Quantum simulators for
unconventional superconductors
and deformable solids
Jim Hague and Calum MacCormick
Department of Physical Sciences
The Open University
arXiv:1109.1225
In Press, New J. Phys
(Deformable solids)
arXiv:1111.5594
(Unconventional superconductors)
Coming up...
•
Importance of electron

phonon interactions in
unconventional superconductors and other
condensed matter systems
•
Rydberg atoms, dressing schemes, bilayers.
•
Proposed cold atoms simulator, mapping to
standard Hamiltonians
•
Efficacy and numerical simulation
•
Readout
Electron

phonon interactions in condensed
matter
•
Essential to understand conventional
superconductivity, polyacetylene, Peierles
distortion, resistance (and others)
•
Isotope effects / other electron

phonon
effects found in contemporary condensed
matter problems: Colossal magnetoresistance,
high Tc, other unconventional
superconductors.
J.P.Hague, C.MacCormick, arXiv:1111.5594
Part I:
Unconventional
superconductors
J.P.Hague, C.MacCormick, arXiv:1111.5594
Isotope effects in cuprate high Tc
•
Significant isotope
effects in cuprates
•
Susceptibility,
Meissner fraction,
penetration depth
and others
G.M.Zhao
et al.
J. Phys.:
Condens. Matter,
13
(2001)
R569
Anom
.
J.P.Hague, C.MacCormick, arXiv:1111.5594
Other unconventional
superconductors
•
Fulleride A
3
C
60
compounds, Tc ~ 40K [1

3]
•
Bismuthates (Tc > 30K) [4

7]
•
Borocarbides and chloronitrides (Tc > 20K) [8

10]
•
Magnesium diboride, Tc ~ 40K (layered)
•
Intercalated graphite compounds ~ 10K (layered)
(see the nice review ‘The Other High Temperature Superconductors’ by Warren Pickett)
J.P.Hague, C.MacCormick, arXiv:1111.5594
Rydberg atoms, dressing and bilayers
•
We consider only Rydberg states with s
symmetry.
•
In the high dipole limit and in the Foerster
regime, the interaction has 1/R
3
form [1]. For
s

symmetry, there is no angular dependence.
•
To enhance Rydberg lifetime, dressed states
are used where laser detuned
D
from
transition

excite virtual Rydberg state.
[1]
PHYSICAL REVIEW A
77
, 032723 2008. T.G.Walker and M.Saffman.
J.P.Hague, C.MacCormick, arXiv:1111.5594
•
Itinerant layer filling changes. Require shallow
well so atoms hop.
•
Phonon layer must be half

filled
–
require
deep well, but shallow base for adabatic
phonons. Achieve this with painted potentials.
J.P.Hague, C.MacCormick, arXiv:1111.5594
J.P.Hague, C.MacCormick, arXiv:1111.5594
C

axis phonons
•
Extend phonon potential perpendicular to
planes to obtain:
W
is Rabi frequency,
D
is tuning,
m
dipole moment,
b
interplane spacing,
r
distance
in plane,
n
fermion number operator in itinerant plane,
d
annihilates phonons.
J.P.Hague, C.MacCormick, arXiv:1111.5594
Tunability
•
Change lattice spacing:
Modify hopping.
•
Increase interplane
distance / change
Rydberg quantum
numbers: modify
interaction.
•
Modify potentials in
phonon layer: change
phonon frequency / no.
of modes
J.P.Hague, C.MacCormick, arXiv:1111.5594
Good agreement with effective
interaction
F
(x) is effective interaction, b is interplane dist, a intraplane dist,
r
=
i
ax
Quantum Monte Carlo
simulations show
excellent agreement.
Here U=4t,
l
is
fermion

phonon
coupling.
b
is interplane
distance,
a
is
interatomic dist, R
s
Froehlich screening
radius
(see JPH+P.Kornilovitch,
PRB for Frohlich bipolaron
in 2D)
J.P.Hague and C.MacCormick,
arXiv:1111.5594
J.P.Hague, C.MacCormick, arXiv:1111.5594
Readout
•
Turn off potential in itinerant layer to obtain
dispersions and correlation functions
•
Phonon occupation numbers can be resolved
using spectroscopically.
•
May also be able to ‘shake’ optical lattice to
probe phonon and electron states.
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
Part II:
Polyacetylene and
other strongly
deformable solids
Rydberg dressing schemes and ‘electron’
transport
•
Calculate hopping from van
Vleck perturbation theory
•
a = W / D
, where
W
is Rabi
frequency and
D
is detuning
•
N is no. of atoms in system
•
V is
m
2
/R
3
See
S. Wuester, C. Ates, A. Eisfeld, and
J. Rost, New J. Phys 13, 073044 (2011).
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
A proposal for a cold atom/ion
‘electron’

phonon simulator
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
Mapping on to a Su

Schrieffer

Heeger
interaction
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
Mapping on to a Su

Schrieffer

Heeger interaction
For momentum independent phonons (i.e. cold atoms)
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
Perturbation
theory
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
Experimental
considerations
J.P.Hague, C.MacCormick, arXiv:1109.1225
(In Press, New J. Phys.)
J.P.Hague, C.MacCormick, arXiv:1111.5594
Summary
•
Summarised the importance of electron

phonon interactions in condensed matter.
•
Demonstrated that bilayers of Rydberg atoms
can be mapped onto fermionic Hubbard

Holstein model (i.e. correlation in the
presence of electron

phonon interactions).
•
Used numerics to examine similarity with
similar problems in cuprate (and other)
unconventional superconductors.
J.P.Hague and C.MacCormick,
arXiv:1111.5594
, arXiv:1109.1225
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