carsten klempt et al- direct observation of vacuum fluctuations in spinor bose-einstein condensates

8/3/2019 Carsten Klempt et al- Direct observation of vacuum fluctuations in spinor Bose-Einstein condensates

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Direct observation

of vacuum fluctuations

in spinor

Bose-Einstein

condensates

Carsten Klempt, Oliver Topic, Manuel Scherer,Thorsten Henninger, Wolfgang Ertmer, and Jan ArltInstitute of Quantum Optics

Gebremedhn Gebreyesus, Philipp Hyllus, and Luis SantosInstitute of Theoretical Physics

of

in


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Vacuum fluctuations in spinor BECs

Introduction

Nonlinear crystal

Optical spontaneous parametric down-conversion

pair creation parametric

amplification

amplification ofvacuum

fluctuations

entangled pairs (EPR)

squeezing


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Spinor BECs

Confined spinor BECs

Vacuum fluctuations

Introduction

Contents

Experiments


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Spinor BECs


Vacuum fluctuations

Introduction

Contents

Experiments


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Atoms with non-zero spin

Spinor gases:

Alkali-atoms

with non-zero spin

Here:

87Rb F=2 mF=0

E= p m + q m2

p ~ B

q ~ B2

< 0


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Energy scales

Competing energy scales define the ground state

mF=0

mF=1

Repulsive interaction

quadratic Zeeman energy interaction energy

mF=0

mF=1

Attractive interaction

quadratic Zeeman effect

interactions


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Ground states of spinor BECs

H. Schmaljohann et al., PRL 92, 040402 (2004).

Ground states ofF =2 Spinor Bose-Einstein Condensates

Ciobanu et al., PRL 61, 033607 (2000).


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Spinor BEC in F=2, mF=0

( ) ( ) ( ) ( )

( )( )( )( )

( )

+

=+=

+

+

r

r

r

r

r

rrrr

r

r

r

r

r

rrrrrrr

2

1

0

1

2

00

0

0

0

0

( ) ( ) ( ) ( )rrUrVM

rrrrhr

0

2

000

22

02

++

=

Condensate Excitations

Scalar Gross-Pitaevskii equation for m=0

Field operator for the spinor BEC in F=2 mF=0


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Hamiltonian for spin excitations

( )[ ]( )[ ]

++

+

=

+

+=

+

1111

1

3

r

qrH

rdHeff

m

meffm

r

r

( ) ( )rnUreffrr

011

Hamiltonian (linear regime)

( ) ( ) ( ) ( ) +++

rnUUrVMrHeff

rrhr01100

22

2

Veff

Veff

Spin changing collisions

This Hamiltonian describes the time evolution of the mF=1 components

homogeneous case

mF=0

Identical to optical parametric amplification !


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Spin Bogoliubov modes

2 possibilities [Lamacraft, PRL 98, 160404 (2007)]

1) Real Eigenvalues: system is stable

no population in mF=1

2) Complex Eigenvalues: system is unstable

Eigenmodes of the Hamiltonian

are Spin Bogoliubov modes in mF=1with wavevector k

which are exponentially amplified: e2 Im(E) t


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Stability diagram (homogeneous)

q>0

stable

qcr


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Measurements on homogeneous system

87Rb F=1

Creation of spatial structure (broken symmetry)Sadler et al., Nature443, 312 (2006)


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Spinor BECs


Vacuum fluctuations

Introduction

Contents

Experiments


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Confined case

What changes when weconsider the trapping potential ?

quadratic Zeeman effect

interactions

confinement


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Hamiltonian for spin excitations

( )[ ]( )[ ]

++

+

=

+

+=

+

1111

1

3

r

qrH

rdHeff

m

meffm

r

r

( ) ( )rnUreffrr

011

Hamiltonian (linear regime)

