Quantum simulators for

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