Vladimir S. Melezhik. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia

Transcription

1 Vladimir S. Melezhik Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia BRZIL-JINR FORUM, Dubna 18 June 2015

2 Results were obtained in collaboration with Peter Schmelcher Panagiotis Giannakeas Shahpoor Saeidian Ji Il Kim Oksana and Eugene Koval ZOQ, Hamburg ZOQ, Hamburg (now:ch.greene group) IASBS, Zanjan, Iran ~ Univ. Sao Paulo, ~ Brazil BLTP JINR, Dubna Innsbruck experiment: Elmar Haller Hans-Chrisroph Nagerl..

3 Outline Ultracold atoms in optical traps: why it is interesting? Confinement-induced resonances (CIRs) Feshbach resonances in quasi-1d atomic traps (bosons and fermions) Dipolar CIRs in quasi-1d traps Anisotropic quantum scattering in two dimensions Resonant molecule formation with energy transfer to CM excitation Conclusion and outlook

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5 2D 1D

6 2D 1D

7 motivation in brief experimental aspects

8 scattering length [1000 a 0 ] Experiments with deterministically prepared quantum systems control interparticle interaction 2 interacting particles in a 1D potential magnetic Feshbach resonance magnetic field [G] control over quantum states and particle number with long lifetime quantum simulation with fully controlled few-body systems.. G.Zurn et. al. Phys. Rev. Lett. 108, (2012)

9 scattering length [1000 a 0 ] Experiments with deterministically prepared quantum systems control interparticle interaction 2 interacting particles in a 1D potential magnetic Feshbach resonance magnetic field [G] control over quantum states and particle number with long lifetime

10 scattering length [1000 a 0 ] Experiments with deterministically prepared quantum systems control interparticle interaction 2 interacting particles in a 1D potential magnetic Feshbach resonance magnetic field [G] control over quantum states and particle number with long lifetime quantum simulation with fully controlled few-body systems.. G.Zurn et. al. Phys. Rev. Lett. 108, (2012)

11 Quantum simulation with fully controlled few-body systems control over: quantum states, particle number, interaction attractive interactions BCS-like pairing in finite systems repulsive int.+splitting of trap entangled pairs of atoms (quantum information processing) + periodic potential quantum many-body physics (systems with low entropy to explore such as quantum magnetism)... Bose-Hubbard Physics

12 Quantum simulation with fully controlled few-body systems control over: quantum states, particle number, interaction attractive interactions BCS-like pairing in finite systems repulsive int.+splitting of trap entangled pairs of atoms (quantum information processing) + periodic potential quantum many-body physics (systems with low entropy to explore such as quantum magnetism)... Bose-Hubbard Physics

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14 motivation in brief theoretical aspects

15 motivation in brief theoretical aspects 3D free-space scattering theory is no longer valid and development of low-dimensional theory including influence of the trap is needed

16 What happens if atoms scatter in confined geometry (quasi-1d)? E What happens in collision of two distinguishable atoms in harmonic trap, or identical atoms in anharmonic trap? non-separable two-body problem

17 Methods: non-direct 2D discrete-variable representation (2D DVR) 1D DVR: J.C.Light et al J.Chem.Phys D DVR: V.Melezhik Phys.Rev. A 1993 Phys.Lett V.Melezhik & D.Baye Phys.Rev. C 1999 V.Melezhik & P.Schmelcher Phys.Rev.Lett multi-channel scattering problem as a boundary-value problem V.Melezhik J.Comp.Phys V.Melezhik & C.-Y. Hu Phys.Rev.Lett S.Saeidian & V. Melezhik & P.Schmelcher Phys.Rev.A 2008 splitting-up method for time-dependent 3D and 4D Schrödinger eqs. G.I.Marchuk 1971 V.Melezhik Phys.Lett V.Melezhik & D.Baye Phys.Rev. C 1999 J.I.Kim & V.Melezhik & P.Schmelcher Phys.Rev. A 2007 V.Melezhik & P.Schmelcher New J. Phys 2009

18 confinement-induced resonances (CIRs) CIR splitting in experiment in anisotropic waveguides dual CIR leading to complete suppression of quantum scattering investigation of strong d-wave correlations in waveguide CIRs in multimode regimes including transverse excitation/deexcitation

19 g 1D [10 a perp hbar perp ] scattering length [1000 a 0 ] Tuning the interaction in 3D 3D Feshbach resonance single-channel pseudopotential magnetic field [G] strong confinement 1D 4 Confinement induced resonance 2 0 single-channel pseudopotential with renormalized interaction constant magnetic field [Gauss] M. Olshanii, PRL 81, 938 (1998).

20 g 1D [10 a perp hbar perp ] scattering length [1000 a 0 ] Tuning the interaction in 3D 3D Feshbach resonance single-channel pseudopotential magnetic field [G] strong confinement 1D 4 Confinement induced resonance 2 0 single-channel pseudopotential with renormalized interaction constant magnetic field [Gauss] M. Olshanii, PRL 81, 938 (1998).

21 g 1D [10 a perp hbar perp ] scattering length [1000 a 0 ] Tuning the interaction in 1D: B and 3D Feshbach resonance single-channel pseudopotential magnetic field [G] strong confinement 1D 4 Confinement induced resonance 2 (CIR) 0 single-channel pseudopotential with renormalized interaction constant magnetic field [Gauss] M. Olshanii, PRL 81, 938 (1998).

22 Feshbach resonances in quasi-1d atomic traps (bosons) CIR splitting in experiment in anisotropic waveguides dual CIR leading to complete suppression of quantum scattering investigation of strong d-wave correlations in waveguide CIRs in multimode regimes including transverse excitation/deexcitation

23 two-channel problem II

24 two-channel problem tensorial sructure of molecular state d g s II

25 two-channel problem tensorial sructure of molecular state d g s s or p II

26 two-channel problem tensorial sructure of molecular state d g s s II Innsbruck experiment with Cs atoms:

27 two-channel model of Lange et. al. Phys.Rev.79,013622(2009) 3 fitting parameters:

28 extension of two-channel model of Lange et. al. to 1D geometry Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) 4-coupled radial equations 4-coupled 2D equations in the plane

29 extension of two-channel model of Lange et. al. to 1D geometry Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) 4-coupled radial equations 4-coupled 2D equations in the plane

30 tensorial structure of the interatomic interaction V(r) Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) s d g region of Innsbruck experiment (d-wave Feshbach resonance)

31 tensorial structure of the interatomic interaction V(r) Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) s d g region of Innsbruck experiment (d-wave Feshbach resonance)

32 tensorial structure of the interatomic interaction V(r) Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) region of Innsbruck experiment (d-wave Feshbach resonance)

33 Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) d-wave FR at 47.8G develops in waveguide as depending on minimums and stable maximum of transmission coefficient T

34 Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) d-wave FR at 47.8G develops in waveguide as depending on minimums and stable maximum of transmission coefficient T experiment

35 Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) d-wave FR at 47.8G develops in waveguide as depending on minimums and stable maximum of transmission coefficient T experiment theory

36 Shifts and widths of Feshbach resonances in atomic waveguides Sh.Saeidian, V.S. Melezhik,and P.Schmelcher, Phys.Rev. A86, (2012) d-wave FR at 47.8G develops in waveguide as depending on minimums and stable maximum of transmission coefficient T experiment theory Olshanii formula works for s,d,and g FRs

37 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

38 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

39 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

40 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

41 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

42 Feshbach resonances in quasi-1d atomic traps (fermions) S.Saeidian, V.S.Melezhik and P.Schmelcher, J. Phys B (2015) (in press)

