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The European Physical Journal D

Differential interferometry using a Bose-Einstein condensate

Matthias Gersemann, Martina Gebbe, Sven Abend, Christian Schubert, Ernst Maria Rasel

Published Oct 1, 2020• 24 citations
Publisher

Abstract

Abstract Out of a single Bose-Einstein condensate (BEC), we create two simultaneous interferometers, as employed for the differentiation between rotations and accelerations. Our method exploits the precise motion control of BECs combined with the precise momentum transfer by double Bragg diffraction for interferometry. In this way, the scheme avoids the complexity of two BEC sources and can be readily extended to a six-axis quantum inertial measurement unit. Graphical abstract

DOI
10.1140/epjd/e2020-10417-8

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Abstract Out of a single Bose-Einstein condensate (BEC), we create two simultaneous interferometers, as employed for the differentiation between rotations and accelerations. Our method exploits the precise motion control of BECs combined with the precise momentum transfer by double Bragg diffraction for interferometry. In this way, the scheme avoids the complexity of two BEC sources and can be readily extended to a six-axis quantum inertial measurement unit. Graphical abstract
New quantum devices based on manipulations of Bose-Einstein condensate (BEC) on microfabricated chips hold great promise for application to high precision inertial navigation. By employing appropriate mechanizations which separate acceleration and rotation sensitivities, atom interferometers can have dual functionality as both accelerometers and gyroscopes. BEC interferometers could offer ten orders of magnitude inertial measurement improvement with possibility of developing highly sensitive inertial measurement unit (IMU) which would provide extremely accurate free-inertial navigation with long-term accuracy. This is very suitable for applications in undersea environments where direct use of the Global Positioning System (GPS) is denied. Due to the high sensitivity of BEC and the complexity of microfabricated structures, application specific sources of decoherence, environmental noises, and errors are modeled and studied.
Inertial sensors based on matter-wave interferometry are currently approaching the precision and accuracy of state-of-the-art classical sensors. While these devices are often realised with ultracold but not Bose-condensed atoms as matter waves, employing Bose-Einstein Condensates (BEC) promises to overcome certain limitations, especially those related to the ensemble's expansion. The point-source like character of BECs also enables utilising spatial interference patterns to measure e.g. rotation rates in single-shot experiments. Matter wave-based inertial sensors are considered for experiments ranging from Gravitational Wave detection to tests of the Universality of Free Fall (UFF) to gain insight into the joint between Quantum Mechanics and General Relativity. In the scope of this thesis, matter-wave interferometry with BECs was demonstrated for the first time in a microgravity environment with the QUANTUS-1 apparatus. The same instrument was then employed as a quantum tiltmeter utilising a novel beam-splitting mechanism known as Bragg Double Diffraction. To this end, the QUANTUS-1 apparatus designed as a BEC instrument to be operated in the drop tower at ZARM at University of Bremen was equipped with optics and laser systems required for performing matter-wave interferometry based on Bragg Diffraction. The apparatus employs an atom chip to create BECs of around 10000 Rubidium 87 atoms within 15 s. With a Mach-Zehnder like interferometer scheme, spatial interference fringes were observed after a free evolution time in the interferometer of up to 677 ms. To achieve these long time scales, a method known as Delta-Kick Collimation (DKC) was adapted to slow the expansion of the BEC to a kinetic energy equivalent below 1 nK, and the atoms were transferred to a non-magnetic Zeeman state via an adiabatic rapid passage (ARP). A similar interferometer scheme with a newly developed beam-splitter mechanism known as Bragg Double Diffraction was used to measure the tilt of the instrument on ground with a precision of up to 4.4 AA rad. This thesis presents an overview of the apparatus including ground-based characterisations of all required experimental steps. Results from over 400 free fall experiments are evaluated for expansion studies of the BEC and matter-wave interferometry in microgravity. The time-evolution of first and second order Bragg Double Diffraction beam splitters is studied, and an interferometer sensitive to the tilt of the instrument is implemented. Based on this work, a gravimeter with a new launch mechanism comprising Bragg beam splitters and Bloch oscillations to enable atomic fountains in atom-chip based devices was developed. The microgravity experiments were adapted for the MAIUS-1 sounding-rocket instrument to create the first man-made BEC in outer space and study the feasibility of operating matter-wave interferometers on space-borne platforms. The results of this thesis lay the groundwork for future space-borne missions using matter-wave interferometry for precision measurements of inertial forces.
We present the experimental implementation of double Bragg diffraction of Bose-Einstein condensates (BECs) as proposed in [E. Giese, A. Roura, G. Tackmann, E. M. Rasel, and W. P. Schleich, Phys. Rev. A \textbf{88}, 053608 (2013)]. We excite Rabi oscillations between the three coupled momentum states ∣0ℏk⟩\left| 0 \hbar k \right\rangle∣0ℏk⟩ and ∣±2ℏk⟩\left| \pm 2 \hbar k \right\rangle∣±2ℏk⟩. By selecting appropriate interaction times we generate highly efficient beamsplitters and mirrors for Bose-Einstein condensates. In addition, we demonstrate higher-order double Bragg diffraction and display beamsplitters with up to $ \pm 6 \hbar k$ momentum transfer. We compare double Bragg diffraction to several other experimental realizations of beamsplitters. Finally, we show that double Bragg diffraction is well suited for matter wave interferometry by realizing a Ramsey-type interferometer in a quasi one-dimensional waveguide.
We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i) first-order, (ii) two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.
Atom interferometery is an exquisite measurement technique sensitive to inertial forces. However, it is commonly limited to a single sensitive axis, allowing high-precision multidimensional sensing only through subsequent or postcorrected measurements. We report on a novel method for multi-axis inertial sensing based on the correlation of simultaneous light-pulse atom interferometers in 2D array arrangements of Bose-Einstein condensates (BEC). Deploying a scalable 3×3 BEC array spanning 1.6 mm^{2} created using time-averaged optical potentials, we perform measurements of linear acceleration induced by gravity and simultaneously demonstrate sensitivity to angular velocity and acceleration of a rotating reference mirror, as well as gravity gradients and higher-order derivatives. Our Letter enables simple, high-precision multi-axis inertial sensing compatible with high rotation rates, e.g., for inertial navigation in dynamic environments. We finally envision further applications of our method, e.g., 3D in situ measurements and reconstruction of laser beam intensities and wave fronts.
A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A $5\ifmmode\times\else\texttimes\fi{}1{0}^{6}\text{ }\text{ }\mathrm{atom}$ F=1F=1F=1 spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb is released into free fall for up to 750 ms and probed with a T=130  msT=130\text{ }\text{ }\mathrm{ms}T=130  ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states $|{m}_{f}=1,0,\ensuremath{-}1⟩$, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of $\mathrm{\ensuremath{\Delta}}g/g=1.45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and the magnetic field gradient to a precision of 120 pT/m120\text{ }\mathrm{pT}/\mathrm{m}120 pT/m.