Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates

Journal of Physics B: Atomic, Molecular and Optical Physics

Volumn 45, Issue 10, 2012, Pages

  Gross, Christian ^a,b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC SYSTEM; BOSE-EINSTEIN CONDENSATES; DIRECT DETECTION; ENTANGLED STATE; EXPERIMENTAL REQUIREMENTS; HYPERFINES; INTERFEROMETRIC SENSOR; LIGHT FIELDS; NOISE LIMIT; POTENTIAL IMPACTS; QUANTUM METROLOGY; SPIN SQUEEZING; SQUEEZED STATE;

BOSE-EINSTEIN CONDENSATION; MEASUREMENTS; MECHANICS; QUANTUM OPTICS; STEAM CONDENSERS; UNITS OF MEASUREMENT;

QUANTUM ENTANGLEMENT;

EID: 84862082737     PISSN: 09534075     EISSN: 13616455     Source Type: Journal    
DOI: 10.1088/0953-4075/45/10/103001     Document Type: Review

References (127)

1. Cramer H 1946 Mathematical Methods of Statistics (Princeton, NJ: Princeton University Press)
2. Braunstein S L and Caves C M 1994 Statistical distance and the geometry of quantum states Phys. Rev. Lett. 72 343943
3. Santarelli C, Laurent P, Lemonde P, Clairon A, Mann A G, Chang S, Luiten A N and Salomon C 1999 Quantum projection noise in an atomic fountain: a high stability cesium frequency standard Phys. Rev. Lett. 82 461922
4. Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J and Mavalvala N 2008 A quantum-enhanced prototype gravitational-wave detector Nature Phys. 4 4726
5. Arcizet O, Cohadon P-F, Briant T, Pinard M, Heidmann A, Mackowski J-M, Michel C, Pinard L, Français O and Rousseau L 2006 High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor Phys. Rev. Lett. 97 133601
6. Wasilewski W, Jensen K, Krauter H, Renema J J, Balabas M V and Polzik E S 2010 Quantum noise limited and entanglement-assisted magnetometry Phys. Rev. Lett. 104 133601
7. Giovannetti V, Lloyd S and Maccone L 2006 Quantum metrology Phys. Rev. Lett. 96 010401
8. Walls D F 1983 Squeezed states of light Nature 306 1416
9. Slusher R, Hollberg L, Yurke B, Mertz J and Valley J 1985 Observation of squeezed states generated by four-wave mixing in an optical cavity Phys. Rev. Lett. 55 240912
10. Kitagawa M and Ueda M 1993 Squeezed spin states Phys. Rev. A 47 513843
11. Wineland D J, Bollinger J J, Itano W M and Heinzen D J 1994 Squeezed atomic states and projection noise in spectroscopy Phys. Rev. A 50 6788
12. Sorensen A S, Duan L M, Cirac J I and Zoller P 2001 Many-particle entanglement with BoseEinstein condensates Nature 409 63
13. Caves C M 1981 Quantum-mechanical noise in an interferometer Phys. Rev. D 23 1693708
14. Wang X G and Sanders B C 2003 Relations between bosonic quadrature squeezing and atomic spin squeezing Phys. Rev. A 68 033812
15. Dalton B J and Ghanbari S 2012 Two mode theory of BoseEinstein condensates: interferometry and the Josephson model J. Mod. Opt. 59 287
16. Arecchi F T, Courtens E and Gilmore R 1972 Atomic coherent states in quantum optics Phys. Rev. A 6 2211
17. Sakurai J J 1993 Modern Quantum Mechanics (New York: Addison-Wesley)
18. Radcliffe J M 1971 Some properties of coherent spin states J. Phys. A: Gen. Phys. 4 31323
19. Zhang W M, Feng D H and Gilmore R 1990 Coherent states - theory and some applications Rev. Mod. Phys. 62 867927
20. Giovannetti V and Lloyd S 2004 Quantum-enhanced measurements: beating the standard quantum limit Science 306 1330
21. Lee C T 1984 Q-representation of the atomic coherent states and the origin of fluctuations in superfluorescence Phys. Rev. A 30 330810
22. Leggett A J 2001 BoseEinstein condensation in the alkali gases: some fundamental concepts Rev. Mod. Phys. 73 30756
23. Amico L, Fazio R, Osterloh A and Vedral V 2008 Entanglement in many-body systems Rev. Mod. Phys. 80 51776
24. Terra Cunha M O, Dunningham J A and Vedral V 2007 Entanglement in single-particle systems Proc. R. Soc. A 463 2277
