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Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

  • Atoms, Molecules, Optics
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Abstract

The universal three-body dynamics in ultracold binary gases confined to one-dimensional motion is studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass m and a different particle of mass m 1, whose interaction is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio m/m 1 at which three-body states occur and the (2 + 1)-scattering length vanishes are determined for both zero and infinite interaction strength λ1 of the identical particles. A number of exact results are listed and asymptotic dependences for both m/m 1 → ∞ and λ1 → −∞ are derived. Combining the numerical and analytic results, we deduce a schematic diagram showing the number of three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and the interaction-strength ratio. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.

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References

  1. A. Görlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. Rosenband, and W. Ketterle, Phys. Rev. Lett. 87, 130 402 (2001).

    Google Scholar 

  2. D. Rychtarik, B. Engeser, H.-C. Nägerl, and R. Grimm, Phys. Rev. Lett. 92, 173 003 (2004).

    Google Scholar 

  3. D. S. Petrov, M. Holzmann, and G. V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000).

    Article  ADS  Google Scholar 

  4. C. Mora, R. Egger, A. O. Gogolin, and A. Komnik, Phys. Rev. Lett. 93, 170 403 (2004).

    Google Scholar 

  5. C. Mora, R. Egger, and A. O. Gogolin, Phys. Rev. A: At., Mol., Opt. Phys. 71, 052 705 (2005).

    Google Scholar 

  6. V. A. Yurovsky, A. Ben-Reuven, and M. Olshanii, Phys. Rev. Lett. 96, 163 201 (2006).

    Google Scholar 

  7. M. Rizzi and A. Imambekov, Phys. Rev. A: At., Mol., Opt. Phys. 77, 023 621 (2008).

    Google Scholar 

  8. A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 93, 106 803 (2004).

    Google Scholar 

  9. A. F. Slachmuylders, B. Partoens, W. Magnus, and F. M. Peeters, Phys. Rev. B: Condens. Matter 76, 075405 (2007).

    Google Scholar 

  10. O. Olendski and L. Mikhailovska, Phys. Rev. B: Condens. Matter 77, 174 405 (2008).

    Google Scholar 

  11. H. Moritz, T. Stöferle, K. Günter, M. Köhl, and T. Esslinger, Phys. Rev. Lett. 94, 210 401 (2005).

    Google Scholar 

  12. L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, Nature (London) 443, 312 (2006).

    Article  ADS  Google Scholar 

  13. C. Ospelkaus, S. Ospelkaus, K. Sengstock, and K. Bongs, Phys. Rev. Lett. 96, 020 401 (2006).

    Google Scholar 

  14. T. Karpiuk, M. Brewczyk, M. Gajda, and K. Rzazewski, J. Phys. B: At., Mol. Opt. Phys. 38, L215 (2005).

    Article  ADS  Google Scholar 

  15. Y. Shin, M. W. Zwierlein, C. H. Schunck, A. Schirotzek, and W. Ketterle, Phys. Rev. Lett. 97, 030 401 (2006).

    Google Scholar 

  16. F. Chevy, Phys. Rev. Lett. 96, 130 401 (2006).

    Google Scholar 

  17. B. Deh, C. Marzok, C. Zimmermann, and P. W. Courteille, Phys. Rev. A: At., Mol., Opt. Phys. 77, 010701 (2008).

    Google Scholar 

  18. M. Taglieber, A.-C. Voigt, T. Aoki, T. W. Hänsch, and K. Dieckmann Phys. Rev. Lett. 100, 010401 (2008).

  19. S. Capponi, G. Roux, P. Lecheminant, P. Azaria, E. Boulat, and S. R. White, Phys. Rev. A: At., Mol., Opt. Phys. 77, 013624 (2008).

