Imprinting magnetic monopolesonto an atomic gas Gareth Conduit

Theory of Condensed Matter Group, Department of Physics

Ways to realize monopoles

Spin iceCastelnovo et al. Nature 2008,Bramwell, Nature 2009

Topological insulatorsQi et al. Science 2009

Anomalous quantum Hall effectFang et al. Science 2003

Superfluid 3HeBlaha, PRL 1976

Cold atom gas

Electrons 87Rb atoms

How to imprint a uniform magnetic field

Laser beam excites transitionDesired Hamiltonian:

=0ei k x

H= p−e A2

2m

B=∇×A

How to imprint a uniform magnetic field

=0ei k x

H= p−e A2

2m

B=∇×A

Lasers

Physical Bfield gradient

GaugeB field

Laser beam excites transitionDesired Hamiltonian:

How to imprint a uniform magnetic field

U=ℏ

2 −2 ' y 0 e

i k x 0

0 e−i k x 0 0 e

i k x

0 0e−i k x 2 ' y

=e i k x cos2

2∣−1 ⟩−

sin

2∣0 ⟩e−i k x sin2

2∣1 ⟩

A= ⟨∣∇ ⟩= ' y0

ex

tan=0

2 '

Spielman PRA (2009)

Synthetic uniform magnetic field

Lin et al. Nature 2009

A line of magnetic monopoles

A line of magnetic monopoles

Lasers

Physical Bfield gradient

GaugeB field

GaugeB field

Lasers

Physical Bfield gradient

Uniform B field Monopolar B field

How to imprint the magnetic monopoles

=0ei−2

z

How to imprint the magnetic monopoles

U=ℏ

2 −2 ' z 0ei−2

0

0e−i−2

0 0ei−2

0 0e−i−2

2 ' z B

B

Bz≈ 2ℏ '

0 100

Single magnetic monopole

Pietilä & Möttönen PRL (2009)

4 monopoles embedded

4 monopoles embedded

12 monopoles embedded

12 monopoles embedded

55 monopoles embedded

55 monopoles embedded

Phase behavior

Energetics of flux escape

E=C6

N 2 L

E=C N L

N=6Crossover at

Collective modes

Collective modes

Proposed an experimental prescription to embed aline of magnetic monopoles onto an atomic gas

The atomic gas undergoes a transition when 6 monopolesare trapped

Summary