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arXiv:1207.2123 · Physical Review A

Delocalization-enhanced Bloch oscillations and driven resonant tunneling in optical lattices for precision force measurements

Marco G. Tarallo, Andrea Alberti, N. Poli, Maria Luisa Chiofalo, F.-Y. Wang, Guglielmo Maria Tino

Published Sep 14, 2012• 47 citations
arXivHTMLPDF

Abstract

In this paper, we describe and compare different methods used for the accurate determination of forces acting on matter-wave packets in optical lattices. The quantum interference nature responsible for the production of both Bloch oscillations and coherent delocalization is investigated in detail. We study conditions for the optimal detection of Bloch oscillation for a thermal ensemble of cold atoms with a large velocity spread. We report on the experimental observation of resonant tunneling in an amplitude-modulated optical lattice up to the sixth harmonic with Fourier-limited linewidth. We then explore the fundamental and technical phenomena which limit both the sensitivity and the final accuracy of the atomic force sensor at a ${10}^{\ensuremath{-}7}$ precision level [Poli et al., Phys. Rev. Lett. 106, 038501 (2011)], with an analysis of the coherence time of the system. We address a few simple setup changes to go beyond the current accuracy.

DOI
10.1103/physreva.86.033615

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In this paper, we describe and compare different methods used for the accurate determination of forces acting on matter-wave packets in optical lattices. The quantum interference nature responsible for the production of both Bloch oscillations and coherent delocalization is investigated in detail. We study conditions for the optimal detection of Bloch oscillation for a thermal ensemble of cold atoms with a large velocity spread. We report on the experimental observation of resonant tunneling in an amplitude-modulated optical lattice up to the sixth harmonic with Fourier-limited linewidth. We then explore the fundamental and technical phenomena which limit both the sensitivity and the final accuracy of the atomic force sensor at a 10\ensuremath−7{10}^{\ensuremath{-}7}10\ensuremath−7 precision level [Poli et al., Phys. Rev. Lett. 106, 038501 (2011)], with an analysis of the coherence time of the system. We address a few simple setup changes to go beyond the current accuracy.
Bloch oscillations of atoms in optical lattices are a powerful technique that can dramatically boost the sensitivity of atom interferometers to a wide range of signals by large momentum transfer. To leverage this method to its full potential, an accurate theoretical description of losses and phases is required, going beyond existing treatments. Here, we present a comprehensive theoretical framework for Bloch-oscillation-enhanced atom interferometry and verify its accuracy through comparison with a numerical solution of the Schrödinger equation. Our approach establishes design criteria to reach the fundamental efficiency and accuracy limits of large momentum transfer using Bloch oscillations and allows us, in a broader context, to define the fundamental efficiency limit of the transport of neutral atoms using optical lattices. We compare these limits to the capabilities of current state-of-the-art experiments and make projections for the next generation of quantum sensors. Published by the American Physical Society 2024
Bloch oscillations of atoms in optical lattices are a powerful technique that can boost the sensitivity of atom interferometers to a wide range of signals by large momentum transfer. To leverage this method to its full potential, an accurate theoretical description of losses and phases is needed going beyond existing treatments. Here, we present a comprehensive theoretical framework for Bloch-oscillation-enhanced atom interferometry and verify its accuracy through comparison with an exact numerical solution of the Schrödinger equation. Our approach establishes design criteria to reach the fundamental efficiency and accuracy limits of large momentum transfer using Bloch oscillations. We compare these limits to the case of current state-of-the-art experiments and make projections for the next generation of quantum sensors.
Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here observed by monitoring the in situ wave-packet extent. By varying the modulation frequency, we find resonances at integer multiples of the Bloch frequency. The resonances show a Fourier-limited width for interrogation times up to 2 s. This can also be used to determine the gravity acceleration with ppm resolution.
We study the ultimate bounds on the sensitivity of a Bloch-oscillation atom interferometer where the external force is estimated from the measurement of the on-site atomic density. For external forces such that the energy difference between lattice sites is smaller than the tunneling energy, the atomic wave function spreads over many lattice sites, increasing the separation between the occupied modes of the lattice and naturally enhancing the sensitivity of the interferometer. To investigate the applicability of this scheme we estimate the effect of uncontrolled fluctuations of the tunneling energy and the finite resolution of the atom detection. Our analysis shows that a horizontal lattice combined with a weak external force allow for high sensitivities. Therefore, this setup is a promising solution for compact devices or for measurements with high spatial resolution.
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We study the propagation of cold-atom wave packets in an interferometer with a Mach-Zehnder topology based on the dynamical phase of Bloch oscillation in a weakly forced optical lattice with a narrow potential barrier that functions as a cold-atom wave-packet splitter. We calculate analytically the atomic wave function, and show that the expected number of atoms in the two outputs of the interferometer oscillates rapidly as a function of the angle between the potential barrier and the forcing direction with period proportional to the external potential difference across a lattice spacing divided by the lattice band energy scale. The interferometer can be used as a high-precision force probe whose principle of operation is different from current interferometers based on the overall position of Bloch oscillating wave packets.