43 Dipolar confinement-induced resonances in waveguides P.Giannakeas, V. Melezhik & P.Schmelcher, PRL,111(2013)

44 Dipolar confinement-induced resonances in waveguides P.Giannakeas, V. Melezhik & P.Schmelcher, PRL,111(2013)

45 Dipolar confinement-induced resonances in waveguides P.Giannakeas, V. Melezhik & P.Schmelcher, PRL,111(2013)

46 Dipolar confinement-induced resonances in waveguides P.Giannakeas, V. Melezhik & P.Schmelcher, PRL,111(2013) analytically derived resonant condition predict position of dipolar confinement-induced resonances

47 Anisotropic quantum scattering in two dimensions E.Koval, O.Koval, V.Melezhik, Phys.Rev.A89, (2014)

48 Anisotropic quantum scattering in two dimensions E.Koval, O.Koval, V.Melezhik, Phys.Rev.A89, (2014)

49 Anisotropic quantum scattering in two dimensions E.Koval, O.Koval, V.Melezhik, Phys.Rev.A89, (2014)

50 Anisotropic quantum scattering in two dimensions E.Koval, O.Koval, V.Melezhik, Phys.Rev.A89, (2014)

51 Mechanism of molecule formation with transferring the energy release to CM excitation of forming molecule was considered in: E.Bolda et.al. Phys.Rev. A71, (2004) (in anharmonic lattices) V.Melezhik &P.Schmelcher, New J.Phys.11, (2009) (distinguishable atoms in harmonic waveguides)

52 non-separability of two-body problem in trap (distinguishable atoms in harmonic trap or identical atoms in anharmonic trap) V. Melezhik & P. Schmelcher, New J. of Phys. 11, (2009) A r B r 1 r 2 z N=0,n=1 N=1,n=0 N=n=0 4D TDSE: A n1=0 + B n2=0 (AB) n=0,n=1

53 An1=0 + Bn2=0 (AB)n=0,N=1

54 An1=0 + Bn2=0 (AB)n=0,N=1

55 An1=0 + Bn2=0 (AB)n=0,N=1

56 An1=0 + Bn2=0 (AB)n=0,N=1

57 Resonant Formation of Ultracold Molecules in Waveguides V. Melezhik & P. Schmelcher, New J. of Phys. 11, (2009) coupling of the deatomic continuum with the CM of excited molecule at (N=1) in closed transverse channels: if the atoms in the colliding pair are identical, then coupling term goes to zero and the effect disappears. A n1=0 + B n2=0 (AB) n=0,n=1 Time evolution of the molecular states (N=0 and 1) population P (t) during a pair collision: N possible applications: - ultracold collisions in atomic waveguides - electron-impurity scattering in quantum wires - atomic interferometry

58 in Heidelberg experiment, S.Sala et. al. Phys.Rev.Lett.110, (2013), the mechanism of molecule formation with transferring energy release to CM molecule excitation was observed in anharmonic waveguide signature of resonant molecule formation

59 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation

60 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation extension to quasi-2d geometry

61 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation extension to quasi-2d geometry

62 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation extension to quasi-2d geometry???

63 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation extension to quasi-2d geometry three-body collisional problem (Efimov resonances) in tight traps

64 Conclusion and outlook confinement-induced resonances in low-dimensional quantum systems s- and p-wave CIRs in quasi-1d traps resonant positions for dipolar CIRs in quasi-1d traps resonant mechanism for molecule formation in traps with energy transfer to CM excitation extension to quasi-2d geometry three-body collisional problem (Efimov resonances) in tight traps non-linear time-dependent Schrödinger equation with CM coupling

65 Quantum simulation with fully controlled few-body systems control over: quantum states, particle number, interaction attractive interactions BCS-like pairing in finite systems repulsive int.+splitting of trap entangled pairs of atoms (quantum information processing) + periodic potential quantum many-body physics (systems with low entropy to explore such as quantum magnetism)... Bose-Hubbard Physics

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