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Physical Review A

Sensitivity bounds of a spatial Bloch-oscillation atom interferometer

Ignacy Nałęcz, L. Masi, Giovanni Ferioli, Tommaso Petrucciani, M. Fattori, Jan Chwedeńczuk

Published Sep 11, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.102.033318

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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.
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.
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.
We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0.1 a_(0) and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry.
Atom interferometers exploit the wave nature of matter to measure inertial forces with high precision, but conventional light-pulse implementations typically require large free-fall distances and complex optical systems. Bloch-band interferometry offers an alternative architecture in which atoms remain confined within an optical lattice and interferometric operations are implemented through controlled transitions between Bloch bands. This thesis investigates Bloch-band interferometry with particular emphasis on robustness to phase decoherence and operation in the deep-lattice regime. The work begins with multi-well models that provide intuition for tunneling, interference, and phase coherence. Phase scrambling was introduced to model loss of coherence, demonstrating that interference contrast is reduced but not eliminated. These insights motivated a full momentum-space simulation of a Bloch-band Michelson interferometer, including splitting, transport, reflection, and recombination. Acceleration scans with site-to-site phase randomness showed that interferometric fringes and sensitivity persist even with reduced coherence. Building on this robustness, Bloch-band interferometry was extended to a deep optical lattice with depth of 27 times the recoil energy. Higher Bloch bands were used to define interferometric pathways, and machine-learned shaking functions were implemented to realize beamsplitter and mirror operations. The resulting deep-lattice interferometer exhibits acceleration-dependent population fringes and measurable sensitivity. To our knowledge, this work presents the first exploration of Bloch-band interferometry in the deep-lattice regime and demonstrates the first realization of a deep-lattice Bloch-band interferometer for inertial sensing. These results suggest that Bloch-band interferometry can remain operational in regimes approaching the insulating limit, providing a potential route toward compact and robust quantum inertial sensors.
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.
We realize an interferometer with an atomic Fermi gas trapped in an optical lattice under the influence of gravity. The single-particle interference between the eigenstates of the lattice results in macroscopic Bloch oscillations of the sample. The absence of interactions between fermions allows a time-resolved study of many periods of the oscillations, leading to a sensitive determination of the acceleration of gravity. The experiment proves the superiority of noninteracting fermions with respect to bosons for precision interferometry and offers a way for the measurement of forces with microscopic spatial resolution.