imprinting magnetic monopoles onto an atomic gas - …gjc29/talks/cmptalk22012.pdf · imprinting...
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Imprinting magnetic monopolesonto an atomic gas Gareth Conduit
Theory of Condensed Matter Group, Department of Physics
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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
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Cold atom gas
Electrons 87Rb atoms
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How to imprint a uniform magnetic field
Laser beam excites transitionDesired Hamiltonian:
=0ei k x
H= p−e A2
2m
B=∇×A
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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:
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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)
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Synthetic uniform magnetic field
Lin et al. Nature 2009
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A line of magnetic monopoles
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A line of magnetic monopoles
Lasers
Physical Bfield gradient
GaugeB field
GaugeB field
Lasers
Physical Bfield gradient
Uniform B field Monopolar B field
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How to imprint the magnetic monopoles
=0ei−2
z
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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
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Single magnetic monopole
Pietilä & Möttönen PRL (2009)
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4 monopoles embedded
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4 monopoles embedded
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12 monopoles embedded
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12 monopoles embedded
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55 monopoles embedded
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55 monopoles embedded
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Phase behavior
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Energetics of flux escape
E=C6
N 2 L
E=C N L
N=6Crossover at
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Collective modes
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Collective modes
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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