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Atomic Physics Tests of Nonlinear Quantum Mechanics

J. J. Bollinger, Daniel J. Heinzen, Wayne M. Itano, S. L. Gilbert, David J. Wineland

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. set limits less than 10 pHz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than- on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. nonlinear addition to quantum mechanics violates causality is discussed. The experiments The possibility that a

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Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. set limits less than 10 pHz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than- on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. nonlinear addition to quantum mechanics violates causality is discussed. The experiments The possibility that a
A hyperfine transition in the ground state of 9Be+^{9}\mathrm{Be}^{+}9Be+ was used to test a nonlinear generalization of quantum mechanics recently formulated by Weinberg. We searched for a dependence of the frequency of a coherent superposition of two hyperfine states on the populations of the states. We are able to set a limit of 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}27}$ on the fraction of binding energy per nucleon of the 9Be+^{9}\mathrm{Be}^{+}9Be+ nucleus that could be due to nonlinear corrections to quantum mechanics.
Measurement of the free precession of nuclear spins in optically pumped ground-state 201Hg^{201}\mathrm{Hg}201Hg atoms has allowed a test of Weinberg's nonlinear generalization of quantum mechanics. Shifts among the three resolved precession frequencies in the spin-3/2 system were studied as a function of the projection of spin polarization along the precession axis. Our results set an upper limit on \ensuremath{\epsilon}, Weinberg's nonlinearity parameter, of \ensuremath{\Vert}\ensuremath{\epsilon}\ensuremath{\Vert}/2\ensuremath{\pi}\ensuremath{\Elzxh}3.8\ensuremath{\mu} Hz, which corresponds to 2.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}27}$ of the binding energy per nucleon. This is the most stringent such limit to date.
It is proposed to set stringent limits on possible nonlinear corrections to ordinary quantum mechanics by searching for the detuning of resonant transitions. A suggested nonlinear generalization of quantum mechanics is used to show that such detuning would be expected in the rf transition in 9Be+^{9}\mathrm{Be}^{+}9Be+ ions that is used to set frequency standards. Measurements at the National Bureau of Standards already set limits of order ${10}^{\ensuremath{-}21}$ on the fraction of the energy of the 9Be^{9}\mathrm{Be}9Be nucleus that could be due to nonlinear corrections to quantum mechanics, with good prospects of improving this by 2-3 orders of magnitude.
We extend a nonlinear generalization of quantum mechanics, recently formulated by Weinberg, to systems of composite spin, such as atoms. We have used hydrogen (H) masers to set a limit of 3.7\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 eV (8.9 \ensuremath{\mu} Hz) on the magnitude of a nonlinear correction to the quantum mechanics of atomic spins. This result is of comparable magnitude to the limit recently set in a single-valued (nuclear) spin system. In the absence of nonlinear effects, the experiment provides a new and stringent test of H-maser clock performance and the applicability of standard maser theory.
A nonlinear generalization of quantum mechanics for internal (spin) degrees of freedom has recently been developed by Weinberg [Phys. Rev. Lett. 62, 485 (1989); Ann. Phys. (N.Y.) 194, 336 (1989)]. We extend this theory to systems of composite, or multivalued, spin, such as atoms and molecules. Results for the generalized Hamiltonian function, energy eigenvalues, and state-vector time dependence are found to be similar for single- and multivalued spin systems, with the important difference that states of spin 0 or 1/2 can exhibit observable nonlinear behavior in a composite spin system. Examples of the application of the composite spin analysis are given for the ground-state hyperfine structure of the hydrogen and deuterium atoms.