Cold spinor atoms in optical lattice introduction Mirosaw

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Cold spinor atoms in optical lattice (introduction) Mirosław Brewczyk Mariusz Gajda Katarzyna Maciaszek Joanna

Cold spinor atoms in optical lattice (introduction) Mirosław Brewczyk Mariusz Gajda Katarzyna Maciaszek Joanna Pietraszewicz Tomasz Sowiński Tomasz Świsłocki October 20, 2010

Optical lattice

Optical lattice

Optical lattice Contact interactions

Optical lattice Contact interactions

Contact interactions

Contact interactions

Contact interactions

Contact interactions

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Dipolar interactions Contact interactions spatial angular momentum and total spin of interacting atoms are

Dipolar interactions Contact interactions spatial angular momentum and total spin of interacting atoms are conserved independently

Dipolar interactions spatial angular momentum is not conserved total spin is not conserved total

Dipolar interactions spatial angular momentum is not conserved total spin is not conserved total angular momentum IS CONSERVED

Hamiltonian Dipolar interactions of the system spatial angular momentum is not conserved total spin

Hamiltonian Dipolar interactions of the system spatial angular momentum is not conserved total spin is not conserved total angular momentum IS CONSERVED

Hamiltonian of the system laser wavelength recoil energy magnetic field unit

Hamiltonian of the system laser wavelength recoil energy magnetic field unit

Hamiltonian of the system laser wavelength recoil energy magnetic field unit

Hamiltonian of the system laser wavelength recoil energy magnetic field unit

Hamiltonian of the system Rubidium spin-1 atoms: Experimental realization:

Hamiltonian of the system Rubidium spin-1 atoms: Experimental realization:

Dipolar interactions Hamiltonian of the system Rubidium spin-1 atoms: Experimental realization:

Dipolar interactions Hamiltonian of the system Rubidium spin-1 atoms: Experimental realization:

Dipolar interactions • Field operator (2 f+1 components) • Ladder spin-f operators

Dipolar interactions • Field operator (2 f+1 components) • Ladder spin-f operators

Dipolar interactions • Field operator (2 f+1 components) • Ladder spin-f operators

Dipolar interactions • Field operator (2 f+1 components) • Ladder spin-f operators

Dipolar interactions

Dipolar interactions

Three scenarios Dipolar interactions for mf=±f

Three scenarios Dipolar interactions for mf=±f

Three scenarios for mf=±f 1. Spin of both atoms remains unchanged just another contribution

Three scenarios for mf=±f 1. Spin of both atoms remains unchanged just another contribution to the contact interaction

Three scenarios for mf=±f 1. Spin of both atoms remains unchanged just another contribution

Three scenarios for mf=±f 1. Spin of both atoms remains unchanged just another contribution to the contact interaction

Three scenarios for mf=±f 2. One of atoms changes spin by ONE quanta since

Three scenarios for mf=±f 2. One of atoms changes spin by ONE quanta since conservation of total angular momentum holds a spatial part of the wave function changes (excitation in z direction is also needed)

Three scenarios for mf=±f 2. One of atoms changes spin by ONE quanta since

Three scenarios for mf=±f 2. One of atoms changes spin by ONE quanta since conservation of total angular momentum holds a spatial part of the wave function changes (excitation in z direction is also needed)

Three scenarios for mf=±f 3. Both atoms change their spins by ONE quanta since

Three scenarios for mf=±f 3. Both atoms change their spins by ONE quanta since conservation of total angular momentum holds both atoms have to reach state with angular momentum (excitation in z direction is possible but not necessary)

Dynamics in periodic potential Mathieu functions Wannier functions

Dynamics in periodic potential Mathieu functions Wannier functions

Wannier Dynamicsfunctions in periodic potential Mathieu functions Wannier functions

Wannier Dynamicsfunctions in periodic potential Mathieu functions Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

Wannier functions

MODEL as simple as possible, but not simpler

MODEL as simple as possible, but not simpler

Model as simple as possible. . . Atoms are in the spatial ground state

Model as simple as possible. . . Atoms are in the spatial ground state

Lowestaspossible transitions Model simple as possible. . . Atoms are in the spatial ground

Lowestaspossible transitions Model simple as possible. . . Atoms are in the spatial ground state

Lowest possible transitions 1. State with „angular momentum” (without z excitation)

Lowest possible transitions 1. State with „angular momentum” (without z excitation)

Lowest possible transitions 1. State with „angular momentum” (without z excitation)

Lowest possible transitions 1. State with „angular momentum” (without z excitation)

Lowest possible transitions 2. State with „angular momentum” (with z excitation)

Lowest possible transitions 2. State with „angular momentum” (with z excitation)

Lowest possible transitions 2. State with „angular momentum” (with z excitation)

Lowest possible transitions 2. State with „angular momentum” (with z excitation)

Two atoms in lattice site initial state: one atom transfer: (z excitation needed) one

Two atoms in lattice site initial state: one atom transfer: (z excitation needed) one atom transfer: (without z excitation) one atom transfer: (with z excitation)

Two Origin atoms of dipolar in lattice resonances site initial state: one atom transfer:

Two Origin atoms of dipolar in lattice resonances site initial state: one atom transfer: (z excitation needed) one atom transfer: (without z excitation) one atom transfer: (with z excitation)

Origin of dipolar resonances

Origin of dipolar resonances

Origin of dipolar resonances

Origin of dipolar resonances

Origin of dipolar resonances RESONANT MAGNETIC FIELD

Origin of dipolar resonances RESONANT MAGNETIC FIELD

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Dipolar transfer

Conclusion Chromium spin-3 NEEDED

Conclusion Chromium spin-3 NEEDED