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![Page 1: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/1.jpg)
Quantum Gases: Past, Present, and Future
Jason Ho
The Ohio State University
Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future
HKU and HKUST, Dec 18-20
![Page 2: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/2.jpg)
Where we stand
What’s new
Fundamental Issues
Challenges
![Page 3: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/3.jpg)
A decade since discovery of BEC :
Still expanding rapidly
Discoveries of new systems, new phenomena, and new techniquekeep being reported in quick succession.
Highly interdisciplinary -- (CM, AMO, QOP, QI, NP) New Centers and New Programs formed all over the world. England, Japan, Australia, CIAR, US (MURI&DARPA)
Puzzling phenomena being to emerge in fermion expts
Worldwide experimental effort to simulate strongly correlated CM systems using cold atoms
![Page 4: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/4.jpg)
Bosons and Fermions with large spins
F=I+J
alkali atoms
Hyperfine spin
J=1/2
I
J
e
Spin F=1, F=2 bosons:
Spin F=1/2, 3/2, 5/2, 7/2, 9/2 fermions
![Page 5: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/5.jpg)
BMagnetic trap
Spinless bosons and fermions
Atoms “lose” their spins!
![Page 6: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/6.jpg)
BMagnetic trap
Mixture of quantum gases:
D.S. Hall, M.R. Matthews, J. R. Ensher, C.E. Wieman, and E.A. Cornell PRL 81, 1539 (1998)Pseudo-spin 1/2 bosons:
Ho and Shenoy, PRL 96
![Page 7: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/7.jpg)
Optical trapping:Focused laser
BEC or cold fermions
All spin states are trapped,
Spin F=1, F=2 bosons:
Spin F=1/2, 3/2, 5/2, 7/2, 9/2 fermions
T.L.Ho, PRL 1998
![Page 8: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/8.jpg)
Quantum Gases
Atomic PhysicsCondensed Matter Physics
Quantum Optics
Nuclear Physics
Quantum Information
BEC
High Energy Physics
![Page 9: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/9.jpg)
Quantum Gases
BBBBFFF F
3D
2D
1D
0D
single trap
lattice
stationary
fast rotating
U(1)Magnetictrap, spins frozen
S0(3)Optical trap, spins released
€
Ω=0
€
Ω→ ωtrap
€
na3 <<1
€
na3 >>1
system environmentssymmetry interaction
![Page 10: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/10.jpg)
1996 Discovery of BEC!1997 Mixture of BEC and pseudo spin-1/2 Condensate interference collective modes solitons1998 Spin-1 Bose gas (Super-radiance)Bosanova Bragg difffration, super-radience, Superfluid-Mott oscillation
1999 Low dimensional Bose gas (Vortices in 2-component BEC)2000 (Vortices in BEC, Slow light in BEC) 2001 Fast Rotating BEC, Optical lattice, BEC on Chips 2002 Quantum degenerate fermions (Spin dynamics of S=1/2 BEC, Coreless vortex in S=1 BEC, evidence of universality near resonance) 2003 Molecular BEC, (Spin dynamics of S=1 BEC, noise measurements)
2004 Fermion pair condensation! (pairing gap, collective mode) BEC-BCS crossover, 2005 Vortices in fermion superfluids, discovery of S=3 Cr Bose condensate,
observation of skymerion in S=1 Bose gas. 2006 Effect of spin asymmetry and rotation on strongly interacting Fermi gas. Boson-Fermion mixture in optical lattices.
![Page 11: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/11.jpg)
New Bose systems: “spin”-1/2, spin-1, spin-2 Bose gas, Molecular Bose gas. (BEC at T=0)
Un-condensed Bose gas: Low dimensional Bose gas, Mott phase in optical lattice Strongly Interacting quantum gases: Atom-molecule mixtures of Bosons near Feshbach resonance Fermion superfluid in strongly interacting region Strongly interacting Fermions in optical lattices
Possible novel states: Bosonic quantum Hall states, Singlet state of spin-S Bose gas, Dimerized state of spin-1 Bose gas on a lattice. Fermion superfluids with non-zero angular momentum
![Page 12: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/12.jpg)
Often described as experimental driven,
but in fact theoretical ideas are crucial.
Bose and Einstein, Laser cooling, Evaporative cooling
![Page 13: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/13.jpg)
What is new ?
