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arXiv:0909.0102 · Physical Review A

Double diffraction in an atomic gravimeter

Nicola Malossi, Quentin Bodart, Sébastien Merlet, Thomas Lévèque, Arnaud Landragin, Franck Pereira dos Santos

Published Jan 20, 2010• 64 citations
arXivHTMLPDF

Abstract

We demonstrate the realization of a scheme for cold-atom gravimetry based on the recently demonstrated use of double-diffraction beam splitters [T. L\'ev\`eque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, Phys. Rev. Lett. 103, 080405 (2009)], where the use of two retro-reflected Raman beams allows symmetric diffraction in $\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}{k}_{\mathrm{eff}}$ momenta. Although in principle restricted to the case of zero Doppler shift, for which the two pairs of Raman beams are simultaneously resonant, such diffraction pulses can remain efficient on atoms with nonzero velocity, such as in a gravimeter, when the frequency of one of the two Raman laser sources is modulated. Such pulses are used to realize an interferometer insensitive to laser phase noise and some of the dominant systematics. This approach reduces the technical requirements and would allow the realization of a simple atomic gravimeter. A sensitivity of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}g$ per shot is demonstrated.

DOI
10.1103/physreva.81.013617

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It discusses the fundamental differences between the mechanisms and geometries with respect to the diffraction efficiency, taking into account the width of the initial wave function and the duration of the light pulse. Additionally, it explores the transition between the two diffraction geometries when starting from an atom initially at rest and increasing its momentum. The results may serve as a reference for experimentalists in selecting the most suitable configuration, based on their aims and requirements in the realization of more advanced atom interferometers. The second contribution (II) is a follow-up to the previous one, but focuses exclusively on a single diffraction type in microgravity, namely the so-called double Raman diffraction. In contrast to the previous article, where we only discussed single two-photon processes, we consider in this article a six-photon process, also known as third-order diffraction, as well as three subsequent two-photon processes, which both lead to the same amount of transferred momentum and can both be used to realize large-momentum transfer (LMT). We demonstrate that third-order double Raman diffraction is a viable and advantageous method for the diffraction of small momentum distributions like Bose-Einstein condensates (BECs) compared to a sequence of three two-photon processes. Furthermore, we show that third-order Raman pulses can be successfully applied to create higher-order Raman atom interferometers. Third-order diffraction can be perfectly combined with other LMT techniques and, moreover, allows for a reduction in the overall duration of the diffraction process and the complexity of the experimental set-up, as only two distinct laser frequencies are required. Moreover, we present a third-order Mach-Zehnder interferometer with spurious paths being disregarded. As demonstrated later on in [3], this interferometer generates optimal contrast and a substantial amplitude. The third contribution (III) extends the semi-classical λ-scheme of single Raman diffraction, as discussed in detail in contribution (I), into a fully quantized multi-atom multi-λ configuration with center-of-mass motion inside a cavity. Therefore, the incorporation of an internal structure allows for a more realistic modeling of the atoms, which is relevant for multi-photon interaction or cooling processes. We use for our analysis the framework of second quantization, i.e., we take into account the field-theoretical nature of the multi-particle atomic field as well as of the diffracting light field. We reduce this model with a Hamiltonian averaging theory applied to the atomic field operators and obtain an effective Hamiltonian, which determines the time evolution of the system. We demonstrate the efficiency of our model by the application of a typical initial state. Moreover, for a specific input state, we obtain the Hong-Ou-Mandel effect simultaneously in the atomic and the optical system. Our many-body formalism is perfectly suited to theoretically describe contemporary high-precision atom interferometric experiments based on entanglement between the atoms, that aim to surpass the shot-noise limit.
The use of retroreflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called ``method of averaging,'' which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequent separation of momentum states for detection. Despite the inherently multi-state nature of atom diffraction, we are able to build a Mach–Zehnder interferometer using Bragg scattering which achieves a sensitivity to the gravitational acceleration of Δ g / g = 2.7 × 10 −9 with an integration time of 1000 s. The device can also be converted to a gravity gradiometer by a simple modification of the light pulse sequence.
Summary form only given. Atom interferometry based on cold atoms and light beamsplitters is a mature technique, which allows for the realization of highly sensitive inertial sensors. In the most advanced inertial sensors based on atom interferometry, atomic wavepackets are manipulated by light beamsplitters using two-photon Raman transitions. The interferometer phase shift, which depends on the acceleration and the rotation of the experimental setup with respect to the inertial reference frame defined by the atoms in free fall, is derived from the relative displacement of the atoms with respect to the beamsplitter laser's equiphases. Wavefront aberrations thus induce parasitic phase shifts, which bias the measurement, and which are linked to the residual ballistic motion of the atoms across the laser beam profile during their free fall and cancels out at zero atomic temperature. The wavefront distortions of the lasers beamsplitters is an important limit in the accuracy of atom interferometers and in particular, the dominating contribution in best cold atom gravimeters (CAG) uncertainty budget. This work clears the way towards unprecedented accuracies for absolute gravimetry, below the 1 μGal level. The method proposed can be applied to any atomic sensor based on light beamsplitters, which are inevitably affected by distortions of the lasers wavefronts. The improved control of systematics it provides will have significant impact in high precision measurements with atom interferometry, with important applications to geodesy, fundamental physics tests and to the development of highest grade inertial sensors.
We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $\ensuremath{\mu}\mathrm{Gal}$ ($1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{Gal}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\mathrm{m}/{\mathrm{s}}^{2}$). We also show that this effect is not compensated when averaging over the two directions of the Raman wave vector kkk. This thus constitutes a limit to the rejection efficiency of the kkk-reversal technique. Our analysis allows us to separate this effect from the effect of the finite speed of light, which we find in perfect agreement with expected values. This study highlights the benefit of chirping symmetrically the two Raman lasers.
An atom interferometer based on Doppler-insensitive Raman transition is proposed, which has sharply peaked interference fringes for multi-wave interference. We show that two sets of counter-propagating Doppler-insensitive Raman beam pairs can be used to construct a new type of multi-wave beam splitter, which can be used to construct an atom interferometer. Although the spacing between adjacent diffraction orders of the interferometer is small, they can be distinguished by the internal state of the atom. Our analysis shows that the width of the fringes of this atom interferometer is inversely proportional to the width (duration) of the beam splitter and the Rabi frequency of the Raman beams, that is, the interferometer can achieve high resolution at high light intensity and long pulse width.