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Photonics

Experimental Realization of a Mach–Zehnder-Type Internal-State Atom Interferometer in Sodium Spinor BEC

Jun Jian, 赵竹芳, Quanxin Zhang, Shunxiang Wang, Wenliang Liu, Jizhou Wu, Yuqing Li, Jie Ma

Published Jan 30, 2026• 0 citations
Publisher

Abstract

This study demonstrates a Mach–Zehnder-type internal-state atom interferometer in a sodium F = 1 spinor Bose–Einstein condensate (BEC), which is realized by applying a three-pulse radio-frequency sequence (π/2–π–π/2) to manipulate the two magnetic sublevels |1,−1⟩ and |1,0⟩. Phase-scanning experiments show that the visibility remains at a high level across all three pulse stages (V>0.77). In the hold-time scanning measurements, the visibility decays exponentially with hold time, yet the system maintains good coherence. This work establishes a foundation for precision measurements based on internal-state atom interferometers, as the approach simplifies the experimental apparatus while maintaining good quantum coherence and high-contrast interference fringes.

DOI
10.3390/photonics13020135

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This study demonstrates a Mach–Zehnder-type internal-state atom interferometer in a sodium F = 1 spinor Bose–Einstein condensate (BEC), which is realized by applying a three-pulse radio-frequency sequence (π/2–π–π/2) to manipulate the two magnetic sublevels |1,−1⟩ and |1,0⟩. Phase-scanning experiments show that the visibility remains at a high level across all three pulse stages (V>0.77). In the hold-time scanning measurements, the visibility decays exponentially with hold time, yet the system maintains good coherence. This work establishes a foundation for precision measurements based on internal-state atom interferometers, as the approach simplifies the experimental apparatus while maintaining good quantum coherence and high-contrast interference fringes.
The role of source cloud spatial coherence in a Mach-Zehnder-type atom interferometer is experimentally investigated. The visibility and contrast of a Bose-Einstein condensate (BEC) and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100100%100 nearly independent of $\ensuremath{\pi}$ pulse efficiency, while thermal sources have fringe visibilities limited to the $\ensuremath{\pi}$ pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond the thermal source.
Atom interferometry with high visibility is of high demand for precision measurements. Here, a parallel multicomponent interferometer is achieved by preparing a spin-2 Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in a hybrid magneto-optical trap. After the preparation of a spinor Bose-Einstein condensate with spin degrees of freedom entangled, we observe four spatial interference patterns in each run of measurements corresponding to four hyperfine states we mainly populate in the experiment. The atomic populations in different Zeeman sublevels are made controllably using magnetic-field-pulse induced Majorana transitions. The spatial separation of atom cloud in different hyperfine states is reached by Stern-Gerlach momentum splitting. The high visibility of the interference fringes is reached by designing a proper overlap of the interfering wave packets. Due to uncontrollable phase accumulation in Majorana transitions, the phase of each individual spin is found to be subjected to unreproducible shift in multiple experimental runs. However, the relative phase across different spins is stable, paving a way towards noise-resilient multicomponent parallel interferometers.
Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach–Zehnder sequence with trapped Bose–Einstein condensates confined on an atom chip. Particle interactions in our Bose–Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors. Atom interferometers exploit wave-particle duality and can be used as sensitive measurement devices. Berrada et al.present a Mach–Zehnder interferometer for Bose–Einstein condensates trapped on an atom chip and demonstrate enhanced performance using non-classical states.
We demonstrate a horizontal, linearly guided Mach-Zehnder atom interferometer in an optical waveguide. Intended as a proof-of-principle experiment, the interferometer utilizes a Bose-Einstein condensate in the magnetically insensitive $\left|F=1,{m}_{F}=0\right\ensuremath{\rangle}$ state of 87{}^{87}87Rb as an acceleration-sensitive test mass. We achieve a modest sensitivity to acceleration of $\ensuremath{\Delta}a=7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ m/s2{}^{2}2. Our fringe visibility is as high as 38% in this optically guided atom interferometer. We observe a time of flight in the waveguide of over 0.5 s, demonstrating the utility of our optical guide for future sensors.
A precision inertial sensor based on the interference of matter waves has been designed and implemented. The apparatus is capable of producing both cold thermal and ultracold Bose-Einstein condensate (BEC) atomic ensembles as the inertial test mass. BECs of up to 5x10^6 Rubidium 87 atoms with an effective temperature of 50nK are produced every 13 seconds using a combination of two and three dimensional magneto-optical traps (2D and 3D MOT) and evaporative cooling in a hybrid magnetic-quadrupole and crossed optical dipole trap. The atomic cloud is then propagated through a vertically oriented Mach-Zehnder interferometer utilizing Bragg diffraction beam splitters. An 2.6m drop tube allows for up to 750ms of free fall and interferometer times of up to 250ms. The drop has four regions of imaging corresponding to 0, 25, 220, 530, and 750ms of expansion. Standard absorption imaging is used for the upper two imaging regions and frequency modulation imaging (FMI) is used for the lower regions. FMI exhibits near atom-shot noise limited signal-to-noise of 948 on a 1x10^6 atom cloud. The inertial reference is provided by the Bragg beam retro-reflector which is suspended via a geometric anti-spring passive vibration isolation system providing 65 dB of isolation at 70 Hz. Prior to the first interferometer pulse the ensemble is placed into a spin superposition of the |F=1> ground state manifold using horizontal co-propagating Raman beams. The three internal spin states remain orthogonal throughout the interferometer sequence resulting in three simultaneous interferometer with separable magnetic gradient and gravitational acceleration signals. The effects of meanfield energy on the interferometric phase uncertainty is explored under current trap conditions. It is found that 30 ms of free expansion prior to the first beam splitter decreases the internal energy such that the expected meanfield phase noise is below 1mrad. No significant decrease in the interferometer contrast is observed for all available T, whereas a thermal test mass interferometer of equivalent longitudinal temperature produces no interference at interferometer times > 100ms. A direct comparison of test mass spatial coherence length in an optically transversely confined interferometer is investigated. The visibility and contrast of a BEC and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100%, nearly independent of p pulse efficiency, while thermal sources have fringe visibilities limited to the p pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond that of the thermal source. A BEC test mass is used for the simultaneous precision measurement of gravity and magnetic field gradients. An 8 hour data run of a 130ms interferometer shows good agreement between the interferometer output and a theoretical model of the solid earth tides. The residual of the theoretical model and the experimental data show a 1000 run precision of dg/g = 1.45x10^9 corresponding to a phase noise of 3.8mrad. The integrated phase noise of the apparatus shows a sensitivity to magnetic field gradients of 120pT/m. By varying the central spatial position of a 40ms interferometer the magnetic field gradient along a portion of the drop tube is measured.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.