View
3
Download
0
Category
Preview:
Citation preview
Tuning Static and Dynamic Properties of a QuasiOne-Dimensional Bose-Einstein Condensate
DPG conference 2016
Javed Akram, Axel Pelster
1: BEC with dimple trap Phys. Rev. A 93, 023606 (2016) andarXiv:1510.07138
2: Impurity in BEC Phys. Rev. A (in press), arXiv:1508.054823: BEC in GOST J. Phys. B: At., Mol. Opt. Phys. (in press),
arXiv:1509.05987
March 4, 2016
1
1.1: Quasi one-dimensionalGross-Pitaevskii equation
Quasi one-dimensional setting1 (aB/lz)Υ 1 , here Υ = lr/lz
ψ(r, t) = ψ(z, t)φ(r⊥, t) here φ(r⊥, t) = e− x2+y2
2Υ2
Υ√
π e−i ωrωz t
i∂∂ t
ψ(z, t) =
−1
2∂ 2
∂z2 +z2
2+ U1D
dT (z) + GB ‖ ψ(z, t) ‖2
ψ(z, t)
Here U1DdT (z) ∝ I(z)
∆ with ∆ = ω−ωA.
For NB = 2×105 atoms of 87Rb GB = 2NBωraB/lzωz = 11435.9
1J. Exp. Theor. Phys. 98, 908 (2003).Javed Akram, Axel Pelster | DPG conference 2016
2
1.2: Stationary condensate wave functionDimple trap vs HGdT potential
U<0 (Red detuned)
−20 −10 0 10 200
0.05
0.1
0.15
0.2
0.25
z
‖ψ(z)‖2
-1000-900-800-700-600-500-400-300-200-1000
U
TEM00 mode dimple trap (dT)
U1DdT (z) = Ue−
z2
w2
−20 −10 0 10 200
0.02
0.04
0.06
0.08
0.1
0.12
0.14
z
‖ψ(z)‖2
-1000-900-800-700-600-500-400-300-200-1000
U
TEM01 Hermite-Gaussian dimpletrap (HGdT)
U1DHGdT (r) = Uz2e−
z2
w2
Here U ∝ 1∆ with ∆ = ω−ωA
Javed Akram, Axel Pelster | DPG conference 2016
3
1.3: Stationary condensate wave functionDimple trap vs HGdT potential
U>0 (blue detuned)
−20 −10 0 10 200
0.005
0.01
0.015
0.02
0.025
0.03
z
‖ψ(z)‖2
10009008007006005004003002001000
U
TEM00 mode dimple trap (dT)
U1DdT (z) = Ue−
z2
w2
−20 −10 0 10 200
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
z
‖ψ(z)‖2
10009008007006005004003002001000
U
TEM01 Hermite-Gaussian dimpletrap (HGdT)
U1DHGdT (r) = Uz2e−
z2
w2
Here U ∝ 1∆ with ∆ = ω−ωA
Javed Akram, Axel Pelster | DPG conference 2016
4
1.4: Excitation of SolitonsAfter having switched off the dT or HGdT
U>0 (Blue detuned)
0 5 10 15 20 250
0.005
0.01
0.015
0.02
0.025
0.03
z
‖ψ(z)‖2
t=0t =0.75
dT potential
U=100
0 5 10 15 20 250
0.005
0.01
0.015
0.02
0.025
0.03
z
‖ψ(z)‖2
t=0
t =5.3
HGdT potential
U=3500
Javed Akram, Axel Pelster | DPG conference 2016
5
2.1: Equilibrium phase diagramLocalization of impurity 133Cs
g IB
-20 -10 0 10 20
g B
0
5
10
15
20
g IB
-20 -10 0 10 20
g B
0
5
10
15
20
g IB
-20 -10 0 10 20
g B
0
5
10
15
20(a) (b) (c)
(a) NB = 20 (b) NB = 200 and (c) NB = 800
Unstable region (Black), localized impurity region (Blue) & impurityexpelled to the condensate border (Red)
Javed Akram, Axel Pelster | DPG conference 2016
6
2.2: Numerical densityProfile of the BEC for GB = 16000
−2 −1 0 1 20.0258
0.026
0.0262
