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arXiv:2608.17576

Magic-wavelength matter-wave interferometry with optical clock states

Jianing Li, Swarup Das, Xinyuan Ma, T. Zanon-Willette, Shau-Yu Lan, Chang Chi Kwong, David Wilkowski

Published Aug 18, 2026• 0 citations
arXivHTMLPDF

Abstract

Optical clocks and atom interferometers provide complementary ways to measure time, motion and gravity. Combining these capabilities requires matter-wave beam splitters that manipulate different clock states in the same way, so that optical internal energy becomes a controlled degree of freedom rather than a source of systematic phase shifts. Here we realized a dual matter-wave interferometer operating simultaneously on the two states of the $^{88}$Sr optical clock transition, $^1S_0$ and $^3P_0$. The interferometer is driven by Bragg pulses at the 813 nm magic wavelength, for which the two clock states experience the same optical coupling strength. This realizes a common matter-wave beam splitter for atoms whose internal energies differ by an optical excitation. With a sensitivity of 30 mrad, our measurement is consistent with a zero differential phase shift between the two clock-state Mach-Zehnder interferometers, translating to an absence of state-dependent acceleration in free fall at the level of $10^{-5}$. We further used the same interferometer to measure state-dependent optical dipole forces and determine a tune-out wavelength of the metastable $^3P_0$ state to be 478.95(8) nm. These results establish magic-wavelength clock-state interferometry as a platform for differential force sensing, excited-state polarizability metrology and future quantum-clock tests of gravity.

