efimov effect in ultracold atomic gas...enhancing the observability of the efimov effect in...
TRANSCRIPT
![Page 1: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/1.jpg)
ENHANCING THE OBSERVABILITY OF THE
Efimov Effect IN ULTRACOLD ATOMIC GAS
MIXTURES
Jose P. D’Incao and Brett D. Esry
Department of Physics, Kansas State University
National Science Foundation
![Page 2: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/2.jpg)
WHAT IS THIS EFIMOV EFFECT?
![Page 3: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/3.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
"quasi-bound"
"weakly bound"
V( )r
V( )r
Resonant Interaction
![Page 4: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/4.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
Eba
12
~
"quasi-bound"
"weakly bound"
V( )r
V( )r
Resonant Interaction
![Page 5: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/5.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
"quasi-bound"
"weakly bound"
V( )r
V( )r
| |a
Resonant Interaction
Eba
12
~
![Page 6: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/6.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
"quasi-bound"
"weakly bound"
V( )r
V( )r
| |a
Resonant Interaction
Eba
12
~
r0 | |a
W R( ) ~
R
R
W R( )
![Page 7: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/7.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
"quasi-bound"
"weakly bound"
V( )r
V( )r
| |a
Resonant Interaction
Eba
12
~
r0 | |a
W R( ) ~
R
R
W R( )
![Page 8: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/8.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
"quasi-bound"
"weakly bound"
V( )r
V( )r
| |a
Resonant Interaction
Eba
12
~
r0
Efimov States !
| |a
W R( ) ~
R
R
W R( )
![Page 9: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/9.jpg)
EFIMOV EFFECT
Vitaly Efimov, “Energy levels arising from resonant two-body forces ina three-body system”, Phys. Lett. 33, 563 (1970)
r
a<0
a>0
"quasi-bound"
"weakly bound"
V( )r
V( )r
| |a
Resonant Interaction
Eba
12
~
r0
Efimov States !
| |a
W R( ) ~
R
R
W R( )
Finite Number of2-Body bound states(short-range interaction)
Large Number of3-Body bound states
![Page 10: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/10.jpg)
EFIMOV EFFECT
Search for Efimov States: Nuclear Physics, Atomic Physics
Limitations: needs to find a system with large a
(at least 3 Efimov states)→ He3: only 1 Efimov state: open question !
→ extremely weakly-bound states !
Ultracold Quantum Gases
Experimentally accessible !Clear signature of the Efimov Effect !
(3-body collisions)
![Page 11: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/11.jpg)
ULTRACOLD QUANTUM GASES
... after evaporativecooling ...
B
K
Feshbach Resonances
![Page 12: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/12.jpg)
ULTRACOLD QUANTUM GASES
... after evaporativecooling ...
B
K
Feshbach Resonances
Scattering Length
![Page 13: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/13.jpg)
ULTRACOLD QUANTUM GASES
... after evaporativecooling ...
B
K
Feshbach Resonances
Scattering Length
Tunability of a !
![Page 14: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/14.jpg)
ULTRACOLD QUANTUM GASES
... after evaporativecooling ...
B
K
Feshbach Resonances
Efimov
Tunability of a !
EffectScattering Length
![Page 15: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/15.jpg)
ULTRACOLD QUANTUM GASES
... after evaporativecooling ...
B
K
Feshbach Resonances
Efimov
Tunability of a !
EffectScattering Length
2-Body Collisions→ Suppressed !3-Body Collisions→ Lifetime, Stability ... Efimov Effect !
![Page 16: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/16.jpg)
ULTRACOLD QUANTUM GASES
B
K
Three-Body Recombination: K3 ∝ (k/µ)σ
++ +
a
+a
12
~( (
Vibrational Relaxation: Vrel ∝ (k/µ)σ
+ +1
2~( (+
a
Rate Equations:nX(t) = −[K3(a)]n
3X − [Vrel(a)]nXnX2
nX2(t) = −[Vrel(a)]nXnX2
nX , nX2: experimental observables !
![Page 17: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/17.jpg)
SIGNATURES OF EFIMOV EFFECT?!
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BUILDING INTUITIVE PICTURE
r0 | |a
R
W R( )
Efimov States !
r0(
(
lnN =
Phase shift jumps of Cross section: Efimov features !
Increasing a ...... we are creating new
New Efimov State:
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SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation + +1
2~( (+
a
+
~
![Page 20: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/20.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation + +1
2~( (+
a
~
+
![Page 21: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/21.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation + +1
2~( (+
a
+
~
+
![Page 22: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/22.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation + +1
2~( (+
a
+
Resonant
Transmission
~
+
![Page 23: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/23.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation + +1
2~( (+
a
+
Resonant
Transmission
Efimov State
~
+
![Page 24: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/24.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation
Vrel = Aηsinh(2η)
sin2[
s0 ln(a
r0)+Φ
]
+sinh2(η)a
Aη , Φ, η: details !
+ +1
2~( (+
a
+
Resonant
Transmission
Efimov State
~
+
![Page 25: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/25.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Vibrational Relaxation
Vrel = Aηsinh(2η)
sin2[
s0 ln(a
r0)+Φ
]
+sinh2(η)a
Aη , Φ, η: details !
+ +1
2~( (+
a
+
Resonant
Transmission
Efimov State
~
+
![Page 26: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/26.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
++
~
![Page 27: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/27.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
++
+
~
~
![Page 28: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/28.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
++
+
~
~
![Page 29: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/29.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
++
+
~
~
![Page 30: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/30.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
Interference
++
+
~
~
![Page 31: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/31.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
~
+
Interference
++
+
~
Small
![Page 32: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/32.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
~
+
Interference
++
+
~
Small
K3 = Bηsin2[
s0 ln(ar0) + Φ
]
a4
Bη , Φ: details !
![Page 33: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/33.jpg)
SIGNATURES OF THE EFIMOV EFFECT
Three-Body Recombination ++ +
a
+a
12
~( (
~
+
Interference
++
+
~
Small
K3 = Bηsin2[
s0 ln(ar0) + Φ
]
a4
Bη , Φ: details !
![Page 34: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/34.jpg)
OBSERVATION OF THE EFIMOV EFFECT
Rate Equations:nX(t) = −[K3(a)]n
3X − [Vrel(a)]nXnX2
nX2(t) = −[Vrel(a)]nXnX2
-
| |
Three features needto be observed !
![Page 35: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/35.jpg)
LIMITATIONS
At finite temperatures only a finte number of featurescan be expected to be observed.
amin ≈ r0[eπ/s0 ]N ⇒ Tmax . 1/ma2min
(spacing: eπ/s0 ≈ 22.7) Large a / Low T !
10-30
10-25
10-20
10-15
10 100 1000 10000 100000
K3
(cm
6 /s)
−a (a.u.)
1 mK
100 µK
10 µK
1 µK
100 nK
10 nK
0.1 nK − 1 nK
−aI−aII−aIII−aIV−aV−aVI−aVII
a4
Three-BodyShape Resonances
AnalyticalFormula
B+B+B Collisions
10 100 1000 10000 100000
a (a.u.)
1 mK
100 µK
10 µK
1 µK
100 nK
10 nK0.1 nK − 1 nK
aI aII aIII aIV aV aVI aVII
a4 scaling
MultichannelInterference Minima
AnalyticalFormula
![Page 36: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/36.jpg)
CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Analytical Formula
400 nK250 nK
10 nK
400 nK
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CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Minimum [Esry PRL (1999)]et. al,
400 nK250 nK
10 nK
400 nK
![Page 38: Efimov Effect IN ULTRACOLD ATOMIC GAS...ENHANCING THE OBSERVABILITY OF THE Efimov Effect IN ULTRACOLD ATOMIC GAS MIXTURES Jose· P. D’Incao and Brett D. Esry Department of Physics,](https://reader030.vdocument.in/reader030/viewer/2022040807/5e4b1d89e2e3836e0d68e4cb/html5/thumbnails/38.jpg)
CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Minimum [Esry PRL (1999)]et. al,
Used to optimize loss !
