OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 17569–17575

Exact density oscillations in the Tonks-Girardeau gas and their optical detection

Mihály G. Benedict, Csaba Benedek, and Attila Czirják  »View Author Affiliations

Optics Express, Vol. 18, Issue 16, pp. 17569-17575 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (743 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We construct the exact time dependent density profile for a superposition of the ground and singly excited states of a harmonically trapped one dimensional Bose gas in the limit of strongly interacting particles, the Tonks-Girardeau gas. We obtain analytic results that allows one to determine the number of particles in the gas, as well as the quantum amplitudes in the superposition, from measurement results in an off-resonant light scattering experiment.

© 2010 Optical Society of America

OCIS Codes
(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing
(140.7010) Lasers and laser optics : Laser trapping
(020.1475) Atomic and molecular physics : Bose-Einstein condensates
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:
Atomic and Molecular Physics

Original Manuscript: June 22, 2010
Manuscript Accepted: July 21, 2010
Published: July 30, 2010

Mihály G. Benedict, Csaba Benedek, and Attila Czirják, "Exact density oscillations in the Tonks-Girardeau gas and their optical detection," Opt. Express 18, 17569-17575 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. P. Gross, “Structure of a quantized vortex in boson systems,” Nuovo Cim. 20, 454 (1961). [CrossRef]
  2. L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961).
  3. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463 (1999). [CrossRef]
  4. E. B. Kolomeisky, T. J. Newman, J. P. Straley, and X. Qi, “Low-dimensional Bose liquids: Beyond the Gross-Pitaevskii approximation,” Phys. Rev. Lett. 85, 1146 (2000). [CrossRef] [PubMed]
  5. H. Moritz, T. Stöferle, M. Köhl, and T. Esslinger, “Exciting collective oscillations in a trapped 1D gas,” Phys. Rev. Lett. 91, 250402 (2003). [CrossRef]
  6. K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “Waveguide for Bose-Einstein condensates,” Phys. Rev. A 63, 031602 (2001). [CrossRef]
  7. A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Sum rule for the dynamical response of a confined Bose-Einstein condensed gas,” Phys. Rev. A 64, 033605 (2001). [CrossRef]
  8. C. Menotti, and S. Stringari, “Collective oscillations of a one-dimensional trapped Bose-Einstein gas,” Phys. Rev. A 66, 043610 (2002). [CrossRef]
  9. M. D. Girardeau, and E. M. Wright, “Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons,” Phys. Rev. Lett. 84, 5239 (2000). [CrossRef] [PubMed]
  10. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Folling, I. Cirac, G. V. Shlyapnikov, T. W. Hansch, and I. Bloch, “Tonks-Girardeau gas of ultracold atoms in an optical lattice,” Nature 429, 277 (2004). [CrossRef] [PubMed]
  11. T. Kinoshita, T. Wenger, and D. S. Weiss, “Observation of a one-dimensional Tonks-Girardeau Gas,” Science 305, 1125 (2004). [CrossRef] [PubMed]
  12. L. Tonks, “The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres,” Phys. Rev. 50, 955 (1936). [CrossRef]
  13. M. D. Girardeau, “Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension,” J. Math. Phys. 1, 516 (1960). [CrossRef]
  14. E. Lieb, and W. Liniger, “Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground,” State Phys. Rev. 130, 1605 (1963).
  15. C. J. Pethick, and H. Smith, Bose-Einstein condensation in dilute gases, (Cambridge, 2008). [CrossRef]
  16. I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008). [CrossRef]
  17. D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, “Regimes of quantum degeneracy in trapped 1D gases,” Phys. Rev. Lett. 85, 3745 (2000). [CrossRef] [PubMed]
  18. V. Dunjko, V. Lorent, and M. Olshanii, “Bosons in cigar-shaped traps: Thomas-Fermi Tonks-Girardean regime, and in between,” Phys. Rev. Lett. 86, 5413 (2001). [CrossRef] [PubMed]
  19. M. Olshanii, and V. Dunjko, “Short-distance correlation properties of the Lieb-Liniger system and momentum distributions of trapped one-dimensional atomic gases,” Phys. Rev. Lett. 91, 090401 (2003). [CrossRef] [PubMed]
  20. P. Pedri, and L. Santos, “Three-dimensional quasi-Tonks gas in a harmonic trap,” Phys. Rev. Lett. 91, 110401 (2003). [CrossRef] [PubMed]
  21. M. D. Girardeau, E. M. Wright, and J. M. Triscari, “Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap,” Phys. Rev. A 63, 033601 (2001). [CrossRef]
  22. I. S. Gradshtein, and I. M. Ryzhik, Table of Integrals, Series, and products, 7th ed. (Academic Press, 2007).
  23. O. Morice, Y. Castin, and J. Dalibard, “Refractive-index of a dilute Bose-gas,” Phys. Rev. A 51, 3896 (1995). [CrossRef] [PubMed]
  24. J. Javanainen, and J. Ruostekoski, “Off-resonance light-scattering from low-temperature Bose and Fermi gases,” Phys. Rev. A 52, 3033 (1995). [CrossRef] [PubMed]
  25. A. Csordás, R. Graham, and P. Szépfalusy, “Off-resonance light scattering from Bose condensates in traps,” Phys. Rev. A 54, R2543 (1996). [CrossRef] [PubMed]
  26. E. A. Ostrovskaya, and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12(1), 19 (2004). [CrossRef] [PubMed]
  27. I. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319 (2007). [CrossRef]
  28. H.-W. Cho, Y.-C. He, T. Peters, Y.-H. Chen, H.-C. Chen, S.-C. Lin, Y.-C. Lee, and I. A. Yu, “Direct Measurement of the Atom Number in a Bose Condensate,” Opt. Express 15(19), 12114 (2007). [CrossRef] [PubMed]
  29. Z. Dutton, M. Budde, C. Slowe, and L. Vestergaard Hau, “Observation of quantum shock waves created with ultra-compressed slow light pulses in a Bose-Einstein condensate,” Science 293, 663 (2001). [CrossRef] [PubMed]
  30. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Dover, New York, 1965).
  31. D. A. Steck, “Rubidium 87 D Line Data,” available at http://steck.us/alkalidata (rev. 2.1.2, 12 August 2009).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1.

Supplementary Material

» Media 1: MOV (208 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited