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Title: Folie 1


1
Ultracold dipolar quantum gases
2
Barcelona Quantum Optics Theory
Ex-Hannoveraner Anna Sanpera (ICREA full prof.
UAB), Dagmar Bruß (C4, Düsseldorf) L. Santos (W3,
Hannover), Veronica Ahufinger (ICREA junior,
UAB), J. Mompart (assoc. prof, UAB), Carla Faria
(lect. UC, London) P. Öhberg (lect., Glasgow), L.
Sanchez-Palencia (CNRS, Orsay), Z. Idziaszek
(ten. track, Warsaw), U.V. Poulsen (ten. track,
Aarhus), B. Damski (res. assoc., Los Alamos), M.
Baranov (res. assoc., Amsterdam), P. Pedri
(postdoc, Orsay), O Gühne (postdoc,
Innsbruck). P. Hyllus (postdoc,
Hannover) A.Kantian (PhD, Innsbruck), T. Meyer
(PhD, Düsseldorf), A. Cojuhovschi (PhD,
Hannover),
PhD ICFO Armand Niederberger, Christian
Trefzger, Ania Kubasiak, Sibylle
Braungardt Postdocs ICFO Ujjwal Sen, Aditi
Sen (De), Chiara Menotti, Jonas Larson, Jarek
Korbicz, Geza Toth, Mirta Rodriguez
3
Barcelona Quantum Optics Theory
Collaborations Theory MPI Garching J. I.
Cirac UAB, Barcelona A. Sanpera (G. Fis.
Teor.), Univ. Hannover L. Santos, H-U. Everts
(ITP), Univ. Düsseldorf D. Bruß Univ.
Paris-Sud, Orsay G. Shlyapnikov (LPT) Univ.
Innsbruck P. Zoller, H. Briegel NIST,
Gaithesburg P. Julienne Oxford University D.
Jaksch CFT, Warsaw K. Rzazewski, M. Kus, Univ.
Jagiellonski, Cracow J. Zakrzewski,
J. Dziarmaga, K. Sacha Univ.
Gdansk P. Horodecki UAB, Barcelona - V.
Ahufinger, J. Mompart, G. Morigi (G. Optica) UB,
Barcelona J.I. Latorre, N. Barberàn, M.
Guillemas, A. Polls ICFO, Barcelona A. Acín,
Ll. Torner Univ. Pavia Ch. Macchiavelo Univ.
Arizona, Tuscon J. Wehr Harvard Univ. R.J.
Glauber
Collaborations Experiments Univ. Hannover - W.
Ertmer, J. Arlt,
E. Tiemann (IQO) Univ. Darmstadt - G. Birkl
(Darmstadt), Univ. Siegen - C. Wunderlich
Univ. Hamburg - K. Sengstock, K. Bongs LENS,
Firenze Massimo Inguscio Univ. Innsbruck - R.
Blatt, N. Bohr. Inst., Kopenhagen - E. Polzik
ICFO J. Eschner, M. Mitchel, J. Biegert
4
Outline
  • Introduction why bother?

  • Ultracold trapped dipolar Bose gases
  • Ultracold trapped dipolar Fermi gases
  • Ultracold dipolar gases in optical lattices
  • Richness of quantum phases
  • Superchemistry in a lattice
  • Metastable states Toward quantum memories?
  • Ultracold dipolar gases in artificial magnetic
    fields
  • Rotating gases
  • Toward fractional quantum Hall effect
  • Wigner cristals?

5
Why is this interesting?
  • The interaction is anisotropic (partially
    attractive)
  • Long-range interaction
  • The properties of the ultracold gas are
    critically dependent on the trap geometry!

Pioneering groups L. You, K. Rzazewski, T.
Pfau, G. Shlyapnikov, M. Baranov, G. Kuritzki...
,
6
Ultracold dipolar gases
  • Trapped dipolar Bose gases
  • L. Santos, G. Shlyapnikov, P.Zoller, M.
    Lewenstein
  • PRL 85, 1791 (2000)
  • L. Santos, G. Shlyapnikov, M. Lewenstein
  • PRL 90, 250403 (2003)

7
Trapped dipolar bosonic gases
L. Santos, G. Shlyapnikov, P. Zoller and M.
Lewenstein, PRL 85, 1791 (2000),
quant-ph/0005009
8
Pancake traps (wrltwz )
Critical trap aspect ratio l (wr/wz ) 1/2 0.4
  • Soft pancake traps, l lt l lt 1, as well as cigar
    ones, l 1

