Solitons in atomic Bose Einstein Condensates BEC Gediminas

Solitons in atomic Bose. Einstein Condensates (BEC) Gediminas Juzeliūnas Institute of Theoretical Physics and Astronomy of Vilnius University, Vilnius, Lithuania

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

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 Bose. Einstein 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) n Wavefunction of a condensate For simplicity V=0 (no trapping potential):

Non-linear Schrödinger equation (Gross-Pitaevskii) n Wavefunction of the condensate - Interaction strength between the atoms

Non-linear Schrödinger equation (Gross-Pitaevskii) n Wavefunction of the condensate Linear wave equation Wave-packet is spreading out

Non-linear Schrödinger equation (Gross-Pitaevskii) n Wavefunction of the condensate Non-linear wave equation Non-spreading wave-packets (solitons) are possible

Non-linear Schrödinger equation (Gross-Pitaevskii) n Wavefunction of the condensate Bright soliton Dark soliton

Non-linear Schrödinger equation (Gross-Pitaevskii) n Wavefunction of the condensate Bright soliton 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) n n Solitons in BEC (dark, bright), since 1999 q q 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) n

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

A very sharp phase slip & a hole in the density are needed:

n n Our method: Adiabatic passage in a tripod configuration 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: Control beam:

Dark state: Destructive interference Cancelation of absorption: - no losses - EIT

Dark state:

Dark state: Atom remains in the dark state: Adiabatic passage (STIRAP) - a smooth transition 1→ 2 by changing the ratio

Dark state: Atom remains in the dark state: Adiabatic passage 1→ 2 → 1 Double STIRAP (two STIRAPs)

Dark state: Adiabatic passage 1→ 2 → 1 π phase slip

Dark state: Atom remains in the dark state: Adiabatic passage 1→ 2 → 1 π phase slip A problem

Dark state: Atom remains in the dark state: Adiabatic transition 1→ 2 → 1 π phase slip The problem by-passed

Tripod configuration Two degenerate dark states: e. g. , n 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 (Double STIRAP BEC initially in the state 1: with a support beam 3) π phase imprinting on the BEC in the state 1:

After the sweeping n Phase imprinting → (dark) soliton formation n π phase slip; n a hole in the density

After the sweeping n Phase imprinting → (dark) soliton formation More specifically - dark-bright soliton pair n π phase slip; n a hole in the density n

A soliton molecule - two component dark soliton (dark-dark soliton pair) n 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 n n n A new method of creating solitons Robust Creation of soliton molecules is possible

Thank you!