A partial list:
Bosons and Fermions with large spins
Fast Rotating Bose gases
Superfluid Insulator Transition in optical lattices
Strongly Interacting Fermi Gases
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Question:
How do Bosons find their ground state?
![Page 15: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/15.jpg)
Conventional Bose condensate : all Bosons condenses into a single state.
How do Bosons find their ground state?
Question:
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What happens when there are several degenerate state for the Bosons to condensed in?
G: Number of degenerate states N: Number of Bosons
![Page 17: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/17.jpg)
What happens when there are several degenerate state for the Bosons to condense in?
G: Number of degenerate states N: Number of Bosons
Pseudo-spin 1/2 Bose gas: G =2
![Page 18: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/18.jpg)
Spin-1 Bose gas : G=3, G<<N
G: Number of degenerate states N: Number of Bosons
![Page 19: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/19.jpg)
Spin-1 Bose gas : G=3, G<<N
Bose gas in optical lattice: G ~N
G: Number of degenerate states N: Number of Bosons
![Page 20: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/20.jpg)
Spin-1 Bose gas : G=3, G<<N
Bose gas in optical lattice: G ~N
Fast Rotating Bose gas: G>>N
G: Number of degenerate states N: Number of Bosons
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Effect of spin degeneracy on BEC
Only the lowest harmonic state is occupied
=> a zero dimensional problem
Spin-1 Bose Gas
Effect of spin degeneracy on BEC
A deep harmonic trap
€
aμ
+
€
μ=1,0,−1
![Page 22: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/22.jpg)
Spin-1 Bose Gas
Spin dynamics of spin-1 Bose gas
A deep harmonic trap
€
H = cr S
2
Hilbert space
![Page 23: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/23.jpg)
Effect of spin degeneracy on BEC
Spin-1 Bose Gas
Effect of spin degeneracy on BEC
A deep harmonic trap
€
Ax = (−a1 + a−1) / 2
€
Ay = (a1 + a−1) / 2i
€
Az = a0
Under spin rotation, rotates like a 3D Cartesean vector .
€
aμ → (e−ir θ ⋅
r S a)μ
€
rA i → R(
r θ )ij
r A j
€
R(r θ ) : 3D rotation
€
aμ
+
€
μ=1,0,−1
![Page 24: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/24.jpg)
Conventional condensate :
€
N0 = 0,
€
N±1 = N /2
€
H = cr S 2 C>0
€
< r
S >= 0
€
ΔN12 ~ N
€
Ax = (−a1 + a−1) / 2
€
Ay = (a1 + a−1) / 2i
€
Az = a0
![Page 25: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/25.jpg)
Exact ground state :
€
| S = 0 >= ΘN / 2 | 0 >
€
< aμ
+aν >=N3
1 0 0
0 1 0
0 0 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
€
N0 = N1 = N−1 = N /3
€
H = cr S 2 C>0
€
Θ=2a1
+a−1
+ − a0
+2
€
ΔN12 ~ N 2
=
Ho and Yip, PRL, 2004
![Page 26: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/26.jpg)
Average the coherrent state over all directions
Relation between singlet state and coherent state
x
y
z
Because
€
ΔN12 ~ N 2
The system is easily damaged
![Page 27: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/27.jpg)
Transformation of singlet into coherent states as a function of External field and field gradient:
If the total spin is non-zero
Bosonic enhancement
![Page 28: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/28.jpg)
Transformation of singlet into coherent states as a function of External field and field gradient:
If the total spin is non-zero
Bosonic enhancement
![Page 29: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/29.jpg)
Transformation of singlet into coherent states as a function of External field and field gradient:
If the total spin is non-zero
![Page 30: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/30.jpg)
Transformation of singlet into coherent states as a function of External field and field gradient:
If the total spin is non-zero
With field gradient
![Page 31: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/31.jpg)
S=2 Cyclic state
S=3 Spin biaxial Nematics
![Page 32: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/32.jpg)
A geometric representation : Generalization of Barnett et.al. PRL 06 & T.L.Ho, to be published
![Page 33: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/33.jpg)
CycleTetrahedron S=2
Cubic S=4
Octegonal S=3
Icosahedral S=6
T.L. Ho, to be published
![Page 34: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/34.jpg)
Rotating the Bose condensate
Generating a rotating quadrupolar field using a pair of rotating off-centered lasers
condensate
K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard PRL. 84, 806 (2000)
![Page 35: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/35.jpg)
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The fate of a fast rotating quautum gas : Superfluidity ----> Strong Correlation
Vortex lattice Overlap => Melting
Quantum Hall Boson
Fermion
Normal Quantum Hall
In superconductors
![Page 37: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/37.jpg)
€
h =(r p − M
r Ω ×
r r )2
2M
€
Ω→ ω as
Rotating quantum gases
in harmonic traps
Electrons in
Magnetic field
€
h =r p 2
2m+
12
Mω2r2 −r Ω •
r r ×
r p
€
h =(r p − M
r Ω ×
r r )2
2M+
12
M (ω2 −Ω2 )r2
trap
external rotation
A remarkable equivalence
![Page 38: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/38.jpg)
, n>0, m>0.
