Twin Matter Waves for Interferometry Beyond the Classical Limit

An entangled state of up to 10,000 atoms is used to enhance the resolution of an atomic interferometer. Interferometers with atomic ensembles are an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to 104 pair-correlated atoms with an interferometric sensitivity −1.61−1.1+0.98decibels beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers.

[1]  Klauder,et al.  SU(2) and SU(1,1) interferometers. , 1986, Physical review. A, General physics.

[2]  Klauder,et al.  SU(2) and SU(1,1) interferometers. , 1986, Physical review. A, General physics.

[3]  M. Oberthaler,et al.  Nonlinear atom interferometer surpasses classical precision limit , 2010, Nature.

[4]  Ulrich Hohenester,et al.  Twin-atom beams , 2010, 1012.2348.

[5]  V. Vuletić,et al.  Erratum: Implementation of Cavity Squeezing of a Collective Atomic Spin [Phys. Rev. Lett. 104 , 073602 (2010)] , 2011 .

[6]  James K Thompson,et al.  Conditional spin squeezing of a large ensemble via the vacuum Rabi splitting. , 2011, Physical review letters.

[7]  Augusto Smerzi,et al.  Not all pure entangled states are useful for sub-shot-noise interferometry , 2009, 0912.4349.

[8]  J J Arlt,et al.  Multiresonant spinor dynamics in a Bose-Einstein condensate. , 2009, Physical review letters.

[9]  P. Meystre,et al.  Creating macroscopic atomic Einstein-Podolsky-Rosen states from Bose-Einstein condensates. , 2000, Physical review letters.

[10]  M. Oberthaler,et al.  Squeezing and Entanglement in a Bose-Einstein Condensate , 2010 .

[11]  J I Cirac,et al.  Squeezing and entanglement of atomic beams. , 2000, Physical review letters.

[12]  V. Vuletić,et al.  Implementation of cavity squeezing of a collective atomic spin. , 2009, Physical review letters.

[13]  R. Wynands,et al.  Atomic fountain clocks , 2005 .

[14]  Jian-Wei Pan,et al.  De Broglie wavelength of a non-local four-photon state , 2003, Nature.

[15]  M. Modugno,et al.  Atom Interferometry with a Weakly Interacting Bose Einstein Condensate , 2008 .

[16]  Norman F. Ramsey,et al.  A Molecular Beam Resonance Method with Separated Oscillating Fields , 1950 .

[17]  Holland,et al.  Interferometric detection of optical phase shifts at the Heisenberg limit. , 1993, Physical review letters.

[18]  Lipo Wang,et al.  Observation of Four-Photon Interference with a Beam Splitter by Pulsed Parametric Down-Conversion , 1999 .

[19]  Jian-Wei Pan,et al.  De Broglie wavelength of a non-local four-photon state , 2003, Nature.

[20]  M. W. Mitchell,et al.  Super-resolving phase measurements with a multiphoton entangled state , 2004, Nature.

[21]  D. Guéry-Odelin,et al.  Strong saturation absorption imaging of dense clouds of ultracold atoms. , 2007, Optics letters.

[22]  Y. Silberberg,et al.  High-NOON States by Mixing Quantum and Classical Light , 2010, Science.

[23]  C. Bordé.  Atomic interferometry with internal state labelling , 1989 .

[24]  J J Arlt,et al.  Parametric amplification of vacuum fluctuations in a spinor condensate. , 2009, Physical review letters.

[25]  L. Pezzè,et al.  Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles. , 2010, Physical review letters.

[26]  André Clairon,et al.  Quantum projection noise in an atomic fountain: a high stability cesium frequency standard , 1999 .

[27]  C. Monroe,et al.  Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. , 2001, Physical review letters.

[28]  Yun Li,et al.  Atom-chip-based generation of entanglement for quantum metrology , 2010, Nature.

[29]  Teich,et al.  Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics. , 1989, Physical review. A, General physics.

[30]  K. Eckert,et al.  Differential atom interferometry beyond the standard quantum limit (10 pages) , 2006 .

[31]  L. Mandel,et al.  Sub-shot-noise interferometric measurements with two-photon states , 1998 .

[32]  R. B. Blakestad,et al.  Creation of a six-atom ‘Schrödinger cat’ state , 2005, Nature.

[33]  John L. Hall,et al.  Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons , 1998 .

[34]  J. V. L. PARRY,et al.  An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator , 1955, Nature.

[35]  B. Sanders,et al.  Asymptotic limits of SU(2) and SU(3) Wigner functions , 2001 .

[36]  Barnett,et al.  Quantum theory of optical phase correlations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[37]  L. Pezzè,et al.  Entanglement, nonlinear dynamics, and the heisenberg limit. , 2007, Physical review letters.

[38]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[39]  J J Arlt,et al.  Spontaneous breaking of spatial and spin symmetry in spinor condensates. , 2010, Physical review letters.

[40]  P. Windpassinger,et al.  Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit , 2008, Proceedings of the National Academy of Sciences.

[41]  Keiji Sasaki,et al.  Beating the Standard Quantum Limit with Four-Entangled Photons , 2007, Science.

[42]  Wineland,et al.  Optimal frequency measurements with maximally correlated states. , 1996, Physical review. A, Atomic, molecular, and optical physics.