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Physical Review A

Measurement of the 671-nm tune-out wavelength of Li7 by atom interferometry

Boris Décamps, J. Vigué, A. Gauguet, M Büchner

Published Mar 18, 2020• 6 citations
Publisher

Abstract

We have measured the tune-out wavelength of lithium isotope $^{7}\mathrm{Li}$ at 671 nm. We have used our atom interferometer to measure the phase shift due to the dynamical Stark effect as a function of the laser frequency when a laser beam was focused on a single interferometer arm. The tune-out wavelength is a function of the hyperfine $F,{m}_{F}$ sublevel, and we have prepared the atoms in the sublevel $F=2,{m}_{F}=+2$ or $\ensuremath{-}2$. We find that the tune-out frequency of the $F=2,{m}_{F}=+2$ sublevel is at $3388(8)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ to the blue of the $^{2}S_{1/2},F=1\ensuremath{\rightarrow}^{2}P_{1/2},{F}^{\ensuremath{'}}=2$ transition, the accuracy of this measurement being limited by imperfect optical pumping. This measurement is in excellent agreement with its theoretical value, and, once corrected for different tensorial contributions, our measurement agrees with the more precise measurement of Copenhaver et al. [Phys. Rev. A 100, 063603 (2019)], who also used atom interferometry but different experimental conditions.

DOI
10.1103/physreva.101.033614

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This Dissertation describes how I used a three nanograting Mach-Zehnder atom beam interferometer to precisely measure a wavelength of light, known as a tune-out wavelength, that causes zero energy shift for an atom. I also describe how such measurements can be remarkably sensitive to rotation rates. It is well known that atom interferometry can be used to measure accelerations and rotations, but it was a surprise to find out that tune-out wavelength measurements can under certain conditions be used to report the absolute rotation rate of the laboratory with respect to an inertial frame of reference. I also describe how we created conditions which improve the accuracy of tune out wavelength measurements. These measurements are important because they serve as a benchmark test for atomic structure calculations of line strengths, oscillator strengths, and dipole matrix elements. I present a new measurement of the longest tune-out wavelength in potassium, λzero = 768.9701(4) nm. To reach sub-picometer precision, an optical cavity surrounding the atom beam paths of the interferometer was used. Although this improved the precision of our experiment by increasing the light-induced phase shifts, the cavity also brought several systematic errors to our attentions. For example, I found that large ±200 pm shifts in tune-out wavelengths can occur due to the Earth's rotation rate. To solve this problem, I demonstrated that controlling the optical polarization, the magnetic field, and the atom beam velocity distribution can either suppress or enhance these systematic shifts. Suppressing these systemic shifts in tune-out wavelengths is useful for precision measurements used to test atomic structure calculations. By enhancing these systematic shifts, the interferometer can be a gyroscope that utilizes tune-out wavelengths.

