Skip to main content

Part of the book series: Springer Theses ((Springer Theses))

  • 835 Accesses

Abstract

Bose-Einstein condensation (BEC) of weakly interacting atomic gases was first experimentally observed in 1995 [1, 2]. In a non-interacting BEC, all atoms occupy the same single-particle wavefunction, and the total quantum state of the system is a simple product of the single-particle states. Weak interactions can be taken into account in a perturbative, mean-field fashion, and the description stays close to the product-state form.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Davis KB, Mewes M-O, Andrews MR, van Druten NJ, Durfee DS, Kurn DM, Ketterle W (1995) Bose-Einstein condensation in a gas of sodium atoms. Phys Rev Lett 75:3969

    Article  ADS  Google Scholar 

  2. Anderson M, Ensher JR, Matthews MR, Wieman CE, Cornell EA (1995) Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269:198–201

    Article  ADS  Google Scholar 

  3. Ketterle W, Durfee DS, Stamper-Kurn DM (1999) Making, probing and understanding Bose-Einstein condensates. In: Inguscio M, Stringari S, Wieman CE (eds) Bose-Einstein condensates in atomic gases. IOS Press, Amsterdam, pp 67–176

    Google Scholar 

  4. Pethick CJ, Smith H (2001) Bose-Einstein condensation in dilute gases. Cambridge University Press, Cambridge

    Book  Google Scholar 

  5. Bloch I, Dalibard J, Zwerger W (2008) Many-body physics with ultracold gases. Rev Mod Phys 80:885–964

    Article  ADS  Google Scholar 

  6. Bloch I, Dalibard J, Nascimbène S (2012) Quantum simulations with ultracold quantum gases. Nat Phys 8:267–276

    Article  Google Scholar 

  7. Greiner M, Mandel O, Esslinger T, Hänsch TW, Bloch I (2002) Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415:39–44

    Article  ADS  Google Scholar 

  8. Jördens R, Strohmaier N, Günter K, Moritz H, Esslinger T (2008) A Mott insulator of fermionic atoms in an optical lattice. Nature 455:204–207

    Article  ADS  Google Scholar 

  9. Schneider U, Hackermüller L, Will S, Best T, Bloch I, Costi TA, Helmes RW, Rasch D, Rosch A (2008) Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322:1520–1525

    Article  ADS  Google Scholar 

  10. Esslinger T (2010) Fermi-Hubbard physics with atoms in an optical lattice. Annu Rev Cond Mat 1:129–152

    Article  Google Scholar 

  11. Regal CA, Greiner M, Jin DS (2004) Observation of resonance condensation of fermionic atom pairs. Phys Rev Lett 92:040403

    Article  ADS  Google Scholar 

  12. Zwierlein M, Stan C, Schunck C, Raupach S, Kerman A, Ketterle W (2004) Condensation of pairs of fermionic atoms near a feshbach resonance. Phys Rev Lett 92:120403

    Article  ADS  Google Scholar 

  13. Randeria M, Zwerger W, Zwierlein M (eds) (2012) The BCS-BEC crossover and the unitary fermi gas. Lecture notes in physics, vol 836. Springer

    Google Scholar 

  14. Fisher MPA, Weichman PB, Grinstein G, Fisher DS (1989) Boson localization and the superfluid-insulator transition. Phys Rev B 40:546–570

    Article  ADS  Google Scholar 

  15. Jaksch D, Bruder C, Cirac JI, Gardiner C, Zoller P (1998) Cold bosonic atoms in optical lattices. Phys Rev Lett 81:3108–3111

    Article  ADS  Google Scholar 

  16. Hubbard J (1963) Electron correlations in narrow energy bands. Proc R Soc A 276:238–257

    Article  ADS  Google Scholar 

  17. Sachdev S (2011) Quantum phase transitions, 2nd edn. Cambridge University Press, Cambridge. ISBN 0521514681

    Google Scholar 

  18. Shin Y-I, Schunck CH, Schirotzek A, Ketterle W (2008) Phase diagram of a two-component fermi gas with resonant interactions. Nature 451:689–693

    Article  ADS  Google Scholar 

  19. Gemelke N, Zhang X, Hung C-L, Chin C (2009) In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460:995–998

    Article  ADS  Google Scholar 

  20. Nascimbène S, Navon N, Jiang KJ, Chevy F, Salomon C (2010) Exploring the thermodynamics of a universal fermi gas. Nature 463:1057–1060

    Article  ADS  Google Scholar 

  21. Haroche S (2012) Nobel lecture: controlling photons in a box and exploring the quantum to classical boundary

    Google Scholar 

  22. Wineland DJ (2012) Nobel lecture: superposition, entanglement, and raising Schroedinger’s Cat

    Google Scholar 

  23. Bakr WS, Gillen JI, Peng A, Fölling S, Greiner M (2009) A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462:74–77

    Article  ADS  Google Scholar 

  24. Bakr WS, Peng A, Tai ME, Ma R, Simon J, Gillen JI, Fölling S, Pollet L, Greiner M (2010) Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329:547–550

    Article  ADS  Google Scholar 

  25. Sherson JF, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S (2010) Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467:68–72

    Article  ADS  Google Scholar 

  26. Endres M, Cheneau M, Fukuhara T, Weitenberg C, Schauss P, Gross C, Mazza L, Banuls MC, Pollet L, Bloch I, Kuhr S (2011) Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334:200–203