25. Goold J, Heaney L, Busch T and Vedral V 2009 Detection and engineering of spatial mode entanglement with ultracold bosons Phys. Rev. A 80 022338
26. Sorensen A S and Molmer K 2001 Entanglement and extreme spin squeezing Phys. Rev. Lett. 86 44314
27. Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Quantum entanglement Rev. Mod. Phys. 81 865942
28. Plenio M B and Virmani S 2007 An introduction to entanglement measures Quantum Inform. Comput. 7 151
29. Benatti F, Floreanini R and Marzolino U 2010 Sub-shot-noise quantum metrology with entangled identical particles Ann. Phys. 325 92435
30. Hines A P, McKenzie R H and Milburn G J 2003 Entanglement of two-mode BoseEinstein condensates Phys. Rev. A 67 013609
31. Hillery M and Zubairy M S 2006 Entanglement conditions for two-mode states Phys. Rev. Lett. 96 050503
32. Dowling M R, Doherty A C and Wiseman H M 2006 Entanglement of indistinguishable particles in condensed-matter physics Phys. Rev. A 73 052323
33. Gross C, Strobel H, Nicklas E, Zibold T, Bar-Gill N, Kurizki G and Oberthaler M K 2011 Atomic homodyne detection of continuous-variable entangled twin-atom states Nature 480 21923
34. Tóth G, Knapp C, Gühne O and Briegel H J 2007 Optimal spin squeezing inequalities detect bound entanglement in spin models Phys. Rev. Lett. 99 250405
35. Tóth G, Knapp C, Gühne O and Briegel H J 2009 Spin squeezing and entanglement Phys. Rev. A 79 042334
36. Korbicz J K, Gühne O, Lewenstein M, Haeffner H, Roos C F and Blatt R 2006 Generalized spin-squeezing inequalities in N-qubit systems: theory and experiment Phys. Rev. A 74 052319
37. Korbicz J K, Cirac J I and Lewenstein M 2005 Spin squeezing inequalities and entanglement of N qubit states Phys. Rev. Lett. 95 120502
38. Korbicz J K, Cirac J I and Lewenstein M 2005 Erratum: spin squeezing inequalities and entanglement of N qubit states Phys. Rev. Lett. 95 259901
39. Wang X G and Sanders B C 2003 Spin squeezing and pairwise entanglement for symmetric multiqubit states Phys. Rev. A 68 012101
40. Vidal J 2006 Concurrence in collective models Phys. Rev. A 73 062318
41. Ramsey N F 1949 A new molecular beam resonance method Phys. Rev. 67 996
42. Ramsey N F 1950 A molecular beam resonance method with separated oscillating fields Phys. Rev. 78 6959
43. Kasevich M A and Chu S 1992 Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer Appl. Phys. B 54 32132
44. Gustavson T L, Bouyer P and Kasevich M A 1997 Precision rotation measurements with an atom interferometer gyroscope Phys. Rev. Lett. 78 20469
45. Cronin A D, Schmiedmayer J and Pritchard D E 2009 Optics and interferometry with atoms and molecules Rev. Mod. Phys. 81 105129
46. Reichel J and Vuletic V 2011 Atom Chips (New York: Wiley-VCH)
47. Lee C, Huang J, Deng H, Dai H and Xu J 2012 Nonlinear quantum interferometry with Bose condensed atoms Front. Phys. 7 10930
48. Gati R, Albiez M, Fölling J, Hemmerling B and Oberthaler M K 2006 Realization of a single Josephson junction for BoseEinstein condensates Appl. Phys. B 82 20710
49. Pegg D T and Barnett S M 1989 Phase properties of the quantized single-mode electromagnetic field Phys. Rev. A 39 166575
50. Pezze L and Smerzi A 2009 Entanglement, nonlinear dynamics and the Heisenberg limit Phys. Rev. Lett. 102 100401
51. Leibfried D, Barrett M D, Schaetz T, Britton J, Chiaverini J, Itano W M, Jost J D, Langer C and Wineland D J 2004 Toward Heisenberg-limited spectroscopy with multiparticle entangled states Science 304 14768
52. Roos C F, Chwalla M, Kim K, Riebe M and Blatt R 2006 Designer atoms for quantum metrology Nature 443 3169
53. Nagata T, Okamoto R, O'Brien J L, Sasaki K and Takeuchi S 2007 Beating the standard quantum limit with four-entangled photons Science 316 7269
