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