1 / 15

Oscillating Spinor Solitons - PowerPoint PPT Presentation

  • Uploaded on

Oscillating Spinor Solitons. The project „ Photonic implementations of quantum-enhanced technologies ” is realized within the TEAM programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund ( Programme Innovative Economy 2007-2013).

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Oscillating Spinor Solitons' - hua

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Oscillating Spinor Solitons

The project „Photonic implementations of quantum-enhanced technologies” isrealizedwithin the TEAM programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund (ProgrammeInnovativeEconomy 2007-2013)

Quantum Technologies Conference, Toruń

Oscillating spinor solitons

Quantum Technologies Conference, Toruń

Oscillating Spinor Solitons

Piotr SzańkowskiMarek TrippenbachEryk Infeld


Bose-Einstein Condensate in the optical trap

Solitons in the spinor BEC

Soliton collisions – creation of the Oscillatons

Mathematical description of the Oscillatons

Collisions of the Oscillatons

Quantum Technologies Conference, Toruń

The system
The system

Bose-Einstein Condensate at T=0 confined in the optical trap.

Spins of trapped atoms are not frozen like in the magnetic trap!

The spinor nature of the condensate can be manifested.

The Hamiltonian of the system:

We will consider atoms with hyperfine spin F=1 (e.g. 87Rb).

the field operator of each spin component

where af is s-wave scattering length of total spin f channel

trapping potential

spin 1 operators

Quantum Technologies Conference, Toruń

Spinor gross pitaevskii equation
Spinor Gross-Pitaevskii equation

Mean-field approximation and variational principleleads to the spinor Gross-Pitaevskii equation


the order parameter (spinor wave function)


Quantum Technologies Conference, Toruń


Generally, spinor GP equation,

Changethesign of c0withFeshbachresonance

Lift trap adiabatically and obtainthesoliton

Theground state for c0 > 0

supports two kinds of soliton solutions:

Polar soliton


The spin of polar and ferromagnetic solitons

rotation operator

Quantum Technologies Conference, Toruń

Complete integrability of the spinor gp equation
Complete Integrability of the spinor GP equation

For γ = 1 spinor GP equation is Completely Integrable.

Solitons collide with each other elastically:

There is no transfer of spin or momentum.

Solitons retain their character after the collision.

What happens when γ is not equal to 1?

( T. Tsuchida and M. Wadati, J. Phys. Soc. Jpn. 67, 1175 (1998) )

Quantum Technologies Conference, Toruń

Soliton collision creation of the oscillatons
Soliton collision: creation of the Oscillatons

Bullet:Ferromagnetic Soliton

Target:Polar Soliton

Quantum Technologies Conference, Toruń

Spin transfer
Spin transfer

Out:Post - polarOscillaton

Out:Post - polarOscillaton

Out: Post - ferromagneticOscillaton

Out: Post - polarOscillaton

Before the collision:

Whatisthe spin afterthecollisionof two polar solitons?

Whatisthe spin afterthecollision?



In: FerromagneticSoliton

In: PolarSoliton

Quantum Technologies Conference, Toruń

Mathematical model of the oscillatons
Mathematical model ofthe Oscillatons


Oscillations of the components:


The Oscillaton equations:

Amplitude of theoscillationsdepends on α!

The frequency of the oscillations:

Quantum Technologies Conference, Toruń

Approximate solutions post polar oscillatons
Approximate solutions:Post-polar Oscillatons

Quantum Technologies Conference, Toruń

Approximate solutions post ferromagnetic oscillatons
Approximate solutions:Post-ferromagnetic Oscillatons

Quantum Technologies Conference, Toruń

Solitons as the special case of oscillatons
Solitons as the special case of Oscillatons

Polar soliton:

Ferromagnetic soliton:

Quantum Technologies Conference, Toruń

Oscillaton collisions

Alice (lesser spin)

Bob (greater spin)

IN:Two Oscillatons created in different soliton collisions

Oscillaton Alice

Oscillaton Bob

OUT:Two, altered Oscillatons!

Quantum Technologies Conference, Toruń


Polar and ferromagnetic solitons in spinor Bose-Einstein condensate

Inelastic collisions of solitons leads to creation of new kind of solutions – the Oscillatons

Solitons are special cases of the Oscillatons

The Oscillatons are similiar to solitons in Completely Integrable systems:they propagate in time without dispersion andretain their character after colliding with each other

Quantum Technologies Conference, Toruń