-The sign of the interaction V changes by
increasing Nd2
The condensate goes from pancake to cigar-shape!
9
  • Hard pancake traps ( llt l)
  • The condensate aspect ratio decreases with Nd 2
  • For wrltltwz

10
Roton-maxon spectrum in dipolar gas
L. Santos, G. Shlyapnikov, and M. Lewenstein, PRL
90, 250403 (2003)
Energy
Momentum
Rotons in cigar shaped BECs with laser-induced
(retarded) dipole interactions (ODell,
Giovanazzi, and Kurizki, PRL (2003))
11
Ultracold dipolar gases
  • Trapped dipolar Fermi gases
  • M. Baranov, L. Dobrek, M. Lewenstein
  • Phys. Rev. Lett. 92, 250403 (2004),
    cond-mat/0307671

12
Dipolar fermionic gases
13
BCS transition in a trapped dipolar Fermi gas
M.A. Baranov, . Dobrek, and M. Lewenstein Phys.
Rev. Lett. 92, 250403 (2004),
  • Is there a critical aspect ratio l ?

14
Dipolar Bose gas in an optical lattice
  • K. Góral, L. Santos, and M. Lewenstein
  • PRL 88, 170406 (2002)

15
3D Optical Lattice Potential (by courtesy of M.
Greiner, O. Mandel, I. Bloch, and T. Hänsch)
V0 up to 22 Erecoil wr up to 2p 30 kHz n ? 1-5
atoms on average per site
  • Resulting potential consists of a simple cubic
    lattice
  • BEC coherently populates more than 100,000
    lattice sites

16
Bose gas in an optical latticeIdea Jaksch,
Bruder, Cirac, Gardiner and P. Zoller
Dipolar Bose gas in an optical lattice (K. Góral,
L. Santos, and M. Lewenstein, PRL 88, 170406
(2002))
17
Superchemistry of dipolar molecules and dipolar
molecular superfluids
  • B. Damski, L. Santos, E. Tiemann, P. Julienne,
  • S. Kotochigova, P. Zoller, and M. Lewenstein
  • PRL 90, 110401 (2003)

18
Creating molecular dipolar superfluid in an
optical lattice
  • Description
  • two component Bose-Hubbard model
  • superfluid-Mott transition
  • photoassociation
  • quantum melting

19
Creating molecular dipolar superfluid in an
optical lattice
20
Dipolar Bose gas in an optical latticeToward
quantum memories?
  • Ch. Menotti, Ch. Trefzger, and M. Lewenstein
  • Phys. Rev. Lett. 98, 235301 (2007)

21
Dipolar bosons in a 2D optical lattice
  • long-range anisotropic interaction
  • A. Griesmaier, J. Werner, S. Hensler, J. Stuhler,
    and T.Pfau, Phys. Rev. Lett. 94, 160401 (2005)
  • J. Stuhler, A.Griesmaier, T. Koch, M. Fattori, T.
    Pfau, S. Giovanazzi, P. Pedri, and L. Santos,
  • Phys. Rev. Lett. 95, 150406 (2005) .
  • many control parameters U, D, q, j
  • novel quantum phases
  • (checkerboard, supersolid)
  • see e.g.
  • G.G. Batrouni and R.T. Scalettar,
    PRL 84, 1599 (2000)
  • K. Góral, L. Santos and M.
    Lewenstein, PRL 88, 170406 (2002)
  • D.L. Kovrizhin, G. Venketeswara
    Pai and S. Sihna, EPL 72, 162 (2005)
  • P. Sengupta, L. P. Pryadko, F.
    Alet, M. Troyer and G. Schmid, PRL 94, 207202
    (2005)
  • existence of metastable states?

22
Extended Bose-Hubbard model
23
Dipolar lattice gas Ground states, metastable
state
Metastable states do they play a role in
cooling dynamics? Are they reachable?
24
Dipolar lattice gas The fate of metastable
states
They appear spontaneously and frequently in
cooling dynamics! But, using supetlattice
techniques they can be prepared on
demand! They lifetimes are long, according
to generalized instanton theory! Quantum
memories?
They can be unambigiously detected using noise
corelations spectroscopy!!!
25
Ultracold gases in artificial gauge fields
rapidly rotating gases
M. Baranov, K. Osterloh M. Lewenstein,
Fractional Quantum Hall States in Ultracold
Rapidly Rotating Dipolar Fermi Gases, Phys. Rev.
Lett. 94, 070404 (2005). N.Barberán,
M.Lewenstein, K.Osterloh, and D.Dagnino, Ordered
structures in rotating ultracold Bose gases,
Phys. Rev. A 73, 063623 (2006). D. Dagnino, N.
Barberán, M. Lewenstein, K. Osterloh, and A.
Riera, Symmetry breaking in small rotating cloud
of trapped ultracold Bose atoms, in print in
Phys. Rev. A K. Osterloh, N. Barberán, and M.
Lewenstein, Strongly correlated states of
mesoscopic samples of dipolar atoms, in print in
Phys. Rev. Lett. H. Fehrmann, M.A. Baranov, and
M. Lewenstein, Wigner Crystallizweation in Fast
Rotating 2D Dipolar Fermi Gases,
cond-mat/0612592
26
Rotating systems
  • Dipolar Fermi particles in a harmonic trap
  • Rotation nucleates
  • Tuning the rotational frequency determines nature
    of the system
  • ? evolution from weakly to strongly
    correlated regime

27
FQHE states in rotating dipolar Fermi gases
  • System ingredients
  • two-dimensional system ? quasi-2D harmonic
    trap
  • perpendicular magnetic field ? rotating trap
  • long-range potential ? dipole-dipole interactions
  • quasi-particle excitations ? laser piercing of
    the probe
  • filling fraction of Landau levels ? fermionic
    particles

28
Fractional quantum Hall regime
  • Close to critical rotation system enters FQHE
    regime

29
Quasi-particle excitations I
  • State with a quasi-hole at x0 represented by
  • Excitation gap ?? derived from
  • two-particle correlation functions gqh and g0 by

30
Ground state analysis
  • Structures are derived from correlation functions

solely provides diagonal part of density matrix
reveals hidden structure patterns
31
Ground state phases
System starts from an ideal Fermi gas,
global correlations manifest themselves
regular bump-hole structures are formed
32
Ground state phases II
  • Regular pattern changes system undergoes
    drastic change,

structure reorganizes until the Laughlin state
is manifested
33
Quasi-particle excitations II
  • To compare with thermodynamic limit calculations!
    finite size filling factor description

34
Competion Laughlin versus Wigner crystal
  • Quantum phase transition Laughlin to Wigner
    crystal occurs below filling factors 1/7


Note for trapped dipolar gases Wigner crystal
appears for large densities!!! For rotating
dipolar gases for small densities!!! H.
Fehrmann, M.A. Baranov M. Lewenstein,
cond-mat/0612592
35
Wigner crystallisation of trapped dipolar gases
G.E. Astrakharchik, J. Boronat, J. Casulleras,
I.L. Kurbakov, and Yu.E. Lozovik Weakly
interacting two-dimensional system of dipoles
limitations of mean-field theory,
arXivcond-mat/0612691 G.E. Astrakharchik, J.
Boronat, I.L. Kurbakov, and Yu.E. Lozovik,
Quantum phase transition in a two-dimensional
system of dipoles, Phys. Rev. Lett. 98, 060405
(2007). H.P. Büchler, E. Demler, M. Lukin, A.
Micheli, N. Prokof'ev, G. Pupillo, and P. Zoller
Strongly correlated 2D quantum phases with cold
polar molecules controlling the shape of the
interaction potential , Phys. Rev. Lett. 98,
060404 (2007). R. Citro, E. Orignac, S. De
Palo, and M.-L. Chiofalo, Evidence of Luttinger
liquid behavior in one-dimensional dipolar
quantum gases, Phys. Rev. A 75, 051602
(2007). A.S.Arkhipov, G.E.Astrakharchik,
A.V.Belikov, Yu.E.Lozovik, Ground-state
properties of a one-dimensional system of
dipoles, arXivcond-mat/0505700.
36
CONCLUSIONS (The Tragedy of Hamlet, by
Shakespeare)
  • There are more thing in heaven and earth,
    Horatio, than are dreamt of in your philosophy.

Wow!!!
  • See Ultracold atoms in optical lattices
    Mimicking condensed matter
  • and beyond, M. Lewenstein, A. Sanpera, V.
    Ahufinger, B. Damski,
  • A. Sen (De) and U. Sen, Advances in Physics,
    56, March 2007, 243 - 379
  • 136 p., 823 refs., cond-mat/06006771
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