250 nK400 nK
10 nK
400 nK
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CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Peak [Esry PRL (1999)]et. al,
400 nK250 nK
10 nK
400 nK
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CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Different slopes [Esry PRL (1999)]et. al,
400 nK250 nK
10 nK
400 nK
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CESIUM EXPERIMENT - INNSBRUCK
RUDI GRIMM’S GROUP
Finite Energy Effects [D'Incao, Suno, Esry PRL (2004)],
400 nK250 nK
10 nK
400 nK
0+
2+
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SINGLE SPECIE ATOMIC GASES
• Large spacing (eπ/s0 ≈ 22.7) between Efimov features
• amin ≈ r0[eπ/s0 ]N → Tmax . 1/ma2min: large a, low T
• 133Cs: amin ≈ 4.× 106 a.u.; Tmax ≈ 8.× 10
−5 nK (✗)
TWO SPECIES ATOMIC GASES
• Spacing (eπ/s0) can be made smaller (✓)
• Experimentally accessible amin and Tmax (✓)
• Competition different 3-body processes: important (?)
• Favorable conditions: Boson-Fermion mixtures (✓)
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TWO SPECIES ATOMIC GASES
EXPERIMENTS: 87Rb-40K (JILA)23Na-6Li (MIT) Interspecies Feshbach resonances !
Two types of collisions are important: XXY and XY Y
Competition !
Recombination (no molecules !)
nX ≈ −[KX+X+Y3 (a)]nYn
2X − [K
X+Y+Y3 (a)]n2
YnX
nY ≈ −[KX+X+Y3 (a)]n2
XnY − [KX+Y+Y3 (a)]nXn
2Y,
Relaxation
nX ≈ −[V XY+Xrel
(a)]nXYnX
nY ≈ −[V XY+Yrel
(a)]nXYnY
nXY ≈ −[V XY+Xrel
(a)]nXnXY − [VXY+Yrel
(a)]nYnXY
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TWO SPECIES ATOMIC GASES
Efimov Physics → a dependence in K3, Vrel.
[Gross scaling, valid for E . 1/2µa2]
Vrel K3 (D3)
Jπ E a > 0 a < 0 E a > 0 a < 0
BBX 0+* const ∗[Ps0 ]a const const(k4) ∗[Ms0 ]a4 ∗[Ps0 ]|a|
4
δ =mXmB
1− k2 a3−2p0 const k2(k6) a6 |a|6−2p0
2+δ<δc* k4 ∗[Ps0 ]a
5 const k4(k8) ∗[Ms0 ]a8 ∗[Ps0 ]|a|
8
2+δ>δck4 a5−2p0 const k4(k8) a8 |a|8−2p0
FFX 0+ const a1−2p0 const k4(k8) a8 |a|8−2p0
δ =mXmF
1−δ<δc* k2 ∗[Ps0 ]a
3 const k2(k6) ∗[Ms0 ]a6 ∗[Ps0 ]|a|
6
1−δ>δck2 a3−2p0 const k2(k6) a6 |a|6−2p0
2+ k4 a5−2p0 const k4(k8) a8 |a|8−2p0
D’Incao and Esry, Submitted to PRL.(*) Efimov Effect !
s0 depends on δ!
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TWO SPECIES ATOMIC GASES
-6
-4
-2
0
2
4
6
δ = mX/mB
(a) BBX
Jπ= 0+
Jπ= 1- Jπ= 2+
-s0
p0 p0
-s0
0.01 1 100
δc
-6
-4
-2
0
2
4
6
δ = mX/mF
(b) FFX
0.01 1 100
Jπ= 0+
Jπ= 1-
Jπ= 2+p0
p0
p0
-s0
δc
* Here !
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TWO SPECIES ATOMIC GASES
-8
-4
0
4
8
δ = mX/mB
BBX Systems
-s0
eπ/s0
0.01 1 100
mB=mX
We want mixtures with heavy Bosons (mB >> mX) !