( ) ( ) ( ) ( ) +++

rnUUrVMrHeff

rrhr01100

22

2

Veff

Veff

This Hamiltonian describes the time evolution of the mF=1 components

confined case

mF=0


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Spin Bogoliubov modes

2 possibilities

1) Real Eigenvalues: System is stable


2) Complex Eigenvalues: System is unstable

Eigenfunctions of the Hamiltonian

are Spin Bogoliubov modes in mF=1composed of the eigenstates of the eff. Potential

which are exponentially amplified


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Stability diagram (homogeneous)

q>0

stable

qcr


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Spinor BECs


Vacuum fluctuations

Introduction

Contents

Experiments


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Experimental setup

Dispenser

MOT cell(10-9 mBar) science cell

(< 10-11 mBar)

differentialpumping stage

LIAD: an efficient, switchable atom sourceC. K., T. van Zoest, T. Henninger, O. Topic, E. Rasel, W. Ertmer und J. Arlt, Phys. Rev. A 73, 13410 (2006).

4109 atomsat 45 K

87Rbmolasses

40Kmolasses

5107 atomsat 260 K


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Optical dipole trap

Optical dipole trap ( =1064 nm, 2 W)whorizontal = 25 m, wvertical = 60 m

T = 1,0 K

center of coils:(100 Hz / 15 Hz)

6 106 87Rb-atoms

3 106 40K-atoms

4 106 87Rb-atoms

2 106 40K-atoms

T = 1,5 K

dipole trap(370 Hz / 170 Hz)

transfer

evaporation

3 105 87Rb-atoms

3 105 40K-atoms

T = 270 nK

B = 8 mG @ 550 G

B = 4 mG @ 1 G


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F=2

mF=-1

mF=0

mF=2

mF=1

mF=-2

78 80 82 84 86

-8

-6

-4

-2

0

2

4

6

8

Energyofc

oupledsystem[

MHz]

Radiofrequency [MHz]

Radio frequency

sweep in 1ms

78 Mhz 82 MHz

B-Field=120G

mF

= -1

mF=0

mF=2

mF

=1

mF= -2

mF=1

mF=0

mF= -2

mF

= -1

mF=2

Spin preparation

87Rb


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Hold time with

magn. field

Stern-Gerlach and

detection

mF=0 preparationat 120 G

297.5mG 395mG 512mG 570.5mG

x=46Hz

y=132Hz

z=176Hz

NBEC

=4x104

thold=21ms

Measuring sequence

Purification:strong gradient

0

-1

+1


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Spin dynamics resonances

exp

theory


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Ground state and excited states

1st Resonance 2nd Resonance

mF=1

mF=0

mF=-1


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Spinor BECs


Vacuum fluctuations

Introduction

Contents

Experiments


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Triggering of spinor dynamics

2 possibilities

1) System is stable


2) System is unstable

Eigenfunctions of the Hamiltonian

are Spin Bogoliubov modes in mF=1composed of the eigenstates of the eff. Potential

which are exponentially amplified

What triggers

the spinor dynamics ?


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Seed

2 possibilities

1) Spurious radiofrequencies or magnetic field noise

produce atoms in mF=1 in the spatial mode of the

initial BEC classical seed

2) No atoms present in mF=1 vacuum fluctuations


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Experimental verification

exp

theory

Produce a classical seeddeliberately:

Radio-frequency pulsewith extreme small amplitudecouples the BEC in mF=0symmetricallyto the states mF=1

(after purification)

V fl t ti i i BEC


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Classical vs quantum seed

exp

theory

classical

seed

vacuum

fluctuations

V fl t ti i i BEC


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Amplification of classical and quantum seed

classical fluctuations vacuum fluctuations

mF=1

mF=0

mF=-1



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Overlap of classical seed

How relevant is the classical seed ?



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Outlook

Analyze spatial structurequantitatively

Quantify fluctuations

Demonstrate squeezing(measure quadratures)

Extract EPR pairs ? Investigate effects ofdipolar interaction



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People

Carsten Klempt, Oliver Topic, ManuelScherer, Thorsten Henninger, WolfgangErtmer, and Jan ArltInstitute of Quantum Optics

Gebremedhn Gebreyesus, Philipp Hyllus,and Luis Santos

Institute of Theoretical Physics

carsten klempt et al- direct observation of vacuum fluctuations in spinor bose-einstein condensates

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