1. Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany

Correspondence to: M. K. Oberthaler¹ Correspondence and requests for materials should be addressed to M.K.O. (Email: entanglement@matterwave.de).

Abstract

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means¹. This results in the standard quantum limit, which is reached in today's best available sensors of various quantities such as time² and position^{3, 4}. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states^{5, 6}) at the two input ports. Bose–Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles^{7, 8, 9}, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.

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