54. Meyer V, Rowe M, Kielpinski D, Sackett C, Itano W, Monroe C and Wineland D 2001 Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions Phys. Rev. Lett. 86 58703
55. Leroux I D, Schleier-Smith M H and Vuletic V 2010 Implementation of cavity squeezing of a collective atomic spin Phys. Rev. Lett. 104 73602
56. Schleier-Smith M H, Leroux I D and Vuletic V 2010 States of an ensemble of two-level atoms with reduced quantum uncertainty Phys. Rev. Lett. 104 73604
57. Leroux I D, Schleier-Smith M H and Vuletic V 2010 Orientation-dependent entanglement lifetime in a squeezed atomic clock Phys. Rev. Lett. 104 250801
58. Fernholz T, Krauter H, Jensen K, Sherson J F, Sorensen A S and Polzik E S 2008 Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement Phys. Rev. Lett. 101 73601
59. Appel J, Windpassinger P J, Oblak D, Hoff U B, Kjaergaard N and Polzik E S 2009 Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit Proc. Natl Acad. Sci. USA 106 109605
60. Vahlbruch H, Mehmet M, Chelkowski S, Hage B, Franzen A, Lastzka N, Gossler S, Danzmann K and Schnabel R 2008 Observation of squeezed light with 10 dB quantum-noise reduction Phys. Rev. Lett. 100 33602
61. Estève J, Gross C, Weller A, Giovanazzi S and Oberthaler M K 2008 Squeezing and entanglement in a BoseEinstein condensate Nature 455 12169
62. Gross C, Zibold T, Nicklas E, Estève J and Oberthaler M K 2010 Nonlinear atom interferometer surpasses classical precision limit Nature 464 1165
63. Lee H, Kok P and Dowling J P 2002 A quantum Rosetta stone for interferometry J. Mod. Opt. 49 232538
64. Bouyer P and Kasevich M A 1997 Heisenberg-limited spectroscopy with degenerate BoseEinstein gases Phys. Rev. A 56 R10836
65. Dowling J P 1998 Correlated input-port, matter-wave interferometer: quantum-noise limits to the atom-laser gyroscope Phys. Rev. A 57 473646
66. Bollinger J J, Itano W M, Wineland D J and Heinzen D J 1996 Optimal frequency measurements with maximally correlated states Phys. Rev. A 54 R464952
67. Holland M J and Burnett K 1993 Interferometric detection of optical phase shifts at the Heisenberg limit Phys. Rev. Lett. 71 13558
68. Dunningham J A, Burnett K and Barnett S M 2002 Interferometry below the standard quantum limit with BoseEinstein condensates Phys. Rev. Lett. 89 150401
69. Dunningham J A and Burnett K 2004 Sub-shot-noise-limited measurements with BoseEinstein condensates Phys. Rev. A 70 033601
70. Bücker R, Grond J, Manz S, Berrada T, Betz T, Koller C, Hohenester U, Schumm T, Perrin A and Schmiedmayer J 2011 Twin-atom beams Nature Phys. 7 60811
71. Lucke B et al 2011 Twin matter waves for interferometry beyond the classical limit Science 334 773
72. Pezze L, Collins L A, Smerzi A, Berman G P and Bishop A R 2005 Sub-shot-noise phase sensitivity with a BoseEinstein condensate MachZehnder interferometer Phys. Rev. A 72 043612
73. Bodet C, Estève J, Oberthaler M K and Gasenzer T 2010 Two-mode Bose gas: beyond classical squeezing Phys. Rev. A 81 063605
74. Grond J, Hohenester U, Mazets I and Schmiedmayer J 2010 Atom interferometry with trapped BoseEinstein condensates: impact of atomatom interactions New J. Phys. 12 065036
75. Pezze L, Smerzi A, Khoury G, Hodelin J F and Bouwmeester D 2007 Phase detection at the quantum limit with multiphoton MachZehnder interferometry Phys. Rev. Lett. 99 223602
76. Wootters W 1981 Statistical distance and Hilbert space Phys. Rev. D 23 35762
77. Helstrom C W 1976 Quantum Detection and Estimation Theory vol 1 (New York: Academic)
78. Hald J, Sorensen J L, Schori C and Polzik E S 1999 Spin squeezed atoms: a macroscopic entangled ensemble created by light Phys. Rev. Lett. 83 131922