    Google Scholar 

  20. S. Zöllner, H.-D. Meyer, and P. Schmelcher, Phys. Rev. A: At., Mol., Opt. Phys. 78, 013629 (2008).

    Google Scholar 

  21. H. D. Cornean, P. Duclos, and B. Ricaud, Few-Body Syst. 38, 125 (2006).

    Article  ADS  Google Scholar 

  22. N. P. Mehta, B. D. Esry, and C. H. Greene, Phys. Rev. A: At., Mol., Opt. Phys. 76, 022711 (2007).

    Google Scholar 

  23. N. P. Mehta and J. R. Shepard, Phys. Rev. A: At., Mol., Opt. Phys. 72, 032728 (2005).

    Google Scholar 

  24. A. Amaya-Tapia, S. Y. Larsen, and J. Popiel, Few-Body Syst. 23, 87 (1998).

    Article  ADS  Google Scholar 

  25. A. Amaya-Tapia, G. Gasaneo, S. Ovchinnikov, J. H. Macek, and S. Y. Larsen, J. Math. Phys. (Melville, NY) 45, 3533 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. O. I. Kartavtsev and A. V. Malykh, Phys. Rev. A: At., Mol., Opt. Phys. 74, 042506 (2006).

    Google Scholar 

  27. J. B. McGuire, J. Math. Phys. 5, 622 (1964).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. Y.-Q. Li, S.-J. Gu, Z.-J. Ying, and U. Eckern, Europhys. Lett. 61, 368 (2003).

    Article  ADS  Google Scholar 

  30. M. D. Girardeau and A. Minguzzi, Phys. Rev. Lett. 99, 230402 (2007).

    Google Scholar 

  31. M. B. Zvonarev, V. V. Cheianov, and T. Giamarchi, Phys. Rev. Lett. 99, 240402 (2007).

    Google Scholar 

  32. X.-W. Guan, M. T. Batchelor, and M. Takahashi, Phys. Rev. A: At., Mol., Opt. Phys. 76, 043617 (2007).

    Google Scholar 

  33. M. Olshanii, Phys. Rev. Lett. 81, 938 (1998).

    Article  ADS  Google Scholar 

  34. Y. N. Demkov and V. N. Ostrovskii, Zero-Range Potentials and Their Applications in Atomic Physics (Plenum, New York, 1988).

    Google Scholar 

  35. K. Wódkiewicz, Phys. Rev. A: At., Mol., Opt. Phys. 43, 68 (1991).

    ADS  Google Scholar 

  36. O. I. Kartavtsev, Few-Body Syst., Suppl. 10, 199 (1999).

    Google Scholar 

  37. O. I. Kartavtsev and A. V. Malykh, J. Phys. B: At., Mol. Opt. Phys. 40, 1429 (2007).

    Article  ADS  Google Scholar 

  38. J. H. Macek, J. Phys. B: At. Mol. Phys. 1, 831 (1968).

    Article  ADS  Google Scholar 

  39. M. Girardeau, J. Math. Phys. 1, 516 (1960).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. O. I. Kartavtsev and A. V. Malykh, Pis’ma Zh. Éksp. Teor. Fiz. 86(10), 713 (2007) [JETP Lett. 86 (10), 625 (2007)].

    Google Scholar 

  41. M. Gaudin and B. Derrida, J. Phys. (Paris) 36, 1183 (1975).

    Google Scholar 

  42. C. M. Rosenthal, J. Chem. Phys. 55, 2474 (1971).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Kaluga oblast, 141980, Russia

    O. I. Kartavtsev & A. V. Malykh

  2. University of South Africa 0003, Pretoria, South Africa

    S. A. Sofianos

Authors
  1. O. I. Kartavtsev
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  2. A. V. Malykh
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  3. S. A. Sofianos
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Correspondence to A. V. Malykh.

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Kartavtsev, O.I., Malykh, A.V. & Sofianos, S.A. Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement. J. Exp. Theor. Phys. 108, 365–373 (2009). https://doi.org/10.1134/S1063776109030017

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  • DOI: https://doi.org/10.1134/S1063776109030017

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