Solitons in atomic Bose-Einstein Condensates (BEC)

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Solitons in atomic Bose-Einstein Condensates (BEC)

• Gediminas Juzeliunas
• Institute of Theoretical Physics and Astronomy of
  Vilnius University, Vilnius, Lithuania

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Collaboration

• P. Öhberg, Heriot-Watt University, Edinburgh,
  Scotland
• J. Ruseckas, Institute of Theoretical Physics and
  Astronomy of Vilnius University
• M. Fleischhauer, Technische Universität
  Kaiserslautern, Germany

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OUTLINE

• Ultra-cold atomic gases
• Atomic Bose-Einstein condensates (BEC)
• Solitons solitons in atomic BEC
• Creation of solitons in atomic BEC
• A new method of creating solitons in BEC
• Conclusions

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Atomic
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Applications
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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 Bose-Einstein condensates (BECs) outside the realm of atomic physics. Physicists at the University of Heidelberg have used a one-dimensional 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)
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Heidelberg Experiment (Applied Physics Letters,
27 June 2006)
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Bose-Einstein Condensation (Velocity
distribution)
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BEC A giant (non-linear) matter wave
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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of a condensate
• For simplicity V0 (no trapping potential)

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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of the condensate

• Interaction strength
• between the atoms

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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of the condensate

Linear wave equation
Wave-packet is spreading out
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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of the condensate

Non-linear wave equation
Non-spreading wave-packets (solitons) are possible
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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of the condensate

Bright soliton
Dark soliton
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Non-linear Schrödinger equation(Gross-Pitaevskii)

• Wavefunction of the condensate

Bright soliton
Dark soliton
What is a bright and a dark soliton?
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Intensity and phase of the condensate
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Intensity and phase of the condensate
Dark soliton
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Difference between dark and bright solitons
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Bright soliton
Dark soliton
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Intensity and phase of the condensate
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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)
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Recreating Russells soliton in 1995
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Currently

• Optical solitons (bright, dark) since the 60s
• (Depends on the sign of non-linearity)
• Solitons in BEC (dark, bright), since 1999
• Rb, Na dark solitons (?gt0)
• Li bright solitons (?lt0)

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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

• Not very sharp phase slip
• No hole in the density
• Sensitive to the duration of illumination
• Not robust method

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A very sharp phase slip a hole in the density
are needed
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Our methodAdiabatic passage in a tripod
configuration

• Robust
• Both solitons and soliton molecules can be
  produced

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How does the adiabatic passage work?
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Adiabatic passage

• ? configuration

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Two beams of lightProbe beam Control beam

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Dark stateDestructive interference
Cancelation of absorption - no
losses- EIT
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Dark state
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Dark stateAtom remains in the dark state
Adiabatic passage (STIRAP) - a smooth transition
1?2 by changing the ratio
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Dark stateAtom remains in the dark state
Adiabatic passage 1?2 ?1 Double STIRAP (two
STIRAPs)
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Dark state Adiabatic passage 1?2 ?1
p phase slip
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Dark stateAtom remains in the dark state
Adiabatic passage 1?2 ?1 p
phase slip A problem

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Dark stateAtom remains in the dark state
Adiabatic transition 1?2 ?1
p phase slip The
problem by-passed
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Tripod configuration

• Two degenerate dark states
• e.g.,
• J. Ruseckas, G. Juzeliunas and P.Öhberg, and M.
  Fleischhauer, Phys. Rev. Letters 95, 010404
  (2005).

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Tripod configuration
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A suggested setup to create solitons in BEC
(Double
STIRAP with
a support beam 3)
BEC initially in the state 1
p phase imprinting on the BEC in the state 1
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After the sweeping

• Phase imprinting ? (dark) soliton formation
• p phase slip
• a hole in the density

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After the sweeping

• Phase imprinting ? (dark) soliton formation
• More specifically - dark-bright soliton pair
• p phase slip
• a hole in the density

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A soliton molecule - two component dark soliton
(dark-dark soliton pair)

• Both components 1 and 2 are populated
• after the sweeping (with a p phase slip)
• Subsequently the solitons oscillate

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Oscillation of solitons forming the molecule
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Conclusions

• A new method of creating solitons
• Robust
• Creation of soliton molecules is possible

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Thank you!