Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at...
-
date post
19-Dec-2015 -
Category
Documents
-
view
223 -
download
1
Transcript of Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at...
![Page 1: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/1.jpg)
Interacting Ultra Cold Atomsa brief overview
Fei Zhou PITP, University of British Columbia
at Quantum Nanoscience conference, Noosa Blue, Australia, Jan 23, 2006
Collaborators: I. Affleck (UBC), E. Demler (Harvard), Z. C. Gu (TsingHua),M. Snoek (Utrecht), C. Wu (UCSB), H. Zhai (TsingHua)
$: Office of the Dean of Science, UBCNSERC, Canada
Sloan foundation, New York
![Page 2: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/2.jpg)
Ultra Cold atoms
Many-body physics (condensed matter
physics)
Quantum information Storages and
quantum computers
Few body physics(Nuclear physics,Atomic physics)
Field theories(emergent gauge fields,color superconductivity,Neutron star physics)
Cosmology and gravity(Kimble mechanism,Unruh Radiation etc)
![Page 3: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/3.jpg)
Topological quantum computer (Kitaev, 97)
2| g1| g
![Page 4: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/4.jpg)
Bosons in optical lattices
• S=0 bosons
• S=1 bosons
![Page 5: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/5.jpg)
S=0 bosons in lattices
In (a) and (b), one boson per site. t is the hopping and can be varied by tuning laser intensities of optical lattices; U is an intra-site interaction energy. In a Mott state, all bosons are localized.
M. P. A. Fisher et al., PRB 40, 546 (1989);On Mott states in a finite trap, seeJaksch et al., PRL. 81, 3108-3111(1998).
U
Mott states ( t << U)
Condensates (t >>U)
![Page 6: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/6.jpg)
Phase diagrams
E(k,x)
n=3
n=2
n=1
x
n
x
2
1
Atomic Mott states in a trapt
n=1
SF or BEC
n=2
n=3
n=4
n
Small t
Large t
![Page 7: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/7.jpg)
.
/
/
),π
R:(,,φB:(
.n|α
|Sn,n|)(n:|
|iφθe
θ||iφθe
φ)(θn|
21
0
21
02
0
1
0
0
01
12
012
)
sincos
sin,
Interacting S=1 bosons
.2,0,,4
)()(
02
,2121
FggM
ag
grrrrU
FF
FF
Stamper-Kurn et al., 98.Ho, 98; Ohmi & Machida, 98; Law,98.
![Page 8: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/8.jpg)
Condensates of S=1 bosons (sodium type)
(d>1)N(Q)
Q
xy
z
(Zhou, 01)
![Page 9: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/9.jpg)
Half vortices in BECs of sodium atoms
In a half vortex, each atom makes a spin rotation; a half vortex carries one half circulation of an integer vortex. A half vortex ring is also a hedgehog.
circulation
y
spin rotation
Z
x
y
x
The vortex is orientated along the z-direction; the spin rotation and circulating current occur in an x-y plane.
z
ring
![Page 10: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/10.jpg)
Each site is characterized by two unit vectors, blue and red ones. a) nematic BECs (nBEC); b) Nematic mott insulators (NMI); c) Spin singlet mott insulators (SSMI).
Mott states of Spin-One Bosons
CCCCO3
12
![Page 11: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/11.jpg)
Nematic-spin singlet transitions (Mott Insulators)
vs. (proportional to hopping) is plotted here. (Snoek and Zhou, 03; Demler, et al., 03; Demler and Zhou, 02)
SSMI NMI
![Page 12: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/12.jpg)
Fermions
• S=1/2 fermions in Optical Lattices
• S=3/2 fermions, quintet pairing, exotic vortices studied (Wu, Hu and Zhang, 2003-2006).
• Feshbach resonances with population difference (Experiments: MIT group, the Rice University’s Group and JILA group; Theory effeorts: Son and Stephanov, 2005; Pao et al.,2005; Sheehy and
Radzihovsky; Gu, Warner and Zhou; …….)
• Lattice Feshbach resonances (Stability of Mott states and invasion of superfluidity, factorized superfluids in 1D; Wu, Gu and Zhou, 2005-2006)
And more…...
![Page 13: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/13.jpg)
S=1/2 Fermions in optical lattices
(small band width)
Neel OrderedSpin liquids Neel ordered only at T=0
![Page 14: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/14.jpg)
S=1/2 femions across Feshbach resonances
B
E (6Li)
F=3/2
F=1/2
Resonances between state 1 of |1/2,1/2> and state 2 of |1/2,-1/2>.
Only electron spins shown
![Page 15: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/15.jpg)
Superfluids near Feshbach Resonances
1 )( Fskax
sa
Binding energy
B
![Page 16: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/16.jpg)
The Chemical potential and Mol. Fraction at resonance
For y <<1, at FbR the many-body states are INDEPENDENT of both two body parameters such as the bg scattering length, the magnetic moments and the many-body parameter: the fermi momentum.
Wide resonance (Ho and Diener, 04)
![Page 17: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/17.jpg)
Energy splitting and population imbalance
A conventional quantum statistical system
I
E(k)
k
E(k)
k
Cold atoms
![Page 18: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/18.jpg)
Energy Landscape 1: Negative Scattering Length (N fixed) (Gu, Warner and Zhou, 05)
![Page 19: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/19.jpg)
Energy Landscape 2: positive scattering length
![Page 20: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/20.jpg)
Energy Landscape 3: Near resonance
![Page 21: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/21.jpg)
Phase Separation in a Constrained Subspace(i.e. population imbalance is conserved)
M-H curve for a global ground state
Critical population imbalance
Phase separated states
I
M M
I
1
N
Gapless SFSF+N
Gapless SF + N
Negative scattering length Positive scattering length
![Page 22: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/22.jpg)
Zwierlein et al., 2005 ; Also studied by the Rice group.
![Page 23: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/23.jpg)
Superfluids of polarized fermi gases
Resonances take place along the blue dashed line (in the “universal regime”). ( Son et al., 2005; also see Sheehy and Radzihovsky, 2005)
LOFF
Partially polarizedF.L.
Fully polarizedF.L.
SF + Fermi sea
Splitting between two chemical potentials
inverse of scattering length
(p, -p+Q)
![Page 24: Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.](https://reader035.fdocuments.net/reader035/viewer/2022062304/56649d2b5503460f949ffc86/html5/thumbnails/24.jpg)
• many important and exciting new issues in many-body cold atomic matter (magnetic superfluids & Mott states, topological phases, superfluids with population imbalance etc).
• Cold atomic matter might also be applied to understand various fundamental concepts/issues in other fields.
• There are a lot we can learn about/from cold atoms.
Summary