79. Kuzmich A, Mandel L and Bigelow N P 2000 Generation of spin squeezing via continuous quantum nondemolition measurement Phys. Rev. Lett. 85 15947
80. Orzel C, Tuchman K, Fenselau M L, Yasuda M and Kasevich M 2001 Squeezed states in a BoseEinstein condensate Science 291 2386
81. Li W, Tuchman A, Chien H-C and Kasevich M 2007 Extended coherence time with atom-number squeezed states Phys. Rev. Lett. 98 040402
82. Gerbier F, Fölling S, Widera A, Mandel O and Bloch I 2006 Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition Phys. Rev. Lett. 96 090401
83. Jo G-B, Shin Y, Will S, Pasquini T A, Saba M, Ketterle W, Pritchard D E, Vengalattore M and Prentiss M 2007 Long phase coherence time and number squeezing of two BoseEinstein condensates on an atom chip Phys. Rev. Lett. 98 30407
84. Sebby-Strabley J, Brown B, Anderlini M, Lee P, Phillips W, Porto J and Johnson P 2007 Preparing and probing atomic number states with an atom interferometer Phys. Rev. Lett. 98 200405
85. Maussang K, Marti G E, Schneider T, Treutlein P, Li Y, Sinatra A, Long R, Estève J and Reichel J 2010 Enhanced and reduced atom number fluctuations in a BEC splitter Phys. Rev. Lett. 105 080403
86. Riedel M F, Böhi P, Li Y, Hänsch T W, Sinatra A and Treutlein P 2010 Atom-chip-based generation of entanglement for quantum metrology Nature 464 11703
87. Louchet-Chauvet A, Appel J, Renema J J, Oblak D, Kjaergaard N and Polzik E S 2010 Entanglement-assisted atomic clock beyond the projection noise limit New J. Phys. 12 065032
88. Hammerer K, Sorensen A S and Polzik E S 2010 Quantum interface between light and atomic ensembles Rev. Mod. Phys. 82 104193
89. Sorensen A S and Molmer K 1999 Spinspin interaction and spin squeezing in an optical lattice Phys. Rev. Lett. 83 22747
90. Milburn G J, Corney J, Wright E M and Walls D F 1997 Quantum dynamics of an atomic BoseEinstein condensate in a double-well potential Phys. Rev. A 55 431824
91. Steel M J and Collett M J 1998 Quantum state of two trapped BoseEinstein condensates with a Josephson coupling Phys. Rev. A 57 292030
92. Gross C 2010 Spin squeezing and non-linear atom interferometry with BoseEinstein condensates PhD Thesis University of Heidelberg
93. Gross C 2012 Spin Squeezing and Nonlinear Atom Interferometry with BoseEinstein Condensates (Springer Thesis) (Berlin: Springer)
94. Streltsov A I, Alon O E and Cederbaum L S 2007 Role of excited states in the splitting of a trapped interacting BoseEinstein condensate by a time-dependent barrier Phys. Rev. Lett. 99 030402
95. Li Y, Treutlein P, Reichel J and Sinatra A 2009 Spin squeezing in a bimodal condensate: spatial dynamics and particle losses Eur. Phys. J. B 68 36581
96. Ananikian D and Bergeman T 2006 GrossPitaevskii equation for Bose particles in a double-well potential: two-mode models and beyond Phys. Rev. A 73 013604
97. Zapata I, Sols F and Leggett A J 1998 Josephson effect between trapped BoseEinstein condensates Phys. Rev. A 57 R2831
98. Albiez M 2005 Observation of nonlinear tunneling of a BoseEinstein condensate in a single Josephson junction PhD Thesis University of Heidelberg
99. Levy S, Lahoud E, Shomroni I and Steinhauer J 2007 The a.c. and d.c. Josephson effects in a BoseEinstein condensate Nature 449 57983
100. Chin C, Grimm R and Julienne P 2010 Feshbach resonances in ultracold gases Rev. Mod. Phys. 82 1225
101. Pezze L, Smerzi A, Berman G P, Bishop A R and Collins L A 2006 Nonlinear beam splitter in BoseEinstein-condensate interferometers Phys. Rev. A 74 033610
102. Vandersypen L M K and Chuang I L 2004 NMR techniques for quantum control and computation Rev. Mod. Phys. 76 103769
103. Bachor H-A and Ralph T C 2004 A Guide to Experiments in Quantum Optics (New York: Wiley-VCH)