m
€
Ω=0, E = hω(n + m)
E
No Rotation : Two dimensional harmonic oscillator
![Page 39: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/39.jpg)
€
Enm = h(ω +Ω)n + h(ω −Ω)m , n>0, m>0.
€
Ω→ ωAs
Angular momentum states organize into Landau levels !
,
m
E
![Page 40: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/40.jpg)
m
E
€
μ
![Page 41: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/41.jpg)
m
E
€
μ
condensate
€
<ψ >
Mean field quantum Hall regime: in Lowest Landau level
€
<ψ >
![Page 42: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/42.jpg)
m
E
€
μ
Strongly correlated case: interaction dominated
€
<ψ >=0
![Page 43: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/43.jpg)
E. Mueller and T.L. Ho,Physical Rev. Lett. 88, 180403 (2002)
![Page 44: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/44.jpg)
Simulate EM field by rotation: Eric Cornell’s latest experiment cond-mat/0607697
TL Ho, PRL 87, 060403(2001)
V. Schweikhard, et.al. PRL 92, 040404 (2004)
(JILA group, reaching LLL)
![Page 45: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/45.jpg)
Boson + Fermion
Fermion quantum Hall
![Page 46: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/46.jpg)
Strongly interacting Fermi gases
![Page 47: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/47.jpg)
Cooling of fermions Pioneered by Debbie Jin
Motivation: To reach the superfluid phase
Depends only on density
For weakly interacting Fermi gas
To increase Tc, use Feshbach resonance, since
Holland et.al. (2001)
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Dilute Fermi Gas
Normal Fermi liquid
Weak coupling BCS superfluid
: S-wave scattering length
Weakcoupling
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Dilute Fermi Gas
Normal Fermi liquid
Weak coupling BCS superfluid
: S-wave scattering length
What Happens?
![Page 50: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/50.jpg)
Key Properties: Universality (Duke, ENS)
Evidence for superfluid phase: Projection expt: Fermion pair condensataion -- JILA, MIT Specific heat -- DukeEvidence for a gap -- Innsbruck
Evidence for phase coherence -- MIT
BEC -- BCS crossover is the correct description
Largest
Origin of universality now understood
![Page 51: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/51.jpg)
BCS
Molecular BEC
Universality : A statement about the energetics at resonance
![Page 52: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/52.jpg)
How Resonance Model acquire universality
has to hybridize with many pairs.
If is large -- strong hybridization, then has relatively little weight in the pair!
Small effect of means universality !
![Page 53: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/53.jpg)
Two channel Model
Single Channel model:
![Page 54: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/54.jpg)
Origin of universality
Scattering amplitude: (from both single and two channel model)
r = effective range
Question: what happen to scattering on Fermi surface
Wide resonance
Narrowresonance
Bruun & Pethick PRL 03Petrov 04Diener and Ho 04Strinati et.al 04Eric Cornell, email
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In two channel model:
Small closed channel contribution <=> pair size are given by interparticle spacing<=> <=> single channel description ok<=> universal energy density
![Page 56: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/56.jpg)
Current Development:
•Unequal spin population
•Rotation
![Page 57: Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649e885503460f94b8d534/html5/thumbnails/57.jpg)
c
To quantum
Hall regime
Melting of vortex lattice
Single vortex
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Other possible Fermion superfluids: P-wave Fermion superfluids.
