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arXiv:2109.05670

Experimental study of tune-out wavelengths for spin-dependent optical lattice in $^{87}$Rb Bose-Einstein condensation

Wen, Kai, Zengming Meng, Liangwei Wang, Liangchao Chen, Lianghui Huang, Pengjun Wang, Jing Zhang

Published Sep 13, 2021• 1 citation
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Abstract

We study the periodic potential of one-dimensional optical lattice originated from scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of optical lattice is measured by Kapitza-Dirac scattering of $^{87}$Rb Bose-Einstein condensate and the characteristics of spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that ac Stark shift cancels can be probed by optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both the scalar and vector shift. Our results provide a clear interpretation for spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.

DOI
10.48550/arxiv.2109.05670

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Experimental study of tune-out wavelengths for spin-dependent optical lattice in 87^{87}87Rb Bose-Einstein condensation
We study the periodic potential of one-dimensional optical lattice originated from scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of optical lattice is measured by Kapitza-Dirac scattering of 87^{87}87Rb Bose-Einstein condensate and the characteristics of spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that ac Stark shift cancels can be probed by optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both the scalar and vector shift. Our results provide a clear interpretation for spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.
We study the periodic potential of a one-dimensional optical lattice originating from a scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of an optical lattice is measured by Kapitza–Dirac scattering of 87 R b Bose–Einstein condensate, and the characteristics of a spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that the ac Stark shift cancels can be probed by the optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both scalar and vector shifts. Our results provide a clear interpretation for a spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.
We report on a precision measurement of the DDD line tune-out wavelength of 87Rb^{87}\text{Rb}87Rb in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at 790nm790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}790nm, where the scalar ac Stark shifts of the D1{D}_{1}D1​ and the D2{D}_{2}D2​ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive mF=0{m}_{F}=0mF​=0 state was determined to 790.01858(23)nm790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}790.01858(23)nm with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.
We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the D1{D}_{1}D1​, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and D2{D}_{2}D2​, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for 133Cs^{133}\mathrm{Cs}133Cs in the ground hyperfine state (F=3,mF=+3)(F=3,{m}_{F}=+3)(F=3,mF​=+3). At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a 133Cs^{133}\mathrm{Cs}133Cs Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.
In recent years, ultracold atomic gases have been used as tools to study strongly-correlated systems reminiscent of interesting systems from solid-state physics. At temperatures just above absolute zero, particles with integer quantum spin ("bosons") begin to congregate in the ground state of the trapping potential. As the temperature of the system falls below a critical temperature Tc (in this experiment near 200 nK) it undergoes a phase transition called Bose-Einstein condensation. A Bose-Einstein condensate is often described as a macroscopic quantum body, and due to its phase coherence (analogous to an "atom laser") can be used to simulate solid-state systems in a periodic potential called an optical lattice, which resembles that experienced by electrons in the periodic Coulomb potential of a solid-state crystal lattice. These optical lattices are formed by the interference pattern of multiple laser beams, and the associated spatially-dependent Stark shift, resulting in trapping potential for the BEC. The lattice analogs of simple atomic structures have been widely studied. In this thesis, we study the possibility of loading a BEC into multi-dimensional optical lattices. The crystallography of four-beam three-dimensional optical lattices is investigated, and an apparatus is constructed to produce two- to four-beam lattice geometries. We study the structure of the lattice through the technique of Kapitza-Dirac scattering.
We report a precision measurement of a tune-out wavelength for 87Rb^{87}\mathrm{Rb}87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb atoms. Recent progress in metrology exploits so-called “magic wavelengths,” whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.