Polarizability of ultracold molecules in the rovibrational ground state of

Media type: E-Article
Title: Polarizability of ultracold molecules in the rovibrational ground state of
Contributor: Deiß, Markus; Drews, Björn; Denschlag, Johannes Hecker; Bouloufa-Maafa, Nadia; Vexiau, Romain; Dulieu, Olivier
Published: IOP Publishing, 2015
Published in: New Journal of Physics, 17 (2015) 6, Seite 065019
Language: Not determined
DOI: 10.1088/1367-2630/17/6/065019
ISSN: 1367-2630
Keywords: General Physics and Astronomy
Origination:
Footnote:
Description: <jats:title>Abstract</jats:title> <jats:p>We study, both theoretically and experimentally, the dynamical polarizability <jats:inline-formula> <jats:tex-math> <?CDATA $\alpha (\omega )$?> </jats:tex-math> <?MML <mml:math> <mml:mi>&agr;</mml:mi> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mi>&ohgr;</mml:mi> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn6.gif" xlink:type="simple" /> </jats:inline-formula> of <jats:inline-formula> <jats:tex-math> <?CDATA ${\mathrm{Rb}}_{2}$?> </jats:tex-math> <?MML <mml:math> <mml:msub> <mml:mrow> <mml:mi>Rb</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn7.gif" xlink:type="simple" /> </jats:inline-formula> molecules in the rovibrational ground state of <jats:inline-formula> <jats:tex-math> <?CDATA ${a}^{3}{\Sigma }_{u}^{+}$?> </jats:tex-math> <?MML <mml:math> <mml:msup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mrow> <mml:mi>&Sgr;</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mo form="prefix"> +</mml:mo> </mml:mrow> </mml:msubsup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn8.gif" xlink:type="simple" /> </jats:inline-formula>. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability <jats:inline-formula> <jats:tex-math> <?CDATA $\alpha (\omega )$?> </jats:tex-math> <?MML <mml:math> <mml:mi>&agr;</mml:mi> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mi>&ohgr;</mml:mi> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn9.gif" xlink:type="simple" /> </jats:inline-formula> for wave numbers up to 20 000 <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{cm}}}^{-1}$?> </jats:tex-math> <?MML <mml:math> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">cm</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn10.gif" xlink:type="simple" /> </jats:inline-formula>. Our calculations are compared to experimental results at <jats:inline-formula> <jats:tex-math> <?CDATA $1064.5\;\mathrm{nm}$?> </jats:tex-math> <?MML <mml:math> <mml:mn>1064.5</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>nm</mml:mi> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn11.gif" xlink:type="simple" /> </jats:inline-formula> (<jats:inline-formula> <jats:tex-math> <?CDATA $\sim 9400\;{{\rm{cm}}}^{-1}$?> </jats:tex-math> <?MML <mml:math> <mml:mspace width="-0.16em"/> <mml:mspace width="-0.16em"/> <mml:mo>&sim;</mml:mo> <mml:mn>9400</mml:mn> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">cm</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn12.gif" xlink:type="simple" /> </jats:inline-formula>) as well as at <jats:inline-formula> <jats:tex-math> <?CDATA $830.4\;\mathrm{nm}$?> </jats:tex-math> <?MML <mml:math> <mml:mn>830.4</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>nm</mml:mi> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn13.gif" xlink:type="simple" /> </jats:inline-formula> (<jats:inline-formula> <jats:tex-math> <?CDATA $\sim 12\;000\;{{\rm{cm}}}^{-1}$?> </jats:tex-math> <?MML <mml:math> <mml:mspace width="-0.16em"/> <mml:mspace width="-0.16em"/> <mml:mo>&sim;</mml:mo> <mml:mn>12</mml:mn> <mml:mspace width="0.25em"/> <mml:mn>000</mml:mn> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">cm</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn14.gif" xlink:type="simple" /> </jats:inline-formula>). Here, we discuss the measurements at <jats:inline-formula> <jats:tex-math> <?CDATA $1064.5\;\mathrm{nm}$?> </jats:tex-math> <?MML <mml:math> <mml:mn>1064.5</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>nm</mml:mi> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn15.gif" xlink:type="simple" /> </jats:inline-formula>. The ultracold Rb<jats:sub>2</jats:sub> molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than <jats:inline-formula> <jats:tex-math> <?CDATA $2\;{\rm{s}}$?> </jats:tex-math> <?MML <mml:math> <mml:mn>2</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn16.gif" xlink:type="simple" /> </jats:inline-formula> are observed. In addition, the dynamical polarizability for the <jats:inline-formula> <jats:tex-math> <?CDATA ${X}^{1}{\Sigma }_{g}^{+}$?> </jats:tex-math> <?MML <mml:math> <mml:msup> <mml:mrow> <mml:mi>X</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mrow> <mml:mi>&Sgr;</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo form="prefix"> +</mml:mo> </mml:mrow> </mml:msubsup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn17.gif" xlink:type="simple" /> </jats:inline-formula> state is calculated. We provide simple analytical expressions that reproduce the numerical results for <jats:inline-formula> <jats:tex-math> <?CDATA $\alpha (\omega )$?> </jats:tex-math> <?MML <mml:math> <mml:mi>&agr;</mml:mi> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mi>&ohgr;</mml:mi> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn18.gif" xlink:type="simple" /> </jats:inline-formula> for all vibrational levels of <jats:inline-formula> <jats:tex-math> <?CDATA ${a}^{3}{\Sigma }_{u}^{+}$?> </jats:tex-math> <?MML <mml:math> <mml:msup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mrow> <mml:mi>&Sgr;</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mo form="prefix"> +</mml:mo> </mml:mrow> </mml:msubsup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn19.gif" xlink:type="simple" /> </jats:inline-formula> as well as <jats:inline-formula> <jats:tex-math> <?CDATA ${X}^{1}{\Sigma }_{g}^{+}$?> </jats:tex-math> <?MML <mml:math> <mml:msup> <mml:mrow> <mml:mi>X</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mrow> <mml:mi>&Sgr;</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo form="prefix"> +</mml:mo> </mml:mrow> </mml:msubsup> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn20.gif" xlink:type="simple" /> </jats:inline-formula>. Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at <jats:inline-formula> <jats:tex-math> <?CDATA $\sim 1064\;\mathrm{nm}$?> </jats:tex-math> <?MML <mml:math> <mml:mspace width="-0.16em"/> <mml:mspace width="-0.16em"/> <mml:mo>&sim;</mml:mo> <mml:mn>1064</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>nm</mml:mi> </mml:math>?> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njp515397ieqn21.gif" xlink:type="simple" /> </jats:inline-formula> is of interest, since here, ultrastable high power lasers are available.</jats:p>
Access State: Open Access

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