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Polarizability of ultracold Rb2 molecules in the rovibrational ground state of a3Σ+u

Nadia Bouloufa-Maafa, Olivier Dulieu, Romain Véxiau, Hecker Denschlag, Johannes, Deiss, Markus, Björn Drews

Published Jan 19, 2015• 0 citations
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Abstract

We study, both theoretically and experimentally, the dynamical polarizability α(ω) of Rb2 molecules in the rovibrational ground state of a3Σ+u. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability α(ω) for wave numbers up to 20000cm−1. Our calculations are compared to experimental results at 1064.5nm (∼9400cm−1) as well as at 830.4nm (∼12000cm−1). Here, we discuss the measurements at 1064.5nm. The ultracold Rb2 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 2s are observed. In addition, the dynamical polarizability for the X1Σ+g state is calculated. We provide simple analytical expressions that reproduce the numerical results for α(ω) for all vibrational levels of a3Σ+u as well as X1Σ+g. 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 ∼1064nm is of interest, since here, ultrastable high power lasers are available.

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Polarizability of ultracold molecules in the rovibrational ground state of

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Abstract We study, both theoretically and experimentally, the dynamical polarizability of molecules in the rovibrational ground state of . Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability for wave numbers up to 20 000 . Our calculations are compared to experimental results at ( ) as well as at ( ). Here, we discuss the measurements at . The ultracold Rb2 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 are observed. In addition, the dynamical polarizability for the state is calculated. We provide simple analytical expressions that reproduce the numerical results for for all vibrational levels of as well as . 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 is of interest, since here, ultrastable high power lasers are available.

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We present a novel method for probing the alignment of the molecular axis of an ultracold, nonpolar dimer. These results are obtained using diatomic ^{87}Rb_{2} molecules in the vibrational ground state of the lowest triplet potential a^{3}Σ_{u}^{+} trapped in a 3D optical lattice. We measure the molecular polarizabilities, which are directly linked to the alignment, along each of the x, y, and z directions of the lab coordinate system. By preparing the molecules in various, precisely defined rotational quantum states we can control the degree of alignment of the molecular axis with high precision over a large range. Furthermore, we derive the dynamical polarizabilities for a laser wavelength of 1064.5 nm parallel and orthogonal to the molecular axis of the dimer, α_{∥}=(8.9±0.9)×10^{3} a.u. and α_{⊥}=(0.9±0.4)×10^{3} a.u., respectively. Our findings highlight that the depth of an optical lattice strongly depends on the rotational state of the molecule, which has to be considered in collision experiments. The present work paves the way for reaction studies between aligned molecules in the ultracold temperature regime.

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In this article we address the general approach for calculating dynamical dipole polarizabilities of small quantum systems, based on a sum-over-states formula involving in principle the entire energy spectrum of the system. We complement this method by a few-parameter model involving a limited number of effective transitions, allowing for a compact and accurate representation of both the isotropic and anisotropic components of the polarizability. We apply the method to the series of ten heteronuclear molecules composed of two of (Li,Na,K,Rb,Cs) alkali-metal atoms. We rely on both up-to-date spectroscopically-determined potential energy curves for the lowest electronic states, and on our systematic studies of these systems performed during the last decade for higher excited states and for permanent and transition dipole moments. Such a compilation is timely for the continuously growing researches on ultracold polar molecules. Indeed the knowledge of the dynamic dipole polarizabilities is crucial to model the optical response of molecules when trapped in optical lattices, and to determine optimal lattice frequencies ensuring optimal transfer to the absolute ground state of initially weakly-bound molecules. When they exist, we determine the so-called ‘magic frequencies’ where the ac-Stark shift and thus the viewed trap depth, is the same for both weakly-bound and ground-state molecules.

