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arXiv:1603.08826

Experimental realization of double Bragg diffraction: robust beamsplitters, mirrors, and interferometers for Bose-Einstein condensates

J. Küber, F. Schmaltz, G. Birkl

Published Mar 29, 2016• 9 citations
arXivHTMLPDF

Abstract

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 $\left| 0 \hbar k \right\rangle$ and $\left| \pm 2 \hbar k \right\rangle$. 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.

DOI
10.48550/arxiv.1603.08826

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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 ±6ℏk \pm 6 \hbar k±6ℏk 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.
Matter wave interferometry offers a novel approach for high precision measurements, such as the determination of physical constants like the local gravity constant g or the fine-structure constant. Since its early demonstration, it has become an important tool in the fields of fundamental and applied physics. The present work covers the implementation of matter wave interferometers as well as the creation of novel guiding potentials for ultra-cold ensembles of atoms and Bose-Einstein condensates for this purpose. In addition, novel techniques for the manipulation of atoms with Bragg lattices are presented, serving as elements for interferometry. The measurements in this work are performed with a Bose-Einstein condensate of 25000 87 rubidium atoms created in a crossed optical dipole trap. The crossed optical dipole trap is loaded from a magneto-optical trap and allows a measurement every 25 s. This work introduces the novel technique of double Bragg diffraction as a tool for atom optics for the first time experimentally. The creation of beamsplitters and mirrors for advanced interferometric measurements is characterized. An in depth discussion on the momentum distribution of atomic clouds and its influence on double Bragg diffraction is given. Additionally experimental results for higher-order Bragg diffraction are explained and double Bragg diffraction is used to implement a full Ramsey-type interferometer. A second central result of this work is the implementation of novel guiding structures for ultra-cold atoms. These structures are created with conical refraction, an effect that occurs when light is guided along one of the optical axis of a bi-axial crystal. The conical refraction crystal used to operate the novel trapping geometries is a KGd(WO4)2 crystal that has been specifically cut orthogonal to one of the optical axis. Two regimes are discussed in detail: the creation of a toroidal matter wave guide and the implementation of a three-dimensional dark focus. Additional geometries accessible with conical refraction are introduced and possible applications are shown. The first regime characterized in detail is the creation of a toroidal wave guide for ultra-cold atoms and Bose-Einstein condensates. With the aid of a lightsheet potential atoms are trapped in a quasi two-dimensional ring geometry. Inside of the geometry atoms are accelerated, decelerated and held for extended storage times of up to two seconds. First attempts for the implementation of a Mach-Zehnder-type interferometer in a toroidal trap are presented. The second regime shown is the creation of a three-dimensional dark focus that is used to trap atoms in a repulsive confinement of light. The parameters of the dark focus are investigated in detail. Future application of a two-dimensional array of dark foci is shown by demonstrating the respective light field.
This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state systematics, and suitability for microgravity experiments, its performance has long been limited by imperfect diffraction and contrast loss. This work overcomes these limitations by constructing an analytic Hamiltonian description of DBD -- including Doppler effects and polarization imperfections -- and by deriving reduced two- and five-level models via a truncated Magnus-expansion approach. These models clarify the origin of AC-Stark shifts, polarization-induced errors, and Doppler selectivity, and they provide accurate predictions for realistic input momentum distributions. Building on this theoretical foundation, the thesis introduces a tri-frequency laser scheme with dynamically tunable detuning and evaluates different detuning-control strategies using a five-level S-matrix formalism. Linear detuning sweeps and optimal-control pulses are shown to provide near-ideal beam-splitter and mirror performance, respectively, ensuring robust contrast across a wide range of experimental imperfections. Complementary full three-dimensional simulations using the GPU-accelerated Universal Atom Interferometer Simulator (UATIS) incorporate interacting Bose-Einstein condensates and realistic optical potentials, revealing transverse effects and polarization-induced distortions that extend the predictions of the one-dimensional non-interacting models. Taken together, this thesis establishes a coherent theoretical and numerical framework demonstrating that, with appropriate detuning control, double-Bragg atom interferometers can achieve the robustness required for precision inertial sensing and future space-based quantum tests of fundamental physics.
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.
Using a three-path contrast interferometer (CI) geometry and laser-pulse diffraction gratings, we create a matter-wave interferometer with ytterbium (Yb) atoms. We present advances in contrast interferometry relevant to high-precision measurements. By comparing to a traditional atom interferometer, we demonstrate the immunity of the CI to vibrations for long interaction times (>20ms>20\phantom{\rule{0.28em}{0ex}}\mathrm{ms}>20ms). We characterize and demonstrate control over the two largest systematic effects for a high-precision measurement of the fine-structure constant via photon recoil with our interferometer: diffraction phases and atomic interactions. Diffraction phases are an important systematic for most interferometers using large-momentum transfer beam splitters; atomic interactions are a key concern for any Bose-Einstein condensate (BEC) interferometer. Finally, we consider the prospects for a future subpart per billion photon recoil measurement using a Yb CI.
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.