibit features interpretable in the realm of classical probability theory. Of course the quantum nature of a coherent state, and ultimately the granularity of the energy of a quantum harmonic oscillator, becomes more and more evident when higher momenta of the Fock distribution are considered. It is of relevance that coherent states of both a mechanical quantum oscillator or a quantized mode of an electromagnetic resonator may be currently proposed in accordance with well-defined protocols. Even more interesting is the fact that they provide the effective possibility of realizing interesting experiments able to bring to the light peculiarities of quantum mechanics. In particular, the very famous gedanken Schrodinger Cat State (SCS) experiment [3] consisting in entangling a microscopic quantum object (an atom) with a macroscopic one (a cat) has been realized. No unfortunate feline has been tortured! Trapped ions have been indeed exploited. In fact, such systems provide the possibility of testing fundamental quantum physics aspects giving at experimentalist’s disposal compound quantum systems consisting of a few-level atomic part and a tri-dimensional harmonic oscillator describing the center of mass motion of an ion confined into a Paul trap. Suitably acting upon the system with Raman lasers it is possible to engineer the Schrodinger Cat-like state [4, 5]