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arXiv:1904.07617 · Physical Review A

Interferometric measurement of interhyperfine scattering lengths in Rb87

Pau Gomez, Chiara Mazzinghi, Ferran Martin Ciurana, Simon Coop, Silvana Palacios, Morgan W. Mitchell

Published Sep 10, 2019• 5 citations
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Abstract

We present interferometeric measurements of the $f=1$ to $f=2$ interhyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of $^{87}\mathrm{Rb}$. The interhyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a noninteracting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of interhyperfine scattering length differences, calibrated to intrahyperfine scattering length differences. We report $({a}_{3}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.27(15)$ and $({a}_{1}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.31(13)$, limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of $\ensuremath{\approx}0.3%$ should be possible with this technique.

DOI
10.1103/physreva.100.032704

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We present interferometeric measurements of the f=1f=1f=1 to f=2f=2f=2 interhyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb. The interhyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a noninteracting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of interhyperfine scattering length differences, calibrated to intrahyperfine scattering length differences. We report (a3(12)\ensuremath−a2(12))/(a2(1)\ensuremath−a0(1))=\ensuremath−1.27(15)({a}_{3}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.27(15)(a3(12)​\ensuremath−a2(12)​)/(a2(1)​\ensuremath−a0(1)​)=\ensuremath−1.27(15) and (a1(12)\ensuremath−a2(12))/(a2(1)\ensuremath−a0(1))=\ensuremath−1.31(13)({a}_{1}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.31(13)(a1(12)​\ensuremath−a2(12)​)/(a2(1)​\ensuremath−a0(1)​)=\ensuremath−1.31(13), limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of \ensuremath≈0.3\ensuremath{\approx}0.3%\ensuremath≈0.3 should be possible with this technique.
Precision measurement of spin-dependent inter-hyperfine scattering lengths in 87^{87}87Rb
We present precision measurements of the f=1f=1f=1 to f=2f=2f=2 inter-hyperfine scattering lengths in a single-domain 87^{87}87Rb spinor Bose-Einstein condensate. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a co-magnetometer strategy to cancel laboratory magnetic noise. We find the scattering length ratios a32(12)/a20(1)=−1.27(15)a_{32}^{(12)}/a_{20}^{(1)}=-1.27(15)a32(12)​/a20(1)​=−1.27(15) and a12(12)/a20(1)=−1.31(13)a_{12}^{(12)}/a_{20}^{(1)}=-1.31(13)a12(12)​/a20(1)​=−1.31(13), limited by atom number fluctuations. Using better control of atom number, we estimate precisions of ∼0.3%\sim 0.3\%∼0.3% should be possible with this technique.
In this work we demonstrate the first realization of a comagnetormeter in the ultracold regime. In comparison to regular magnetometers, which are designed to maximize their magnetic field sensitivity, a comagnetometer uses paired magnetometers in a differential configuration to cancel the effects of the magnetic field and resolve weak dynamics that differently affect its constituents. Here, we implement a omagnetometer within the f=1 and f=2 ground state hyperfine manifolds of a Rb87 spinor Bose-Einstein condensate (SBEC). The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. A fundamental limitation of the comagnetometer is f=2--> f=1 hyperfine relaxing collisions, where the liberated kinetic energy expels colliding atoms from the optical trap. These collisions are state-dependent and can be avoided by preserving the f=2 spin state in a stretched configuration. We show how this can be achieved at low magnetic fields, where the spin-dependent contact interaction is the dominant energy contribution and stabilizes the spin orientation of the SBEC. Under these conditions, the comagnetometer coherence time can be extended to ~1 s and the observed common magnetic field suppression is 44.0(8)dB. The technique is applied to precision measurement of the interhyperfine interaction in 87Rb. The uncertainty in the obtained interhyperfine scattering lengths is reduced by more than a factor three with respect to previously reported values. We also present preliminary studies on phase-resolved parametric amplification within a SBEC comagnetometer. In this case, the f=2 manifold undergoes parametric amplification, while the f=1 manifold keeps track of the rotating reference frame