0.0264
0.0266
0.0268
0.027
0.0272
z
nB(z)
-10-8-6-20
−0.4 −0.2 0 0.2 0.40
0.005
0.01
0.015
0.02
0.025
0.03
z
nB(z)
020406080100120
(a) (b)
gIBgIB
Interspecies coupling strength,(a) attractive (gIB < 0) (b) repulsive (gIB > 0)
here NB = 800 and gIBc ≈ 110
Javed Akram, Axel Pelster | DPG conference 2016
7
2.3: Density profile of the BECInterspecies coupling strength switched off i.e. gIB = 0 at t = 0
0 2 4 6 8 10−30
−20
−10
0
10
20
30
t
z R,z
L
-8-6-4-2
attractive (gIB < 0)
z(t) =√
2µ sin(
t/√
2)
0 2 4 6 8 10−30
−20
−10
0
10
20
30
t
z R,z
L
12010080604020
repulsive (gIB > 0)
Soliton Freq.2 Ω/ωz = 1/√
2,Hamburg3 & Heidelberg Exp.4
2Phys. Rev. Lett. 84, 2298 (2000).3Nature Phys. 4, 496 (2008).4Phys. Rev. Lett. 101, 130401 (2008).
Javed Akram, Axel Pelster | DPG conference 2016
8
3.1: Gravito-optical surface trap (GOST)Experimental setup and potential
V (z) = V0e−z + z
0 5 10 15 20 250
5
10
15
20
25
z
V
Javed Akram, Axel Pelster | DPG conference 2016
9
3.2: Stationary mirror solutionThomas-Fermi approximation for the BEC
0 10 20 30 40 50 600
0.02
0.04
0.06
0.08
0.1
0.12
z
‖ψ(z)‖2
103
104
105
0 200 400 600 800 1000 12000
1
2
3
4
5x 10
−3
z‖ψ(z)‖2
106
107
108
(a) (b)
NB NB
TF solution (circles) Numerical solution (solid lines)
Javed Akram, Axel Pelster | DPG conference 2016
10
3.3: Innsbruck experimentFraction of remaining atoms during time-of-flight
Innsbruck Exp.5 (black-circles) & our numerical results(red-solid line) V0 = 453 and NB = 2400 133Cs atoms
0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
t (ms)
Rem
aining
Fraction
5Phys. Rev. Lett. 92, 173003 (2004).Javed Akram, Axel Pelster | DPG conference 2016
Announcement
616th Wilhelm and Else Heraeus Seminar
Ultracold Quantum Gases -
Current Trends and Future Perspectives
organized by Carlos S a de Melo and Axel Pelster
Bad Honnef (Germany); May 9 – 13, 2016
Invited Speakers: Eugene Demler (USA), Rembert Duine (Netherthelands), Tilman
Esslinger (Switzerland), Michael Fleischhauer (Germany), Thierry Giamarchi (Switzer-
land), Rudi Grimm (Austria), Johannes Hecker-Denschlag (Germany), Andreas Hem-
merich (Germany), Jason Ho (USA), Walter Hofstetter (Germany), Randy Hulet (USA),
Massimo Inguscio (Italy), Corinna Kollath (Germany), Stefan Kuhr (UK), Kazimierz
Rzazewski (Poland), Anna Sanpera (Spain), Luis Santos (Germany), Jorg Schmied-
mayer (Austria), Dan Stamper-Kurn (USA), Sandro Stringari (Italy), Leticia Tarruell
(Spain), Jacques Tempere (Belgium), Paivi Torma (Finland), Matthias Weidemuller
(Germany), Eugene Zaremba (Canada), Peter Zoller (Austria)
http://www-user.rhrk.uni-kl.de/˜apelster/Heraeus4/i ndex.html
Recommended