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EFIMOV EFFECT IN BOSON-BOSON MIXTURES
mB À mb BB b collisions: s0 large→ eπ/s0 small (✓)B b b collisions: s0 small→ eπ/s0 large (✗)
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EFIMOV EFFECT IN BOSON-BOSON MIXTURES
mB À mb BB b collisions: s0 large→ eπ/s0 small (✓)B b b collisions: s0 small→ eπ/s0 large (✗)
Three-Body Recombination
B+B+b
B+b+b
?
| |
B+B+b
B+b+b
?
| |
| |
Condition: nB À nb
nB = −KB+B+b3 nbnB
2
nb = −KB+B+b3 n2
Bnb
enough signal ? (✗)
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EFIMOV EFFECT IN BOSON-BOSON MIXTURES
mB À mb BB b collisions: s0 large→ eπ/s0 small (✓)B b b collisions: s0 small→ eπ/s0 large (✗)
Three-Body Recombination
B+B+b
B+b+b
?
| |
B+B+b
B+b+b
?
| |
| |
Condition: nB À nb
nB = −KB+B+b3 nbnB
2
nb = −KB+B+b3 n2
Bnb
enough signal ? (✗)
Vibrational Relaxation
Bb+b
Bb+B
?
Condition: nb = 0
nB = −VBb+Brel
nBnBb
nBb = −VBb+Brel
nBbnB
Bb+Bb collisions can be important ! (✗)
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EFIMOV EFFECT IN BOSON-FERMION MIXTURES
mB À mF BBF collisions: s0 large→ eπ/s0 small (✓)BFF collisions: no Efimov Effect (✗)
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EFIMOV EFFECT IN BOSON-FERMION MIXTURES
mB À mF BBF collisions: s0 large→ eπ/s0 small (✓)BFF collisions: no Efimov Effect (✗)
Three-Body Recombination
B+B+F
B+F+F
6k
| |
| |
| |k
B+B+F
B+F+F
Condition: T . Tmax (✓)nB = −K
B+B+F3 nFnB
2
nF = −KB+B+F3 n2
BnF
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EFIMOV EFFECT IN BOSON-FERMION MIXTURES
mB À mF BBF collisions: s0 large→ eπ/s0 small (✓)BFF collisions: no Efimov Effect (✗)
Three-Body Recombination
B+B+F
B+F+F
6k
| |
| |
| |k
B+B+F
B+F+F
Condition: T . Tmax (✓)nB = −K
B+B+F3 nFnB
2
nF = −KB+B+F3 n2
BnF
Vibrational Relaxation
BF+B
BF+F
-3.33
Condition: T . Tmax (✓)nB = −V
BF+Brel
nBnBF
nBF = −VBF+Brel
nBFnB
BF +BF collisions suppressed (p-wave)
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BOSON-FERMION MIXTURES
KB+B+F3 and V BF+B
rel
B − F eπ/s0 |amin|(a.u.) Tmax(nK)133Cs−6Li 4.877 1.6× 104 60.0 ✓
87Rb−6Li 6.856 5.6× 104 5.00 ✓
23Na−6Li 36.28 3.3× 108 ¿ 0.1 ✗ (MIT)7Li−6Li > 100 À 108 ¿ 0.1 ✗
133Cs−40K 47.02 9.2× 107 ¿ 0.1 ✗
87Rb−40K > 100 À 108 ¿ 0.1 ✗ (JILA)23Na−40K > 100 À 108 ¿ 0.1 ✗
7Li−40K > 100 À 108 ¿ 0.1 ✗
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BOSON-FERMION MIXTURES
7.5
5
2.5
0 1000 10000
K3/
a4 (10
-39 c
m2 /s
)
a (a.u.)
a4
eπ/s0
s-wave CsLi*
133Cs + 133Cs + 6Li
p-wave CsLi
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SUMMARY
• Ultracold Quantum Gases: clear signature of EFIMOV EFFECT
• Boson-Fermion mixtures (mB À mF ): favorable system
• Extremely long-lived BF molecules: EFIMOV PHYSICS