induced by the applied external magnetic field. We describe technical improvements to the experimental system in two areas: magnetic control and manipulation, and optical trapping and probing. The first group of improvements includes the implementation of radiofrequency (rf) and microwave (mw) driving and the development of a real-time rf source. The second group of improvements includes a pulsed optical trapping technique, a digital implementation of the laser locking scheme, and a hyperfine-selective Faraday probing method. Aquesta tesi demostra el primer comagnetòmetre implementat en un sistema d’àtoms ultrafreds. Els magnetòmetres són altament sensibles a canvis en el camp magnètic. Els comagnetòmetres, en canvi, utilitzen magnetòmetres aparellats diferencialment per a cancel·lar la dependència del camp magnètic extern i discernir camps o interaccions que afecten de forma diferent als seus constituents. En aquest treball, s’implementa un comagnetòmetre mitjançant una superposició coherent dels estats hiperfins f=1 i f=2 d’un condensat spinorial de Bose-Einstein de Rb87. Aquests estats tenen fraccions giromagnètiques gairebé oposades, de manera que la suma dels seus angles de precessió no depèn del camp magnètic però es veu doblement afectada per interaccions que roten els dos estats en la mateixa direcció. Col·lisions de relaxació hiperfina f=2 --> f=1 limiten el temps de coherència del comagnetòmetre. En concret, els àtoms que hi participen són expulsats de la trampa òptica degut a l’energia cinètica alliberada en la col·lisió. Aquest tipus de col·lisió depenen de l’estat de spin i es cancel·len per a estats que maximitzen el spin a f =2. En aquesta tesis demostrem la cancel·lació de col·lisions de relaxació hiperfina a camps magnètics baixos, on la interacció de spin és la contribució energètica dominant i estabilitza l’estat a f = 2. Sota aquestes condicions, el temps de coherència del comagnetòmetre s’estén fins a ~1 s i el soroll de camp magnètic es veu atenuat per 44.0(8) dB. El comagnetòmetre s’ha usat per caracteritzar la interacció hiperfina en àtoms de Rb87. En comparació a estudis experimentals anteriors, s’ha aconseguit reduir en un factor tres la incertesa en les longituds de dispersió entre estats hiperfins. També presentem experiments preliminars d’amplificació paramètrica amb resolució de phase, on l’amplificació paramètrica té lloc a f=2 i les rotacions magnètiques del sistema de referència són mesurades de forma simultània a f=1. Els avenços tècnics es divideixen en millores del control i de la manipulació magnètica, així com en millores del confinament i de la detecció òptica. Els primers inclouen els sistemes de manipulació atòmica mitjançant radiofreqüència i microones, com també el desenvolupament d’una font de radiofreqüència amb control en temps real. Els segons inclouen una tècnica de confinament polsat, la digitalització del sistema d’estabilització làser i la detecció òptica d’ambdós estats hiperfins.
We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.
We measure inter-state interactions in a Bose-Einstein Condensate (BEC) set in a superposition of two states, using microwave spectroscopy. We introduce a population imbalanced dynamic-decoupling scheme that accumulates a phase due to inter-state interactions while canceling intra-state density shifts and external noise sources. Uncertainties of the measured scattering lengths were 0.02a0a_{0}a0​ (where a0a_{0}a0​ is the Bohr radius) for both magnetic sensitive and insensitive transitions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is twisted by the nonlinear interactions, as predicted by Harber et. al and that the twist rate depends on the difference between inter-state and intra-state scattering lengths a22+a11−2a12a_{22}+a_{11}-2a_{12}a22​+a11​−2a12​. Our results allow for a better understanding of inter-atomic potentials in 87Rb^{87}Rb87Rb. Our scheme can be used for spin squeezing and observing polaron physics close to a Feshbach resonance, where interactions diverge, and strong magnetic noises are ever present.
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 report on precision measurements of spin-dependent interaction-strengths in the 87 Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction Hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87 Rb in the f = 1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87 Rb in the f = 2 manifold, the data point towards an antiferromagnetic ground state; however our error bars do not exclude a possible cyclic phase.