## Multi-mode description of an interacting Bose-Einstein condensate

Optics Express, Vol. 8, Issue 2, pp. 92-98 (2001)

http://dx.doi.org/10.1364/OE.8.000092

Enhanced HTML Acrobat PDF (207 KB)

### Abstract

We study the equilibrium dynamics of a weakly interacting Bose-Einstein condensate trapped in a box. In our approach we use a semiclassical approximation similar to the description of a multi-mode laser. In dynamical equations derived from a full *N*-body quantum Hamiltonian we substitute all creation (and annihilation) operators (of a particle in a given box state) by appropriate c-number amplitudes. The set of nonlinear equations obtained in this way is solved numerically. We show that on the time scale of a few miliseconds the system exhibits relaxation – reaches an equilibrium with populations of different eigenstates fluctuating around their mean values.

© Optical Society of America

**OCIS Codes**

(000.6590) General : Statistical mechanics

(000.6800) General : Theoretical physics

(270.0270) Quantum optics : Quantum optics

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

**ToC Category:**

Focus Issue: Quantum control of photons and matter

**History**

Original Manuscript: November 9, 2000

Published: January 15, 2001

**Citation**

Krzysztof Goral, Mariusz Gajda, and Kazimierz Rzazewski, "Multi-mode description of an interacting Bose-Einstein condensate," Opt. Express **8**, 92-98 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-2-92

