Quantum measurement in a tangle

Atom interferometers, which rely on the wave properties of particles, are used in a variety of ultra-high-precision measurements, from determining the gravitational constant to defining the time standard. The precision of interferometers is generally limited by classical statistics, arising from the finite number of atoms used in the experiment. Two papers in this issue demonstrate the potential of 'spin-squeezing' in Bose–Einstein condensates (BECs) to facilitate measurements that are more precise than classical statistics allow. Using a specially prepared BEC as the input to an interferometer, Gross et al. beat the classical precision limit. In the second study, Riedel et al. create similar 'spin-squeezed' states in a BEC confined to an 'atom chip' by controlling elastic collisional interactions with a state-dependent potential. This demonstration of multi-particle entanglement on a chip raises the prospect of chip-based portable atomic clocks that also beat the classical precision limits.

News and Views: Quantum measurement: A condensate's main squeeze

Entanglement between particles permits the quantum uncertainty in one variable to be reduced at the cost of increasing that in another. Condensates are an ideal system in which this technique can be studied.

Charles A. Sackett

doi:10.1038/4641133a

Full Text | PDF (1,050K)

Letter: Nonlinear atom interferometer surpasses classical precision limit

C. Gross, T. Zibold, E. Nicklas, J. Estève & M. K. Oberthaler

doi:10.1038/nature08919

First paragraph | Full Text | PDF (671K) | Supplementary information

Letter: Atom-chip-based generation of entanglement for quantum metrology

Max F. Riedel, Pascal Böhi, Yun Li, Theodor W. Hänsch, Alice Sinatra & Philipp Treutlein

doi:10.1038/nature08988

First paragraph | Full Text | PDF (385K) | Supplementary information

Nature 464, 1165-1169 (22 April 2010) | doi:10.1038/nature08919; Received 18 November 2009; Accepted 4 February 2010; Published online 31 March 2010

Nonlinear atom interferometer surpasses classical precision limit

C. Gross¹, T. Zibold¹, E. Nicklas¹, J. Estève^1,² & M. K. Oberthaler¹

Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
Present address: Laboratoire Kastler Brossel, CNRS, UPMC, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.

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

Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements^1,². Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest³. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose–Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states^4,^5,^6,^7,⁸. Extending quantum interferometry⁹ to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the ‘one-axis-twisting’ scheme¹⁰ and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11–15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms¹⁶.

Nature 464, 1170-1173 (22 April 2010) | doi:10.1038/nature08988; Received 18 November 2009; Accepted 10 March 2010; Published online 31 March 2010

Atom-chip-based generation of entanglement for quantum metrology

Max F. Riedel^1,², Pascal Böhi^1,², Yun Li^3,⁴, Theodor W. Hänsch^1,², Alice Sinatra³ & Philipp Treutlein^1,^2,⁵

Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
Laboratoire Kastler Brossel, ENS, 24 rue Lhomond, F-75005 Paris, France
State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, China
Departement Physik, Universität Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Correspondence to: Alice Sinatra³Philipp Treutlein^1,^2,⁵ Correspondence and requests for materials should be addressed to P.T. (Email: philipp.treutlein@unibas.ch) and A.S. (Email: alice.sinatra@lkb.ens.fr).

Atom chips provide a versatile quantum laboratory for experiments with ultracold atomic gases¹. They have been used in diverse experiments involving low-dimensional quantum gases², cavity quantum electrodynamics³, atom–surface interactions^4,⁵, and chip-based atomic clocks⁶ and interferometers^7,⁸. However, a severe limitation of atom chips is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations⁹, quantum information processing¹⁰ and quantum metrology¹¹. Here we report the experimental generation of multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential¹². We use this technique to generate spin-squeezed states of a two-component Bose–Einstein condensate¹³; such states are a useful resource for quantum metrology. The observed reduction in spin noise of -3.7 ± 0.4 dB, combined with the spin coherence, implies four-partite entanglement between the condensate atoms¹⁴; this could be used to improve an interferometric measurement by -2.5 ± 0.6 dB over the standard quantum limit¹⁵. Our data show good agreement with a dynamical multi-mode simulation¹⁶ and allow us to reconstruct the Wigner function¹⁷ of the spin-squeezed condensate. The techniques reported here could be directly applied to chip-based atomic clocks, currently under development¹⁸.