104. Wright E M, Walls D F and Garrison J C 1996 Collapses and revivals of BoseEinstein condensates formed in small atomic samples Phys. Rev. Lett. 77 215861
105. Yurke B and Stoler D 1986 Generating quantum-mechanical superpositions of macroscopically distinguishable states via amplitude dispersion Phys. Rev. Lett. 57 136
106. Greiner M, Mandel O, Hänsch T W and Bloch I 2002 Collapse and revival of the matter wave field of a BoseEinstein condensate Nature 419 514
107. Ferrini G, Minguzzi A and Hekking F W J 2008 Number squeezing, quantum fluctuations and oscillations in mesoscopic BoseJosephson junctions Phys. Rev. A 78 023606
108. Sinatra A and Castin Y 1998 Phase dynamics of BoseEinstein condensates: losses versus revivals Eur. Phys. J. D 4 24760
109. Zibold T, Nicklas E, Gross C and Oberthaler M K 2010 Classical bifurcation at the transition from Rabi to Josephson dynamics Phys. Rev. Lett. 105 204101
110. Micheli A, Jaksch D, Cirac J and Zoller P 2003 Many-particle entanglement in two-component BoseEinstein condensates Phys. Rev. A 67 013607
111. Lapert M, Ferrini G and Sugny D 2012 Optimal control of quantum superpositions in a bosonic Josephson junction Phys. Rev A 85 023611
112. Li Y, Castin Y and Sinatra A 2008 Optimum spin squeezing in BoseEinstein condensates with particle losses Phys. Rev. Lett. 100 210401
113. Sinatra A, Witkowska E, Dornstetter J-C, Li Y and Castin Y 2011 Limit of spin squeezing in finite-temperature BoseEinstein condensates Phys. Rev. Lett. 107 060404
114. Sinatra A, Dornstetter J-C and Castin Y 2012 Spin squeezing in BoseEinstein condensates: limits imposed by decoherence and non-zero temperature Front. Phys. 7 8697
115. Ketterle W, Durfee D S and Stamper-Kurn D M 1999 Making, probing and understanding BoseEinstein condensates arXiv:cond-mat/9904034v2
116. Gati R, Hemmerling B, Fölling J, Albiez M and Oberthaler M K 2006 Noise thermometry with two weakly coupled BoseEinstein condensates Phys. Rev. Lett. 96 130404
117. Bakr W S, Gillen J I, Peng A, Fölling S and Greiner M 2009 A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice Nature 462 74
118. Sherson J F, Weitenberg C, Endres M, Cheneau M, Bloch I and Kuhr S 2010 Single-atom-resolved fluorescence imaging of an atomic Mott insulator Nature 467 6872
119. Reinaudi G, Lahaye T, Wang Z and Guéry-Odelin D 2007 Strong saturation absorption imaging of dense clouds of ultracold atoms Opt. Lett. 32 31435
120. Itah A, Veksler H, Lahav O, Blumkin A, Moreno C, Gordon C and Steinhauer J 2010 Direct observation of a sub-poissonian number distribution of atoms in an optical lattice Phys. Rev. Lett. 104 113001
121. Whitlock S, Ockeloen C F and Spreeuw R J C 2010 Sub-Poissonian atom-number fluctuations by three-body loss in mesoscopic ensembles Phys. Rev. Lett. 104 120402
122. Albiez M, Gati R, Fölling J, Hunsmann S, Cristiani M and Oberthaler M K 2005 Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction Phys. Rev. Lett. 95 010402
123. Pitaevskii L P and Stringari S 2003 BoseEinstein Condensation (Oxford: Oxford University Press)
124. Pitaevskii L P and Stringari S 2001 Thermal versus quantum decoherence in double well trapped BoseEinstein condensates Phys. Rev. Lett. 87 180402
125. Gross C, Estève J, Oberthaler M K, Martin A and Ruostekoski J 2011 Local and spatially extended sub-Poisson atom-number fluctuations in optical lattices Phys. Rev. A 84 011609
126. Kaufman A M, Anderson R P, Hanna T M, Tiesinga E, Julienne P S and Hall D S 2009 Radio-frequency dressing of multiple Feshbach resonances Phys. Rev. A 80 050701
127. Gross C, Estève J, Weller A, Giovanazzi S and Oberthaler M K 2009 Squeezing and entanglement in a BoseEinstein condensate Laser Spectroscopy: Proc. 19th Int. Conf. (Singapore: World Scientific) pp 1928