Sort: Journal | Reset

### References

- M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, "Observation of Bose Einstein Condensation in a Dilute Atomic Vapor," Science 269, 198-201 (1995). [CrossRef] [PubMed]
- K.B. Davis, M. O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, "Bose Einstein condensation in a gas of sodium atoms," Phys. Rev. Lett. 75, 3969-3972 (1995). [CrossRef] [PubMed]
- C.C. Bradle , C.A. Sackett, J.J. Tollett, and R.G. Hulet, "Evidence of Bose Einstein condensation in an atomic gas with attractive interactions," Phys. Rev. Lett. 75, 1687-1690 (1995) and Erratum 79, 1170(E) (1997). [CrossRef] [PubMed]
- D.G. Fried, T.C. Killian, L. Willmann, D. Landhuis, S.C. Moss, D. Kleppner, and T.J. Greytak, "Bose Einstein condensation of atomic hydrogen," Phys. Rev. Lett. 81, 3811-3814 (1998). [CrossRef]
- P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzazewski, "Fourth statistical ensemble for the Bose Einstein condensate," Phys. Rev. Lett. 79, 1789-1792 (1997). [CrossRef]
- M. Gajda and K. Rzazewski, "Fluctuations of Bose Einstein condensate," Phys. Rev. Lett. 78, 2686-2689 (1997). [CrossRef]
- S. Grossmann and M. Holthaus, "Fluctuations of the particle number in a trapped Bose Einstein condensate," Phys. Rev. Lett. 79, 3557-3560 (1997). [CrossRef]
- S. Grossmann and M. Holthaus, "Maxwell's Demon at work: Two t pes of Bose condensate fluctuations in power law traps," Opt. Express 1, 262-271 (1997), http://www.opticsexpress.org/oearchive/source/2288.htm [CrossRef] [PubMed]
- H. D. Politzer, "Condensate fluctuations of a trapped, ideal Bose gas," Phys. Rev. A 54, 5048-5054 (1996). [CrossRef] [PubMed]
- M. Wilkens and C. Weiss, "Particle number fluctuations in an ideal Bose gas," J. Mod. Opt. 44, 1801-1814 (1997). [CrossRef]
- M. Wilkens and C. Weiss, "Particle number counting statistics in ideal Bose gases," Opt. Express 1, 272-283 (1997), http://www.opticsexpress.org/oearchive/source/2372.htm [CrossRef] [PubMed]
- S. Giorgini, L.P. Pitaevskii, and S. Stringari, "Anomalous fluctuations of the condensate in interacting Bose gases," Phys. Rev. Lett 80, 5040-5043 (1998). [CrossRef]
- Z.Idziaszek, M.Gajda, P. Navez, M. Wilkens, and K.Rzazewski, "Fluctuations of the weakly interacting Bose Einstein condensate," Phys. Rev. Lett. 82, 4376-4379 (1999). [CrossRef]
- F. Meier and W. Zwerger, "Anomalous condensate fluctuations in strongly interacting superfluids," Phys. Rev. A 60, 5133-5135 (1999). [CrossRef]
- V.V. Kocharovsk , V.V. Kocharovsk , and M.O. Scull , "Condensate statistics in interacting and ideal dilute Bose gases," Phys. Rev. Lett. 84, 2306-2309 (2000). [CrossRef] [PubMed]
- F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, "Theory of Bose Einstein condensation in trapped gases," Rev. Mod. Phys. 71, 463-512 (1999). [CrossRef]
- R. Graham, "Condensate fluctuations in finite Bose Einstein condensates at finite temperature," Phys. Rev. A 62, 023609 (2000). [CrossRef]
- R. Graham, "Decoherence of Bose Einstein condensates in traps at finite temperature," Phys. Rev. Lett. 81, 5262-5265 (1998). [CrossRef]
- C.W. Gardiner and P. Zoller, "Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential," Phys. Rev. A 55, 2902-2921 (1997). [CrossRef]
- D. Jaksch, C.W. Gardiner, and P. Zoller, "Quantum kinetic theory. 2.Simulation of the quantum Boltzmann master equation," Phys. Rev. A 56, 575- 586 (1997). [CrossRef]
- R. Walser, J. Williams, J. Cooper, and M. Holland, "Quantum kinetic theory for a condensed bosonic gas," Phys. Rev. A 59, 3878-3889 (1999). [CrossRef]
- R. Walser, J. Williams, and M. Holland, "Reversible and irreversible evolution of a condensed bosonic gas," preprint cond mat/0004257, http://xxx.lanl.gov/abs/cond mat/0004257
- The case of boundary conditions different from the periodic ones (e.g. a rectangular trap) presents an interesting and challenging problem. In this case there are no universal eigenstates of a one-particle density matrix and therefore the definition of a condensate is unclear.
- A.L. Fetter and J.D.Walecka, Quantum theory of many-particle systems (McGraw Hill, New York, 1991).
- E. Fermi, J. Pasta, and S. Ulam, "Studies of Nonlinear Problems. I," in Collected Papers of Enrico Fermi (Accademia Nazionale dei Lincei and University of Chicago, Roma, 1965), Vol. II, p. 978.
- P. Villain and M. Lewenstein, "Fermi Pasta Ulam problem revisited with a Bose Einstein condensate," Phys. Rev. A 62, 043601 (2000). [CrossRef]
- F.M. Izrailev and B.V. Chirikov, "Statistical properties of a nonlinear string," Dokl. Akad. Nauk SSSR 166, 57-59 (1966) [Sov. Phys. Dokl. 11, 30-32 (1966)].
- J.H. Eberly, N.B. Narozhny, and J.J. Sanchez Mondragon, "Periodic spontaneous collapse and revival in a simple quantum model," Phys. Rev. Lett. 44, 1323-1326 (1980). [CrossRef]
- In a recent preprint M.J. Davis, S.A. Morgan, and K. Burnett, "Simulations of Bose fields at finite temperature," preprint cond-mat/0011431, http://xxx.lanl.gov/abs/cond mat/0011431, using similar methods, the authors establish a link between the energy and the temperature for temperatures below the critical region.
- K. G�ral, M.Gajda, and K. Rzazewski, "Multi-mode dynamics of a coupled ultracold atomic molecular system," preprint cond-mat/0006192, http://xxx.lanl.gov/abs/cond mat/0006192

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.