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Squeezing and entanglement in a Bose–Einstein condensate

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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 position3,4. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states5,6) 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 particles7,8,9, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.

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Figure 1: Observing spin squeezing in a Bose–Einstein condensate confined in a double- or six-well trap.
Figure 2: Number squeezing and phase coherence as a criterion for quantum metrology and entanglement.
Figure 3: Systematics of number squeezing and phase coherence during the splitting of a condensate.
Figure 4: Random loss restores Poissonian fluctuations.

Change history

  • 30 October 2008

    The AOP version of this paper contained inaccuracies in the main text. This was corrected for print on 30 October 2008.


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We gratefully acknowledge support from the DFG, GIF and EC (MIDAS STREP). J.E. acknowledges support from the EC Marie-Curie program. C.G. acknowledges support from the Landesgraduiertenförderung Baden-Württemberg.

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Correspondence to M. K. Oberthaler.

Supplementary information

Supplementary Information

This file contains a discussion of experimental techniques: (I) Calculation of the Number Squeezing Factor; (II) Atom Number Measurement and Calibration; (III) Measuring the Phase Coherence; and Supplementary Figures I and II with Legends (PDF 395 kb)

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Estève, J., Gross, C., Weller, A. et al. Squeezing and entanglement in a Bose–Einstein condensate. Nature 455, 1216–1219 (2008).

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