Precision Measurement with Cold Atoms

Abstract

In a light-pulse atom interferometer, we use a tip-tilt mirror to remove the influence of the Coriolis force from Earth's rotation and to characterize configuration space wave packets. For interferometers with a large momentum transfer and large pulse separation time, we improve the contrast by up to 350% and suppress systematic effects. We also reach what is to our knowledge the largest space-time area enclosed in any atom interferometer to date. We discuss implications for future high-performance instruments. DOI: 10.1103/PhysRevLett.108.090402 PACS numbers: 03.75.Dg, 06.30.Gv, 37.25.+k, 67.85.Àd Light-pulse atom interferometers use atom-photon interactions to coherently split, guide, and recombine freely falling matter-waves [1]. They are important in measurements of local gravity [2], the gravity gradient [3], the Sagnac effect [4], Newton's gravitational constant [5], the fine structure constant [6], and tests of fundamental laws of physics [7][8][9]. Recent progress in increased momentum transfer led to larger areas enclosed between the interferometer arms [10][11][12] and, combined with commonmode noise rejection between simultaneous interferometers [13,14], to strongly increased sensitivity. With these advances, what used to be a minuscule systematic effect now impacts interferometer performance: The Coriolis force caused by Earth's rotation has long been known to cause systematic effects [2]. In this Letter, we not only demonstrate that it causes severe loss of contrast in large space-time atom interferometers, but also use a tip-tilt mirror [15] to compensate for it, improving contrast (by up to 350%), pulse separation time, and sensitivity, and characterize the configuration space wave packets. In addition, we remove the systematic shift arising from the Sagnac effect [16]. This leads to the largest space-time area enclosed in any atom interferometer yet demonstrated, given by a momentum transfer of 10@k, where @k is the momentum of one photon, and a pulse separation time of 250 ms. Figure 1 shows the atom's trajectories in our apparatus. We first consider the upper two paths: At a time t 0 , an atom of mass m in free fall is illuminated by a laser pulse of wave number k. Atom-photon interactions coherently transfer the momentum of a number 2n of photons to the atom with about 50% probability, placing the atom into a coherent superposition of two quantum states that separate with a relative velocity of 2nv r , where v r ¼ @k=m is the recoil velocity. An interval T later, a second pulse stops that relative motion and another interval T 0 later, a third pulse directs the wave packets towards each other. The packets meet again at t 4 ¼ t 1 þ 2T þ T 0 when a final pulse overlaps the atoms. The probability of detecting an atom in a particular output of the interferometer is given by cos 2 ðÁ=2Þ, where Á is the phase difference accumulated by the matter wave between the two paths. It can be calculated to be Á AE ¼ 8n 2 ð@k 2 =2mÞT AE nkgTðT þ T 0 Þ, the sum of a recoil-induced term 8n 2 ð@k 2 =2mÞT, and...

Theory of a Kaptiza-Dirac Interferometer with Cold Trapped Atoms

“…As an alternative to the atomic fountains, where the atoms follow ballistic trajectories, the interferometric operations can be implemented with trapped clouds [20] [21] [22]. We have recently proposed [23] a multi-mode interferometer with harmonically confined atoms where multi beam-splitter and mirror operations are realized with Kapitza-Dirac (KD) pulses, namely, the impulse application of an off-resonant standing optical wave.…”