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We have measured the tune-out wavelength of lithium isotope 7Li^{7}\mathrm{Li}7Li at 671 nm. We have used our atom interferometer to measure the phase shift due to the dynamical Stark effect as a function of the laser frequency when a laser beam was focused on a single interferometer arm. The tune-out wavelength is a function of the hyperfine F,mFF,{m}_{F}F,mF​ sublevel, and we have prepared the atoms in the sublevel F=2,mF=+2F=2,{m}_{F}=+2F=2,mF​=+2 or \ensuremath−2\ensuremath{-}2\ensuremath−2. We find that the tune-out frequency of the F=2,mF=+2F=2,{m}_{F}=+2F=2,mF​=+2 sublevel is at 3388(8)MHz3388(8)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}3388(8)MHz to the blue of the 2S1/2,F=1\ensuremath→2P1/2,F\ensuremath′=2^{2}S_{1/2},F=1\ensuremath{\rightarrow}^{2}P_{1/2},{F}^{\ensuremath{'}}=22S1/2​,F=1\ensuremath→2P1/2​,F\ensuremath′=2 transition, the accuracy of this measurement being limited by imperfect optical pumping. This measurement is in excellent agreement with its theoretical value, and, once corrected for different tensorial contributions, our measurement agrees with the more precise measurement of Copenhaver et al. [Phys. Rev. A 100, 063603 (2019)], who also used atom interferometry but different experimental conditions.
Atom interferometers typically use the total populations at the interferometer's output ports as the signal, but useful information can be encoded into spatial phase patterns. An interferometer translates the phase pattern into a measurable pattern in the atomic density that we use to perform a direct precision measurement of the 7Li^{7}\mathrm{Li}7Li tune-out wavelength near 671 nm. Expressed as a detuning from the $|2{S}_{1/2},F=2\ensuremath{\rangle}\ensuremath{\rightarrow}|2{P}_{1/2},{F}^{\ensuremath{'}}=2\ensuremath{\rangle}$ transition, we find 3329.5(1.4) MHz for the tensor-shifted tune out of the $|2{S}_{1/2},F=2,{m}_{F}=0\ensuremath{\rangle}$ state with ${\ensuremath{\sigma}}^{\ifmmode\pm\else\textpm\fi{}}$ light polarization and 3310.6(4.9) MHz for the tune out of the scalar polarizability. This technique may be generalized for directly sensing spatially varying phase profiles.
Atom interferometry deploys atoms as sensors, delivering precision measurements that span the gamut of physics. Laser-cooled samples simplify uniform detection strategies and allow meticulous control over degrees of freedom and systematic effects. Advanced cooling and interferometry techniques do apply readily to a few atomic species, but they leave behind a large class of species otherwise suited for precision sensing. This thesis describes atom interferometry with a sample of lukewarm 7^77Li, near the Doppler temperature. High thermal speeds demand rapid atom optics and complicate detection. We nevertheless develop interferometer techniques that considerably relax cooling requirements, including a recoil-sensitive scheme capable of measuring the fine-structure constant that takes advantage of 7^77Li's low mass. We also establish a phase-patterning protocol to inscribe and sense spatially-varying phases with matter-wave interferometers whose sample sizes exceed the arm separation. Phase patterning forms the basis of the first precision measurement of 7^77Li's red tune-out wavelength, the wavelength where AC Stark shifts from the DDD-line transitions cancel and the polarizability vanishes. Our measurement registers a 3-sigma\\sigmasigma tension with \\emph{ab initio} atomic theory regarding the tensor-shifted tune-out wavelength and a 2-sigma\\sigmasigma tension regarding the size of the tensor shift, but agrees with theory regarding the scalar tune-out wavelength. These results motivate further work on lithium's polarizability, enable direct measurements of hyperpolarizability, and empower an assortment of future applications of phase patterning in matter-wave interferometry.
Ushered forth by advances in time and frequency metrology, atom interferometry remains an indispensable measurement tool in atomic physics due to its precision and versatility. A sequence of four pi/2\\pi/2pi/2 beam splitter pulses can create either an interferometer sensitive to the atom's recoil frequency when the momentum imparted by the light reverses direction between pulse pairs or, when constructed from pulses without such reversal, sensitive to the perturbing potential from an external optical field. Here, we demonstrate the first atom interferometer with laser-cooled lithium, advantageous for its low mass and simple atomic structure. We study both a recoil-sensitive Ramsey-Bord\\'e interferometer and interferometry sensitive to the dynamic polarizability of the ground state of lithium. Recoil-sensitive Ramsey-Bord\\'e interferometry benefits from lithium's high recoil frequency, a consequence of its low mass. At an interrogation time of 10 ms, a Ramsey-Bord\\'e lithium interferometer could achieve sensitivities comparable to those realized at much longer times with heavier alkali atoms. However, in contrast with other atoms that are used for atom interferometry, lithium's unresolved excited-state hyperfine structure precludes the the cycling transition necessary for efficient cooling. Without sub-Doppler cooling techniques. As as result, a lithium atomic gas is typically laser cooled to temperatures around 300 mu\\mumuK, above the Doppler limit, and well above the recoil temperature of 6 mu\\mumuK. This higher temperature gas expands rapidly during the operation of an atom interferometer, limiting the experimental interrogation time and preventing spatially resolved detection. In this work, a light-pulse lithium matter-wave interferometer is demonstrated in spite of these limitation. Two-photon Raman interferometer pulses coherently couple the atom's spin and momentum and are