# Tunneling of a Many-Boson System to Open Space Without a Threshold

- 411 Downloads

## Abstract

The scope of the present chapter is to analyze the many-body tunneling to open space process with numerically exact many-body computations done with the MCTDHB method. The tunneling process lies at the very heart of quantum mechanics and has been a matter of discussion since the advent of quantum mechanics. In contrast to the tunneling of single particles, nearly nothing is known about the many-body tunneling process. Here, the time-dependent many-boson Schrödinger equation of the process is solved for \(N=2,4,\) and \(N=101\) bosons numerically-exactly with the MCTDHB. It turns out that initially parabolically trapped and coherent samples gradually develop fragmentation in the process: the ejected particles lose their coherence both among each other and with the source. The whole process can be assembled by single particle emission processes which emerge from systems of different particle number. In each of these processes, an emitted boson converts the chemical potential of systems with decreasing particle number to a specific kinetic energy which manifests in the occurence of peaks in the momentum distributions. The prospects of the stystem for the use as a quantum simulator for ionization processes or as an atom laser are discussed.

## Keywords

Momentum Distribution Momentum Spectrum Tunneling Process Natural Occupation Characteristic Momentum## Supplementary material

## References

- 1.A.U.J. Lode, A.I. Streltsov, K. Sakmann, O.E. Alon, L.S. Cederbaum, How an interacting many-body system tunnels through a potential barrier to open space. Proc. Natl. Acad. Sci. USA
**109**, 13521 (2012)ADSCrossRefGoogle Scholar - 2.G. Gamow, Zur Quantentheorie Des Atomkernes. Z. F. Phys.
**51**(3–4), 204–212 (1928)Google Scholar - 3.B.S. Bhandari, Resonant tunneling and the bimodal symmetric fission of \(^{{258}}\)Fm. Phys. Rev. Lett.
**66**, 1034–1037 (1991)Google Scholar - 4.N. Takigawa, A.B. Balantekin, Quantum tunneling in nuclear fusion. Rev. Mod. Phys.
**70**, 77–100 (1998)Google Scholar - 5.J. Keller, J. Weiner, Direct measurement of the potential-barrier height in the \(B^1\Pi _u\) state of the sodium dimer. Phys. Rev. A
**29**, 2943–2945 (1984)Google Scholar - 6.M. Vatasescu et al., Multichannel tunneling in the Cs\(_2\)0\(_g^-\) photoassociation spectrum. Phys. Rev. A
**61**, 044701 (2000)Google Scholar - 7.R.W. Gurney, E.U. Condon, Quantum Mechanics and Radioactive Disintegration. Nature
**122**, 439 (1928)Google Scholar - 8.R.W. Gurney, E.U. Condon, Quantum Mechanics and Radioactive Disintegration. Phys. Rev.
**33**, 127–140 (1929)Google Scholar - 9.H.A. Kramers, Wellenmechanik und halbzählige Quantisierung. Zeitschr. F. Physik A
**39**(10–11), 828–840 (1926)Google Scholar - 10.M. Razavy,
*Quantum Theory of Tunneling*(World Scientific Publishing Co., Singapore, 2003)CrossRefzbMATHGoogle Scholar - 11.L.P. Pitaevskii, S. Stringari,
*Bose–Einstein Condensation*. (Oxford University Press, Oxford, 2003)Google Scholar - 12.E.H. Lieb, W. Liniger, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State. Phys. Rev.
**130**, 1605 (1963)Google Scholar - 13.E.H. Lieb, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum. Phys. Rev.
**130**, 1616 (1963)Google Scholar - 14.M. Gaudin, Boundary Energy of a Bose Gas in One Dimension. Phys. Rev. A
**4**, 386–394 (1971)Google Scholar - 15.A. Öttl, S. Ritter, M. Köhl, T. Esslinger, Correlations and Counting Statistics of an Atom Laser. Phys. Rev. Lett.
**95**, 090404 (2005)Google Scholar - 16.I. Bloch, T.W. Hänsch, T. Esslinger, Atom Laser with a cw Output Coupler. Phys. Rev. Lett.
**82**, 3008 (1999)Google Scholar - 17.A. Del Campo, I. Lizuain, M. Pons, J.G. Muga, M. Moshinsky, Atom laser dynamics in a tight-waveguide. J. Phys. Conf. Ser.
**99**, 012003 (2008)Google Scholar - 18.M. Köhl, Th. Busch, K. Mølmer, T.W. Hänsch, T. Esslinger, Observing the profile of an atom laser beam. Phys. Rev. A
**72**, 063618 (2005)Google Scholar - 19.W. Ketterle, Nobel lecture: When atoms behave as waves: Bose–Einstein condensation and the atom laser. Rev. Mod. Phys.
**74**, 1131–1151 (2002)Google Scholar - 20.W. Ketterle and H.-J. Miesner, Coherence properties of Bose–Einstein condensates and atom lasers. Phys. Rev. A
**56**, 3291 (1997)Google Scholar - 21.T. Gericke, P. Würtz, D. Reitz, T. Langen, H. Ott, High-resolution scanning electron microscopy of an ultracold quantum gas. Nat. Phys.
**4**, 949–953 (2008)CrossRefGoogle Scholar - 22.F. Serwane et al., Deterministic Preparation of a Tunable Few-Fermion System. Science
**332**(6027), 336–338 (2011)Google Scholar - 23.D. Heine et al., A single-atom detector integrated on an atom chip: fabrication, characterization and application. New J. Phys.
**12**, 095005 (2010)ADSCrossRefGoogle Scholar - 24.L.S. Cederbaum, A.I. Streltsov, Best mean-field for condensates. Phys. Lett. A
**318**, 564–569 (2003)ADSCrossRefzbMATHGoogle Scholar