Transcript Pavadinimas - VU Teorinės fizikos ir astronomijos institutas

Solitons in atomic BoseEinstein Condensates (BEC)
Gediminas Juzeliūnas
Institute of Theoretical Physics and Astronomy of
Vilnius University, Vilnius, Lithuania
Collaboration
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P. Öhberg, Heriot-Watt University,
Edinburgh, Scotland
J. Ruseckas, Institute of Theoretical Physics
and Astronomy of Vilnius University
M. Fleischhauer, Technische Universität
Kaiserslautern, Germany
OUTLINE
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Ultra-cold atomic gases
Atomic Bose-Einstein condensates (BEC)
Solitons & solitons in atomic BEC
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Creation of solitons in atomic BEC
A new method of creating solitons in BEC
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Conclusions
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Atomic
Applications
Number 785 #1, July 17, 2006 by Phil Schewe and Ben Stein
A New BEC Magnetometer
A new BEC magnetometer represents the first application for BoseEinstein condensates (BECs) outside the realm of atomic physics.
Physicists at the University of Heidelberg have used a onedimensional BEC as a sensitive probe of the magnetic fields sample
surface.
The field sensitivity achieved thereby is at the level of magnetic
fields of nanotesla strength (equivalent to an energy scale of about
10-14 electronvolt) with a spatial resolution of only 3 microns.
…
(Applied Physics Letters, 27 June 2006)
Heidelberg Experiment
(Applied Physics Letters, 27 June 2006)
Bose-Einstein Condensation
(Velocity distribution)
BEC – A giant (non-linear) matter wave
Non-linear Schrödinger equation
(Gross-Pitaevskii)
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Wavefunction of a condensate
For simplicity V=0 (no trapping potential):
Non-linear Schrödinger equation
(Gross-Pitaevskii)
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Wavefunction of the condensate

- Interaction strength
between the atoms
Non-linear Schrödinger equation
(Gross-Pitaevskii)
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Wavefunction of the condensate
 0
Linear wave equation
Wave-packet is
spreading out
Non-linear Schrödinger equation
(Gross-Pitaevskii)

Wavefunction of the condensate
 0
Non-linear wave equation
Non-spreading wave-packets
(solitons) are possible
Non-linear Schrödinger equation
(Gross-Pitaevskii)
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Wavefunction of the condensate
 0
Bright soliton
 0
Dark soliton
Non-linear Schrödinger equation
(Gross-Pitaevskii)
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Wavefunction of the condensate
 0
Bright soliton
 0
Dark soliton
What is a bright and a dark soliton?
Intensity and phase of the condensate
Intensity and phase of the condensate
Dark soliton:
Difference between dark and bright solitons
Bright soliton
Dark soliton
Intensity and phase of the condensate
First observation of (bright) solitons
(1844, J. Scott Russell )
Observed a solitary water wave
in a water canal near Edinburgh
John Scott Russell
(1808 – 1882)
Recreating Russell’s soliton in 1995
Currently
Optical solitons (bright, dark) since the 60’s
(Depends on the sign of non-linearity)
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Solitons in BEC (dark, bright), since 1999
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Rb, Na – dark solitons (κ>0)
Li
– bright solitons (κ<0)
Usual way to create a (dark) soliton in
BEC
To imprint the phase
(by illuminating a half
of the BEC)
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Drawbacks
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Not very sharp phase slip
No hole in the density
Sensitive to the duration of illumination
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Not robust method
A very sharp phase slip &
a hole in the density
are needed:
Our method:
Adiabatic passage in a tripod configuration
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Robust
Both solitons and soliton molecules can be
produced
How does the adiabatic passage work?
Adiabatic passage
Λ configuration:
Two beams of light:
Probe beam:
 p  13 E p / 
Control beam: c  23 Ec / 
Dark state:
c2 / c1   p / c
D  1 c1  2 c2
Destructive interference
Cancelation of absorption: c3  0
- no losses
- EIT
Dark state:
D  1 c1  2 c2 ,
 p / c  0,
D 1
c1 / c2  c /  p
Dark state:
c2 / c1  1 / 2
D  1 c1  2 c2
Atom remains in the dark state:
Adiabatic passage (STIRAP) - a smooth
transition 1→2 by changing the ratio  2 / 1
Dark state:
c2 / c1  1 / 2
D  1 c1  2 c2
Atom remains in the dark state:
Adiabatic passage 1→2 →1
Double STIRAP (two STIRAPs)
Dark state:
c2 / c1  1 / 2
D  1 c1  2 c2
Adiabatic passage 1→2 →1
1  1  π phase slip
Dark state:
c2 / c1  1 / 2
D  1 c1  2 c2
Atom remains in the dark state:
Adiabatic passage 1→2 →1
1  1  π phase slip
1  0  A problem
Dark state:
c2 / c1  1 / 2
D  1 c1  2 c2
Atom remains in the dark state:
Adiabatic transition 1→2 →1
1  1  π phase slip
1  0, 3  0 
The problem by-passed
Tripod configuration
Two degenerate dark states:
e.g.,
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J. Ruseckas, G. Juzeliūnas and P.Öhberg, and M.
Fleischhauer, Phys. Rev. Letters 95, 010404 (2005).
Tripod configuration
A suggested setup
to create solitons in BEC
BEC initially in the state 1: (Double STIRAP with
a support beam 3)
'1  '1 
π phase imprinting on the BEC in the state 1:
After the sweeping
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Phase imprinting → (dark) soliton formation
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π phase slip;
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a hole in the density
After the sweeping
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Phase imprinting → (dark) soliton formation
More specifically - dark-bright soliton pair
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π phase slip;
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a hole in the density
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A soliton molecule - two component dark
soliton (dark-dark soliton pair)
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Both components 1 and 2 are populated
after the sweeping (with a π phase slip)
Subsequently the solitons oscillate:
Oscillation of solitons forming the molecule
Conclusions
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A new method of creating solitons
Robust
Creation of soliton molecules is possible
Thank you!