thus able to spectrally resolve the outputs. These fast pulses drive conjugate interferometers simultaneously which beat with a fast frequency component proportional to the atomic recoil frequency and an envelope modulated by the two-photon detuning of the Raman transition. We detect the summed signal at short experimental times, preventing perturbation of the signal from vibration noise. This demonstration of a sub-recoil measurement with a super-recoil sample opens the door to similar scheme with other particles that are difficult to trap and cool well, like electrons. An interferometer instead composed of pi/2\\pi/2pi/2-pulses with a single direction of momentum transfer, can be sensitive to the dynamic polarizability of the atomic ground state. By scanning the frequency of an external driving field, such a measurement can be used to determine the atom's tune-out wavelength. This is the wavelength at which the frequency-dependent polarizability vanishes due to compensating ac-Stark shifts from other atomic states. Lithium's simple atomic structure allows for a precise computation of properties with only {\\em ab initio} wave functions and spectroscopic data. A direct interferometric measurement of lithium's red tune-out wavelength at 670.971626(1) nm, is a precise comparison to existing `all-order' atomic theory computations. It also provides another way to experimentally determine the S−S-S− to P−P-P− transitions matrix elements, for which large correlations and small values complicate computations. Finally, a future measurement of lithium's ultraviolet tune-out wavelength of at 324.192(2) nm would be sensitive to relativistic approximations in the atomic structure description.Atom interferometry simultaneously verifies existing atomic theory with measurements of atomic properties and searches for exotic physics lurking in plain sight. The techniques developed here broaden the applicability of interferometry and increase measurement sensitivity by simplifying cooling, increasing atom number and reducing the cycle time. Overcoming the current experimental limitations on interrogation time would allow for ultra-precise measurements of both the tune-out wavelength and the fine structure constant.
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.
This Dissertation describes how I used a three nanograting Mach-Zehnder atom beam interferometer to precisely measure a wavelength of light, known as a tune-out wavelength, that causes zero energy shift for an atom. I also describe how such measurements can be remarkably sensitive to rotation rates. It is well known that atom interferometry can be used to measure accelerations and rotations, but it was a surprise to find out that tune-out wavelength measurements can under certain conditions be used to report the absolute rotation rate of the laboratory with respect to an inertial frame of reference. I also describe how we created conditions which improve the accuracy of tune out wavelength measurements. These measurements are important because they serve as a benchmark test for atomic structure calculations of line strengths, oscillator strengths, and dipole matrix elements. I present a new measurement of the longest tune-out wavelength in potassium, λzero = 768.9701(4) nm. To reach sub-picometer precision, an optical cavity surrounding the atom beam paths of the interferometer was used. Although this improved the precision of our experiment by increasing the light-induced phase shifts, the cavity also brought several systematic errors to our attentions. For example, I found that large ±200 pm shifts in tune-out wavelengths can occur due to the Earth's rotation rate. To solve this problem, I demonstrated that controlling the optical polarization, the magnetic field, and the atom beam velocity distribution can either suppress or enhance these systematic shifts. Suppressing these systemic shifts in tune-out wavelengths is useful for precision measurements used to test atomic structure calculations. By enhancing these systematic shifts, the interferometer can be a gyroscope that utilizes tune-out wavelengths.
The First Measurement of the 23 ⁣S1−23 ⁣P/33 ⁣P2^{3\!}S_1 - 2^{3\!}P / 3^{3\!}P23S1​−23P/33P Tune-Out Wavelength in He*
The workhorse of atomic physics, quantum electrodynamics, is one of the best-tested theories in physics. However recent discrepancies have shed doubt on its accuracy for complex atomic systems. To facilitate the development of the theory further we aim to measure transition dipole matrix elements of metastable helium (He*) (the ideal 3 body test-bed) to the highest accuracy thus far. We have undertaken a measurement of the `tune-out wavelength' which occurs when the contributions to the dynamic polarizability from all atomic transitions sum to zero; thus illuminating an atom with this wavelength of light then produces no net energy shift. This provides a strict constraint on the transition dipole matrix elements without the complication and inaccuracy of other methods. Using a novel atom-laser based technique we have made the first measurement of the tune-out wavelength in metastable helium between the 33P1,2,33^{3}P_{1,2,3}33P1,2,3​ and 23P1,2,32^{3}P_{1,2,3}23P1,2,3​ states at 413.07(2) nm which compares well with the predicted value [PhysRevA.88.052515] of 413.02(9) nm. We have additionally developed many of the methods necessary to improve this measurement to the 100 fm level of accuracy where it will form the most accurate determination of transition rate information ever made in He* and provide a stringent test for atomic QED simulations. We believe this measurement to be one of the most sensitive ever made of an optical dipole potential, able to detect changes in potentials of $\sim$200 pK and is widely applicable to other species and areas of atom optics.