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Physical Review Letters

Search for Exchange-Antisymmetric States for Spin-0 Particles at the 10−11 Level

Davide Mazzotti, Pablo Cancio, Giovanni Giusfredi, M. Inguscio, Paolo De Natale

Published Mar 5, 2001• 38 citations
Publisher

Abstract

We set a new upper limit of $1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ to the probability that two spin-0 ${}^{16}\mathrm{O}$ nuclei are in forbidden exchange-antisymmetric states, testing the validity of fundamental principles of quantum mechanics. A newly designed difference-frequency spectrometer is used to look for the existence of these states. The experimental test was performed by tuning the spectrometer across a molecular transition of ${}^{12}\mathrm{C}{}^{16}\mathrm{O}{}_{2}$ belonging to the rovibrational band at $4.25\ensuremath{\mu}\mathrm{m}$, connecting the forbidden states $({00}^{0}0,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}25)$ and $({00}^{0}1,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}26)$.

DOI
10.1103/physrevlett.86.1919

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We set a new upper limit of 1.7\ifmmode×\else\texttimes\fi10\ensuremath−111.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}1.7\ifmmode×\else\texttimes\fi10\ensuremath−11 to the probability that two spin-0 16O{}^{16}\mathrm{O}16O nuclei are in forbidden exchange-antisymmetric states, testing the validity of fundamental principles of quantum mechanics. A newly designed difference-frequency spectrometer is used to look for the existence of these states. The experimental test was performed by tuning the spectrometer across a molecular transition of 12C16O2{}^{12}\mathrm{C}{}^{16}\mathrm{O}{}_{2}12C16O2​ belonging to the rovibrational band at 4.25\ensuremathμm4.25\ensuremath{\mu}\mathrm{m}4.25\ensuremathμm, connecting the forbidden states (0000,J=25)({00}^{0}0,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}25)(0000,J=25) and (0001,J=26)({00}^{0}1,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}26)(0001,J=26).
We investigated the spectrum of the 16O2{}^{16}{\mathrm{O}}_{2}16O2​ molecule by high-sensitivity laser spectroscopy and searched for transitions involving states which are antisymmetric under the exchange of the nuclei. These states are forbidden by the symmetrization postulate of quantum mechanics. This is the first reported experiment to test the symmetrization postulate for integer-spin particles to high precision. Our data set an upper limit of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ to a possible violation of this postulate.
In order to probe the transitions of a nuclear spin sss from one of its substate quantum numbers mmm to another substate m′m'm′, the experimenter applies a magnetic field B0{\bm B}_0B0​ in some particular direction, such along z^\hat{\bm z}z^, and then applies an weaker field B1(t){\bm B}_1(t)B1​(t) that is oscillatory in time with the angular frequency ωωω, and is normally perpendicular to B0{\bm B}_0B0​, such as B1(t)=B1x^cos⁡(ωt){\bm B}_1(t)=B_1\hat{\bm x}\cos(ωt)B1​(t)=B1​x^cos(ωt). In the rotating wave approximation, B1(t)=B1[x^cos⁡(ωt)+y^sin⁡(ωt)]{\bm B}_1(t)=B_1[\hat{\bm x}\cos(ωt)+\hat{\bm y}\sin(ωt)]B1​(t)=B1​[x^cos(ωt)+y^​sin(ωt)]. Although this problem is solved for spin 12\frac{1}{2}21​ in every quantum mechanics textbook, for the general spin sss case, its general solution has been published only for the overall probability of a transition between the states, but the time dependence of the probability of finding the nucleus in each of the substates has not previously been published. Here we present an elementary method to solve this problem exactly, and present figures for the time dependencies of the various substates states for a variety of initial substate probabilities for a variety of sss values. We found a new result: unlike the s=12s=\frac{1}{2}s=21​ case, for which if the initial probability of finding the particle in one of the substates was 1, and the time dependence of the probabilities of each of the substates oscillates between 0 and 1, for higher spin values, the time dependencies of the probabilities finding the particle in each of its substates, which periodic, is considerably more complicated.
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