    Article  ADS  Google Scholar 

  27. Endres SKM, Cheneau M, Fukuhara T, Weitenberg C, Schauss P, Gross C, Mazza L, Banuls MC, Pollet L, Bloch I (2013) Single-site- and single-atom-resolved measurement of correlation functions. Appl Phys B 113:27–39

    Article  ADS  Google Scholar 

  28. Anfuso F, Rosch A (2007) Fragility of string orders. Phys Rev B 76:085124

    Article  ADS  Google Scholar 

  29. den Nijs M, Rommelse K (1989) Preroughening transistions in crystal surfaces and valence-bond phases in quantum spin chains. Phys Rev B 40:4709

    Article  ADS  Google Scholar 

  30. Kitaev A, Preskill J (2006) Topological entanglement entropy. Phys Rev Lett 96:110404

    Article  MathSciNet  ADS  Google Scholar 

  31. Haegeman J, Pérez-García D, Cirac I, Schuch N (2012) Order parameter for symmetry-protected phases in one dimension. Phys Rev Lett 109:050402

    Article  ADS  Google Scholar 

  32. Berg E, Dalla Torre EG, Giamarchi T, Altman E (2008) Rise and fall of hidden string order of lattice bosons. Phys Rev B 77:245119

    Article  ADS  Google Scholar 

  33. Rath SP, Simeth W, Endres M, Zwerger W (2013) Non-local order in Mott insulators, duality and Wilson loops. Ann Phys 334:256–271

    Article  ADS  Google Scholar 

  34. Endres M, Fukuhara T, Pekker D, Cheneau M, Schauss P, Gross C, Demler E, Kuhr S, Bloch I (2012) The ’Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 487:454–458

    Article  ADS  Google Scholar 

  35. Chubukov AV, Sachdev S, Ye J (1994) Theory of two-dimensional quantum Heisenberg antiferromagnets with a nearly critical ground state. Phys Rev B 49:11919–11961

    Article  ADS  Google Scholar 

  36. Sachdev S (1999) Universal relaxational dynamics near two-dimensional quantum critical points. Phys Rev B 59:14054–14073

    Article  ADS  Google Scholar 

  37. Zwerger W (2004) Anomalous fluctuations in phases with a broken continuous symmetry. Phys Rev Lett 92:027203

    Article  ADS  Google Scholar 

  38. Podolsky D, Auerbach A, Arovas DP (2011) Visibility of the amplitude (Higgs) mode in condensed matter. Phys Rev B 84:174522

    Article  ADS  Google Scholar 

  39. Pollet L, Prokof’ev N (2012) Higgs mode in a two-dimensional superfluid. Phys Rev Lett 109:010401

    Article  ADS  Google Scholar 

  40. Cottingham D, Greenwood WN (2007) An introduction to the standard model of particle physics, 2nd edn. Cambridge University Press, Cambridge. ISBN 0521852498

    Google Scholar 

  41. Podolsky D, Sachdev S (2012) Spectral functions of the Higgs mode near two-dimensional quantum critical points. Phys Rev B 86:054508

    Article  ADS  Google Scholar 

  42. Stöferle T, Moritz H, Schori C, Köhl M, Esslinger T (2004) Transition from a strongly Interacting 1D superfluid to a Mott insulator. Phys Rev Lett 92:130403

    Article  ADS  Google Scholar 

  43. Cheneau M, Barmettler P, Poletti D, Endres M, Schauss P, Fukuhara T, Gross C, Bloch I, Kollath C, Kuhr S (2012) Light-cone-like spreading of correlations in a quantum many-body system. Nature 481:484–487

    Article  ADS  Google Scholar 

  44. Schauß P, Cheneau M, Endres M, Fukuhara T, Hild S, Omran A, Pohl T, Gross C, Kuhr S, Bloch I (2012) Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491:87–91

    Article  ADS  Google Scholar 

  45. Weitenberg C, Endres M, Sherson JF, Cheneau M, Schauß P, Fukuhara T, Bloch I, Kuhr S (2011) Single-spin addressing in an atomic Mott insulator. Nature 471:319–324

    Article  ADS  Google Scholar 

  46. Weitenberg C (2011) Single-atom resolved imaging and manipulation in an atomic Mott insulator. PhD thesis, Ludwig-Maximilians-Universität München

    Google Scholar 

  47. Fukuhara T, Kantian A, Endres M, Cheneau M, Schauss P, Hild S, Bellem D, Schollwöck U, Giamarchi T, Gross C, Bloch I, Kuhr S (2013) Quantum dynamics of a mobile spin impurity. Nat Phys 9:235–241

    Article  Google Scholar 

  48. Fukuhara T, Schauß P, Endres M, Hild S, Cheneau M, Bloch I, Gross C (2013) Microscopic observation of magnon bound states and their dynamics. Nature 502:76–79

    Article  ADS  Google Scholar 

  49. Simon J, Bakr WS, Ma R, Tai ME, Preiss PM, Greiner M (2011) Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472:307–312

    Article  ADS  Google Scholar 

  50. Bakr WS, Preiss PM, Tai ME, Ma R, Simon J, Greiner M (2011) Orbital excitation blockade and algorithmic cooling in quantum gases. Nature 480:500–503

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manuel Endres .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Endres, M. (2014). Introduction. In: Probing Correlated Quantum Many-Body Systems at the Single-Particle Level. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-05753-8_1

Download citation

Publish with us

Policies and ethics