BBo a>0 a<0
Molecular condensateFermion Superfluid
Ho and Diener, to appear in PRL
Optiuum phase
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Many quantum phenomenon observed:
Condensate interference collective modes solitons Bosanova Bragg difffration, super-radience, Superfluid-Mott oscillation Engineering quantum states in optical lattices, vortices and spin-dynamics of spin-1/2 Bose gas, phase fluctuation in low dimensional Bose gas,spatial fragmention of BEC on chips, slow light in Bose gases, large vortex lattice, Skymerion vortices in spin-1 Bose gas, spin dynamics of spin-1 and spin-2 Bose gas, dynamics in optical lattices
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Unique Capability for Lattice Quantum Gases•Solid State environment without disorder•Simulate electro-magnetic field by rotation•Great Ease to change dimensionality•Great Ease to change interactions
Major Incentive:•Observation of Superfluid-insulator transition -- a QPT in a strongly correlated system•Realization of Fermion Superfluid using Feshbach resonance
Exciting Prospects: •Novel States due to unique degrees of freedom of cold atoms Bose and Fermion superfluids with large spin Quantum Hall state with large spin Lattice gases in resonance regime
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Superfluid :
Mott :
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Superfluid State :
+ +
ODLRO
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Superfluid State :
+ +
ODLRO
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Mott State
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Mott State
Resists addition of boson require energy U,hence insulating
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Nature, 419, 51-54 (2002)
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Figure 2 Absorption images of multiple matter wave interference patterns. These were obtained after suddenly releasing the atoms from an optical lattice potential with different potential depths V0 after a time of flight of 15 ms. Values of V0 were: a, 0 Er; b, 3 Er; c, 7 Er; d, 10 Er; e, 13 Er; f, 14 Er; g, 16 Er; and h, 20 Er.
M. Greiner et.al, Nature 415, 39 (2002)M. Greiner, O. Mandel. Theodor, W. Hansch & I. Bloch,Nature (2002)
Observation of Superfluid-insulator transition
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Phase diagram of Boson-Hubbard Model
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Part IC
Current experiments
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I. Bloch, et.al, PRA72, 053606 (2005) Ketterle et.al, cond-mat/0607004
Esslinger, PRL 96, 180402 (2006) Sengstock et.al. PRL 96, 180403 (2006)
Expts involving superfluid-insulator transitions:
F-B mixture
Fermions in optical lattice, 2 fermions per site
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Band insulator
2 atoms per site 2 to 3 bands occupied
0
ETH Experiment: very deep lattice, less than two toms per site
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2 fermions Per site
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Part I: Why cold atoms for condensed matter?
A. Major developments in CM and Long Standing Problems
B. The Promise of cold atoms
C. Current experimental situation
Part II: Necessary conditions to do strongly correlated physics: Quantum Degeneracy and method of detection:
A. The current method of detecting superfluidity in lattices is misleading
B. B. A precise determination of superfluidity => illustration of far from
quantum degeneracy in the current systems.
Part III: Solid state physics with ultra-cold fermions:
A. Metallic and semi-conductor physics with cold fermions
B. Studying semiclassical electron motions with cold fermions
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Part II Necessary conditions for studying
strongly correlated physics:
* Quantum Degeneracy
* Method of Detection:
* Quantum Degeneracy
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Condition for quantum degeneracy
Condition for BEC :
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Free space
Lattice
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Free space Quantum degeneracyLowest temperature attainable:
Optical lattice
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I. Bloch, et.al, PRA72, 053606 (2005) Ketterle et.al, cond-mat/0607004
Esslinger, PRL 96, 180402 (2006) Sengstock et.al. PRL 96, 180403 (2006)
Current method of identifying superfluidity: sharpness of n(k)
F-B mixture
Fermions in optical lattice, 2 fermions per site
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However, a normal gas above Tc can also have sharp peak!
Diener, Zhao, Zhai, Ho, to be published.
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I. Bloch, et.al, PRA72, 053606 (2005) Ketterle et.al, cond-mat/0607004
Esslinger, PRL 96, 180402 (2006) Sengstock et.al. PRL 96, 180403 (2006)
Current method of identifying superfluidity: sharpness of n(k)
F-B mixture
Fermions in optical lattice, 2 fermions per site
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Part II Necessary conditions for studying
strongly correlated physics:
* Quantum Degeneracy
* Method of Detection: * Method of Detection
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An accurate method for detecting superfluidity:
Visibility
Reciprocal lattice vector
Not a reciprocal lattice vector
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DZZH, to be published T=0 visibility
2nd Mott shell
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Main message:
Current Experiments in optical lattice are far from quantum degeneracy
Need new ways to cool down to lower temperature
Need reliable temperature scale
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Finite temperature effect becomes important
More intriguing More intriguing physics of quantum physics of quantum critical behavior can critical behavior can
be expected be expected