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We study, both theoretically and experimentally, the dynamical polarizability α(ω) of Rb2 molecules in the rovibrational ground state of a3Σ+u. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability α(ω) for wave numbers up to 20000cm−1. Our calculations are compared to experimental results at 1064.5nm (∼9400cm−1) as well as at 830.4nm (∼12000cm−1). Here, we discuss the measurements at 1064.5nm. The ultracold Rb2 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 2s are observed. In addition, the dynamical polarizability for the X1Σ+g state is calculated. We provide simple analytical expressions that reproduce the numerical results for α(ω) for all vibrational levels of a3Σ+u as well as X1Σ+g. 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 ∼1064nm is of interest, since here, ultrastable high power lasers are available.
Abstract We study, both theoretically and experimentally, the dynamical polarizability of molecules in the rovibrational ground state of . Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability for wave numbers up to 20 000 . Our calculations are compared to experimental results at ( ) as well as at ( ). Here, we discuss the measurements at . The ultracold Rb2 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 are observed. In addition, the dynamical polarizability for the state is calculated. We provide simple analytical expressions that reproduce the numerical results for for all vibrational levels of as well as . 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 is of interest, since here, ultrastable high power lasers are available.
We present a novel method for probing the alignment of the molecular axis of an ultracold, nonpolar dimer. These results are obtained using diatomic ^{87}Rb_{2} molecules in the vibrational ground state of the lowest triplet potential a^{3}Σ_{u}^{+} trapped in a 3D optical lattice. We measure the molecular polarizabilities, which are directly linked to the alignment, along each of the x, y, and z directions of the lab coordinate system. By preparing the molecules in various, precisely defined rotational quantum states we can control the degree of alignment of the molecular axis with high precision over a large range. Furthermore, we derive the dynamical polarizabilities for a laser wavelength of 1064.5 nm parallel and orthogonal to the molecular axis of the dimer, α_{∥}=(8.9±0.9)×10^{3} a.u. and α_{⊥}=(0.9±0.4)×10^{3} a.u., respectively. Our findings highlight that the depth of an optical lattice strongly depends on the rotational state of the molecule, which has to be considered in collision experiments. The present work paves the way for reaction studies between aligned molecules in the ultracold temperature regime.
Probing the alignment of ultracold spin-polarized Rb2\textrm{Rb}_2Rb2​ molecules
We demonstrate a method to probe the alignment of the molecular axis of spin-polarized ultracold dimers. Diatomic 87^{87}87Rb2_22​ molecules are held in the lowest Bloch band of a far-off resonance 3D optical lattice. Using lattice modulation spectroscopy we measure the molecular polarizabilities, which are directly linked to the alignment, along each of the xxx-, yyy-, and zzz-directions of the lab coordinate system. In contrast to nonrotating molecules, we observe that rotating molecules have an anisotropic orientation of the molecular axis. Furthermore, we derive the dynamical polarizabilities for a laser wavelength of 1064.5 nm parallel and orthogonal to the molecular axis of the dimer, α∥=(8.9±0.9)×103 a.u.\alpha_\parallel=(8.9 \pm 0.9)\times10^3\:\textrm{a.u.}α∥​=(8.9±0.9)×103a.u. and α⊥=(0.9±0.4)×103 a.u.\alpha_\perp=(0.9 \pm 0.4)\times10^3\:\textrm{a.u.}α⊥​=(0.9±0.4)×103a.u., respectively.
We demonstrate efficient transfer of ultracold molecules into a deeply bound rovibrational level of the singlet ground state potential in the presence of an optical lattice. The overall molecule creation efficiency is 25%, and the transfer efficiency to the rovibrational level | v =73, J =2⟩ is above 80%. We find that the molecules in | v =73, J =2⟩ are trapped in the optical lattice, and that the lifetime in the lattice is limited by optical excitation by the lattice light. The molecule trapping time for a lattice depth of 15 atomic recoil energies is about 20 ms. We determine the trapping frequency by the lattice phase and amplitude modulation technique. It will now be possible to transfer the molecules to the rovibrational ground state | v =0, J =0⟩ in the presence of the optical lattice.
In this article we address the general approach for calculating dynamical dipole polarizabilities of small quantum systems, based on a sum-over-states formula involving in principle the entire energy spectrum of the system. We complement this method by a few-parameter model involving a limited number of effective transitions, allowing for a compact and accurate representation of both the isotropic and anisotropic components of the polarizability. We apply the method to the series of ten heteronuclear molecules composed of two of (Li,Na,K,Rb,Cs) alkali-metal atoms. We rely on both up-to-date spectroscopically-determined potential energy curves for the lowest electronic states, and on our systematic studies of these systems performed during the last decade for higher excited states and for permanent and transition dipole moments. Such a compilation is timely for the continuously growing researches on ultracold polar molecules. Indeed the knowledge of the dynamic dipole polarizabilities is crucial to model the optical response of molecules when trapped in optical lattices, and to determine optimal lattice frequencies ensuring optimal transfer to the absolute ground state of initially weakly-bound molecules. When they exist, we determine the so-called ‘magic frequencies’ where the ac-Stark shift and thus the viewed trap depth, is the same for both weakly-bound and ground-state molecules.