Quantum simulators for

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Nov 15, 2013 (3 years and 10 months ago)

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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