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arXiv:1301.5415 · Physical Review A

State-labeling Wannier-Stark atomic interferometers

Bruno Pelle, Adèle Hilico, Gunnar Tackmann, Quentin Beaufils, Franck Pereira dos Santos

Published Feb 4, 2013• 32 citations
arXivHTMLPDF

Abstract

Using cold ${}^{87}$Rb atoms trapped in a one-dimensional (1D)-optical lattice, atomic interferometers involving coherent superpositions between different Wannier-Stark atomic states are realized. Two different kinds of trapped interferometer schemes are presented: a Ramsey-type interferometer sensitive both to clock frequency and external forces, and a symmetric accordion-type interferometer, sensitive to external forces only. We evaluate the limits in terms of sensitivity and accuracy of those schemes and discuss their application as force sensors. As a first step, we apply these interferometers to the measurement of the Bloch frequency and the demonstration of a compact gravimeter.

DOI
10.1103/physreva.87.023601

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Using cold 87{}^{87}87Rb atoms trapped in a one-dimensional (1D)-optical lattice, atomic interferometers involving coherent superpositions between different Wannier-Stark atomic states are realized. Two different kinds of trapped interferometer schemes are presented: a Ramsey-type interferometer sensitive both to clock frequency and external forces, and a symmetric accordion-type interferometer, sensitive to external forces only. We evaluate the limits in terms of sensitivity and accuracy of those schemes and discuss their application as force sensors. As a first step, we apply these interferometers to the measurement of the Bloch frequency and the demonstration of a compact gravimeter.
A multiwave atom interferometer using multiple Wannier-Stark states is experimentally realized in a vertical optical lattice. Atoms are coherently driven by stimulated Raman transitions into a superposition of several adjacent lattice sites, in which they evolve at multiples of Bloch frequency in the same internal state to form an interference pattern. We observe coherent evolution for more than 500 Bloch periods. The noise analysis shows that the phase resolution of this interferometer is detection noise limited. This multiwave interferometer could be a potential instrument for gravimetry and short-range forces measurement.
A Ramsey-Raman interferometer is used to realize a compact force sensor using cold 87Rb^{87}\mathrm{Rb}87Rb atoms trapped in a vertical optical lattice. The sensitivity and accuracy of the force measurements are discussed and the limits in short-term sensitivity evaluated. We reach a relative sensitivity on the Bloch frequency and thus on the gravity acceleration of $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 1 s. We perform an experimental study of the influence of the transverse confinement onto the decay of the interferometer contrast and compare the measurements with a simple semiclassical model. It is shown that vertical gradients of the trapping potential can contribute significantly to the loss of contrast.
Raman laser pulses are used to induce coherent tunneling between neighboring sites of a vertical 1D optical lattice. Such tunneling occurs when the detuning of a probe laser from the atomic transition frequency matches multiples of the Bloch frequency, allowing for a spectroscopic control of the coupling between Wannier-Stark (WS) states. In particular, we prepare coherent superpositions of WS states of adjacent sites, and investigate the coherence time of these superpositions by realizing a spatial interferometer. This scheme provides a powerful tool for coherent manipulation of external degrees of freedom of cold atoms, which is a key issue for quantum information processing.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states is combined with the subsequent application of a compound pulse sequence that allows us to separate atoms by several lattice sites. This, together with the capability to load small atomic clouds in the lattice at micrometric distances from a surface, make our setup ideal for sensing short-range forces. We show that for arrays of 10^{4} atoms, our protocol can reduce the required averaging time by a factor of 10 compared to unentangled lattice-based interferometers after accounting for primary sources of decoherence.
We report on the use of an ultracold ensemble of 87 Rb atoms trapped in a vertical lattice as a source for a quantum force sensor based on a Ramsey–Raman type interferometer. We reach spatial resolution in the low micrometer range in the vertical direction thanks to evaporative cooling down to ultracold temperatures in a crossed optical dipole trap. In this configuration, the coherence time of the atomic ensemble is degraded by inhomogeneous dephasing arising from atomic interactions. By weakening the confinement in the transverse direction only, we dilute the cloud and drastically reduce the strength of these interactions, without affecting the vertical resolution. This allows us to maintain an excellent relative sensitivity on the Bloch frequency, which is related to the local gravitational force, of 5 × 10 −6 at 1 s which integrates down to 8 × 10 −8 after one hour averaging time.