DOI
10.48550/arxiv.2608.17576

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Optical clocks and atom interferometers provide complementary ways to measure time, motion and gravity. Combining these capabilities requires matter-wave beam splitters that manipulate different clock states in the same way, so that optical internal energy becomes a controlled degree of freedom rather than a source of systematic phase shifts. Here we realized a dual matter-wave interferometer operating simultaneously on the two states of the 88^{88}88Sr optical clock transition, 1S0^1S_01S0​ and 3P0^3P_03P0​. The interferometer is driven by Bragg pulses at the 813 nm magic wavelength, for which the two clock states experience the same optical coupling strength. This realizes a common matter-wave beam splitter for atoms whose internal energies differ by an optical excitation. With a sensitivity of 30 mrad, our measurement is consistent with a zero differential phase shift between the two clock-state Mach-Zehnder interferometers, translating to an absence of state-dependent acceleration in free fall at the level of 10−510^{-5}10−5. We further used the same interferometer to measure state-dependent optical dipole forces and determine a tune-out wavelength of the metastable 3P0^3P_03P0​ state to be 478.95(8) nm. These results establish magic-wavelength clock-state interferometry as a platform for differential force sensing, excited-state polarizability metrology and future quantum-clock tests of gravity.
The utilization of light-pulse atom interferometry presents a valuable technique that has found application in both fundamental scientific inquiries, such as investigating constants such as measurements of fine structure constant α and gravitational constant G, and practical endeavors including acceleration sensing and rotation measurements. This thesis delves into our implementation of a dual atom interferometer design involving the clock transition 1S0 → 3P0 in strontium, concurrently conducting the interferometric sequence on atoms in both ground and excited states. To facilitate the dual atom interferometer’s operation, we have firstly established a compact experimental setup with a transversely loaded bi-dimensional magneto-optical-trap (2D-MOT) to create a high flux source of cold strontium atoms. Introducing a novel cross-polarized bi-color atomic beam slower, we simultaneously addresses two excited Zeeman substates of the transition 1S0 → 1P1 in strontium-88, significantly enhancing the number of atoms prepared in the 461 nm MOT by around 10-fold. Following the 461 nm MOT, the atomic ensemble undergoes cooling in a 689 nm MOT, achieving atomic temperatures below 1 µK. We also install a network of eight magnetic field probes arranged around the cold atomic sample, enabling precise three-axis active control of magnetic fields down to the milligauss level. With the atoms confined in a 2D lattice at the magic-wavelength of 813.427 nm after the initial preparation phase, we conduct the magnetically-induced clock transition to create a statistical mixture state of ground and excited states. After a velocity selection stage, implementing a Mach-Zehnder interferometer with Bragg pulses operating at the magic-wavelength along the vertical axis, we conduct tests of the weak equivalence principle (WEP). The Eötvös ratio we found in our system stood at (1.8 ± 3.1) × 10−4, mainly limited by the finite temperature of the atomic cloud constraining the interrogation time. Furthermore, the dual atom interferometer scheme enables the measurement of state-dependent force and eventually polarizability difference via the phase shift between the atoms in different states, and we experimentally demonstrate this by introducing an additional light field gradient.
We report the experimental measurement of a magic wavelength at 476.823 62(8) nm for the ${}^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}5{s}^{2}{\phantom{\rule{0.1em}{0ex}}}^{1}{\mathrm{S}}_{0}\ensuremath{\rightarrow}5s5p{\phantom{\rule{0.1em}{0ex}}}^{3}{\mathrm{P}}_{0}$ clock transition. The magic wavelength is determined through an ac Stark shift spectroscopy of atoms in an optical dipole trap. The value is in reasonable agreement with the theoretical prediction, differing by 0.061(54) nm. This magic wavelength, being shorter than the commonly used one at 813 nm, will be important for applications such as Bragg-pulse matter-wave interferometry involving both clock states. This work also paves the way for quantum simulation with a shorter lattice constant.
We report the realization of a matter-wave interferometer based on Raman transitions which simultaneously interrogates two different atomic species (87{}^{87}87Rb and 85{}^{85}85Rb). The simultaneous aspect of our experiment presents encouraging preliminary results for future dual-species atom interferometry projects and seems very promising by taking advantage of a differential acceleration measurement. Indeed, the resolution of our differential accelerometer remains lower than $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ even with vibration levels up to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ thanks to common-mode vibration noise rejection. An atom-based test of the weak equivalence principle has also been carried out leading to a differential free fall measurement between both isotopes of $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
We demonstrate an atom interferometer operating on the 1 S 0 – 3 P 0 clock transition of 87 Sr atoms in a "magic" optical guide, where the light shift perturbations of the guiding potential are canceled. As a proof-of-principle demonstration, a Mach–Zehnder interferometer is set horizontally to map the acceleration introduced by the focused optical guide. This magic guide interferometer on the clock transition is applicable to atomic elements where magic wavelengths can be found. Possible applications of the magic guide interferometer, including a hollow-core fiber interferometer and gradiometer, are discussed.
Atom interferometers are excellent tools for measuring inertial forces. Their high accuracy and sensitivity allow them to test fundamental physics, e.g., Einstein’s equivalence principle (EEP). One of the main assumptions of EEP is the universality of gravitational redshift (UGR), which states that the ticking rate measured by two idealised clocks at different points in a gravitational field is independent of their internal composition [1]. Although UGR has been successfully tested with two independent atomic clocks, the same effect on a single clock in a delocalised superposition of states has not been observed yet [2]. A promising approach for a delocalised test of UGR is quantum clock interferometry (QCI), which uses a sequence of light pulses to split, redirect, and recombine coherent wave packets and drive transitions between the internal states of the atoms to measure differences in proper time imprinted in the interferometer’s phase shift [3]. An experimental realisation of such schemes requires atomic species with large internal transitions. In this work, we propose an interferometry sensitive to gravitational redshift. By performing a double differential measurement in a single shot, this configuration benefits from a common-mode rejection of spurious effects in the interferometer’s phase. The feasibility of QCI experiments measuring gravitational redshift depends on the availability of long-lived internal states with large energy differences, making the ytterbium (Yb) optical transition an ideal candidate. The clock transition is excited through a two-photon Doppler-free E1-M1 mechanism [4]. This process requires a narrow linewidth, 1 kHz, and a high-power, 20 W, light source. We present our frequency stabilisation scheme and power amplification of an 1156 nm laser to drive the clock transition on a cold Yb cloud. [1] F. Di Pumpo et al., Phys. Rev. D 107, 064007 (2023). [2] A. Roura et al., Phys. Rev. D 104 084001 (2021). [3] C. Ufrecht et al., Phys. Rev. Research 2 043240 (2020). [4] E. A. Alden et al., Phys. Rev. A 90, 012523 (2014)
State-of-the-art optical clocks based on neutral atoms have already surpassed the world's best microwave atomic clocks in both accuracy and stability, paving the way to high-precision measurements of elementary aspects of nature, like the search for the drift of fundamental constants or the application of relativistic geodesy.These clocks operate with ensembles trapped in an optical lattice.Normally, high-power trapping laser fields induce a large AC Stark shift on the clock's transition frequency, as the clock states have different polarizabilities.A key feature of lattice clocks is the magic wavelength, for which the atomic polarizabilities of the clock states are equal, therefore compensating a differential frequency shift on the clock transition.In the periodic potential of the optical lattice, the energy spectrum of motional states features a band structure, analogous to electrons in a crystalline structure well-known from solid state physics.Within this band structure, atoms can tunnel between adjacent lattice sites.As a consequence from tunneling motion, the clock transition experiences a frequency shift and a broadening, which becomes pronounced in the shallow lattice regime.This work presents the first demonstration of a 24 Mg optical lattice clock including the precise determination of the frequency of the clock transition, its magic wavelength and its second-order Zeeman shift.Furthermore, the effect of tunneling in an optical lattice for magnesium has been extensively studied via optical spectroscopy of Bloch bands and substantiated with theoretical models, that were initially developed for a strontium optical lattice clock.Measuring lattice light induced frequency shifts of the clock transition for various lattice wavelengths and intensities, yielded a value of the magic wavelength of the 1 S 0 → 3 P 0 clock transition in 24 Mg of 468.463(207) nm.This value is in well agreement with a recent theoretical calculation of 468.45(23) nm, using a refined atomic structure model.The experimental value for the magic wavelength was independently verified with optical spectroscopy of Bloch bands carried out on the clock transition.Here, the AC Stark modified band structure is directly probed by a single frequency scan of the carrier resonance, featuring an asymmetric line shape, that is strongly dependent on the lattice wavelength.This technique demonstrates a novel method for the determination of the magic wavelength and could also be applied to other atomic species.In bosonic isotopes of alkaline earth(-like) elements, like 24 Mg, optical dipole excitation of the spin-forbidden 1 S 0 → 3 P 0 clock transition can be enhanced, e.g. by applying an external magnetic field.While these bosons are insensitive to first-order Zeeman shifts, the second-order Zeeman effect displays a dominant contribution to the clock's error budget.In this thesis, the magnetic polarizability β is measured to be -206.6(2.0)MHz/T 2 , consistent with a theoretical calculation, and the clock transition frequency was found to be 655 058 646 691(101) kHz.