Optical latticesA new tool in condensed matter physics

research

Emil Lundh

Optical lattices – p. 1

Bottomline

Laser beams meet: interference pattern

Optical lattices – p. 2

Bottomline

Laser beams meet: interference pattern

Optical lattices – p. 2

Bottomline

Laser beams meet: interference pattern

Cold atoms see a periodic potential

Optical lattices – p. 2

Bottomline

Laser beams meet: interference pattern

Cold atoms see a periodic potential

We have created an artificial crystal.

Optical lattices – p. 2

Bottomline

Laser beams meet: interference pattern

Cold atoms see a periodic potential

We have created an artificial crystal.

Can be made in 1, 2 or 3 dimensions.

Optical lattices – p. 2

Why?

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scales

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scalesEasy to control - many buttons to tweak

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scalesEasy to control - many buttons to tweakEasy to detect

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scalesEasy to control - many buttons to tweakEasy to detect

Test condensed-matter theories

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scalesEasy to control - many buttons to tweakEasy to detect

Test condensed-matter theories

Quantum computing

Optical lattices – p. 3

Why?

Optical lattices have advantages over solids:Larger length scalesEasy to control - many buttons to tweakEasy to detect

Test condensed-matter theories

Quantum computing

Precision measurements

Optical lattices – p. 3

How to make an optical lattice

Optical lattices – p. 4

How to make an optical lattice

1. Laser light

Optical lattices – p. 4

How to make an optical lattice

1. Laser light

2. Ultracold atoms

Optical lattices – p. 4

How to make an optical lattice

1. Laser light

2. Ultracold atoms

3. Put 2 in 1

Optical lattices – p. 4

1. Laser light

Two laser beams meet: interference fringes –spots of high and low intensity

Two, three dimensions: use more beamsOptical lattices – p. 5

2. Cold atoms

Optical lattices – p. 6

2. Cold atoms

1. Laser cooling: T ≈ 1µK

Optical lattices – p. 6

2. Cold atoms

1. Laser cooling: T ≈ 1µK

2. Evaporative cooling: T ≈ 10 nK

Optical lattices – p. 6

2. Cold atoms

1. Laser cooling: T ≈ 1µK

2. Evaporative cooling: T ≈ 10 nK

3. Contain atoms in magnetic trap

Optical lattices – p. 6

2. Cold atoms

1. Laser cooling: T ≈ 1µK

2. Evaporative cooling: T ≈ 10 nK

3. Contain atoms in magnetic trap

4. Size of gas sample: ∼ 1µm

Optical lattices – p. 6

2. Cold atoms

1. Laser cooling: T ≈ 1µK

2. Evaporative cooling: T ≈ 10 nK

3. Contain atoms in magnetic trap

4. Size of gas sample: ∼ 1µm

5. To make observations: release atoms fromtrap, take picture

Optical lattices – p. 6

3. Put atoms in lattice

How does an E-field create a potential for atoms?

Optical lattices – p. 7

3. Put atoms in lattice

• An unperturbed atom has noelectric dipole moment.

Optical lattices – p. 7

3. Put atoms in lattice

• An unperturbed atom has noelectric dipole moment.

First order perturbation theory

• An electric field induces a dipolemoment.

Optical lattices – p. 7

3. Put atoms in lattice

• An unperturbed atom has noelectric dipole moment.

First order perturbation theory

• An electric field induces a dipolemoment.

• An oscillating electric field(light!) induces an oscillatingdipole moment.

Optical lattices – p. 7

3. Put atoms in lattice

Second order perturbation theory

An electric field interacts with adipole.An oscillating electric field inter-acts with an oscillating dipole.Energy is

Edip = 〈 ~E · ~µ〉

(The induced dipole moment µ depends sensitively onfrequency and details of the atomic structure.)E-field varies in space : dipole force on atom.

Optical lattices – p. 8

The result

The result is a periodic potential that traps atoms.

Potentials are shallow: for most purposes need ultra-coldatoms!

Optical lattices – p. 9

Use of optical lattices

Example: Bloch oscillations

Optical lattices – p. 10

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

dp

dt= F

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Velocity

〈v〉 = 〈dE

dp〉.

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Velocity

〈v〉 = 〈dE

dp〉.

v = 0

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Velocity

〈v〉 = 〈dE

dp〉.

v > 0

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Velocity

〈v〉 = 〈dE

dp〉.

v = 0

Optical lattices – p. 11

Bloch oscillations

Put a force F on a particle in a periodic potential.Crystal momentum

d〈p〉

dt= 〈F 〉

(Ehrenfest’s principle.)

Velocity

〈v〉 = 〈dE

dp〉.

v < 0!!

Optical lattices – p. 11

Bloch oscillations

Bloch oscillations cannot be seen in solids -because collisions destroy them! Demonstratedexperimentally in OL in 1996

Optical lattices – p. 12

Optical lattice vs solid

Real solid Optical lattice

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Optical lattice

Standing light wave

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Phonons

Optical lattice

Standing light wave

No phonons

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Phonons

Lattice const ∼ 1 Å

Optical lattice

Standing light wave

No phonons

∼ 1µm

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Phonons

Lattice const ∼ 1 Å

Electrons

Optical lattice

Standing light wave

No phonons

∼ 1µm

Atoms

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Phonons

Lattice const ∼ 1 Å

Electrons

Spin 1/2

Optical lattice

Standing light wave

No phonons

∼ 1µm

Atoms

Any spin

Optical lattices – p. 13

Optical lattice vs solid

Real solid

Ions

Phonons

Lattice const ∼ 1 Å

Electrons

Spin 1/2

Difficult to manipu-late

Optical lattice

Standing light wave

No phonons

∼ 1µm

Atoms

Any spin

Easy to tune all pa-rameters

Optical lattices – p. 13

Cold atom research

Optical lattices – p. 14

Cold atom research

• A new field of physics – 10-20 years old

Optical lattices – p. 14

Cold atom research

• A new field of physics – 10-20 years old• Nobel prizes since 1996

Optical lattices – p. 14

Cold atom research

• A new field of physics – 10-20 years old• Nobel prizes since 1996

• Umeå: Both theoretical and experimentalresearch on cold atoms.

Optical lattices – p. 14

Optical lattice lab in Umeå

Optical lattices – p. 15