so we have been looking at implementation
of quantum computing in terms of commercial
devices now will be looking at the other important
aspect where spin place an important role
and we mentioned about it earlier also spintronic
approach so let us see what this idea was
spintronic come from typical conventional
electronic devices ignore the spin property
and rely strictly on the transport of the
electrical charge of electrons adding the
spin degree of freedom provides new effects
new capabilities and new functionalities this
advantage of spin essentially gives raise
to these spintronic devices that offer the
possibility of enhanced functionality higher
speed and reduced power consumption so what
are the advantages of this spin the information
is stored into spin as one of two possible
orientations circular going clockwise or going
counter clockwise the spin lifetime is relatively
long on the order of nanoseconds spin currents
can be manipulated spin devices may combine
logic and storage functionality eliminating
the need for separate components the magnetic
storage is non-volatile
so that is actually a very important issue
because most of the time whenever we talk
about spin what happens is that it induces
magnetic behaviour one way or the other and
that can be utilized in terms of storage which
will be non-volatile binary spin polarization
offers the possibility of applications as
qubits in quantum computers and part of that
has already been seen when we even looked
at the commercial procedure of quantum any
link where the spin of these individual qubits
were used and similarly ah in a mode processing
the spin of the nucleus was used as one of
the principles of quantum computing here one
thing we should remember however at this spin
we are talking about is mostly to do with
a electrons spin or the spin of the system
and not the nuclear spin so what is it that
we are relying on when we talk about the magnetic
field as well as the spin so the most important
term in this area is the gmr or the giant
magneto resistivity so gaint magneto resistivity
was discovered in nineteen eighty eight in
france and is often accepted as the birth
of spintronics a gaint magneto resistive device
is made of at least two ferromagnetic layers
separated by a spacer layer
so when the magnetization of the two outside
layers is aligned lowest resistance is seen
so for example you have two ferromagnetic
layers the blue one and the pink one and these
spacer is the yellow part which is in the
middle spacer layer when the magnetization
of the two outside layers are aligned we get
the lowest resistance r of the system on the
other hand when the magnetization vectors
are anti parallel in the same device then
the resistance is high so this is again the
spacer and these are the two magnetic layers
and when the magnetic layers are aligned then
it is lowest resistance and when the magnetic
layers are anti parallel then its the highest
resistance
so this gaint magneto resistance is one of
the most important concept which gave raise
to the birth of spintronics so in some ways
the small fields which are necessary for making
this alignment go in parallel verses the opposite
directions are the ones which can produce
big effects and therefore this particular
approach has been one of the most critical
in the development of spintronics and this
can be achieved by simply a providing parallel
and perpendicular current so in more general
the idea of spintronics is to employ electronic
spin in electronic devices and that is why
i wanted to mention that this is distinct
from the concept of n m r where its the nuclear
spin
so here the electrons spin is the one which
is been used for electronic devices so the
gaint magneto resistance effect that i just
mentioned is the one which is ah important
in making sure that we have low r in one case
and high r in the other case and this principle
this resistance r is resistance this resistance
is the hallmark of ah giving raise to the
effect and the idea of having the ferromagnetic
layers being in parallel verses counter parallel
can be achieved by simply providing low currents
and that is why this amplification processes
is very important so similarly this can be
also be utilized in terms of spin transistor
spin orbit coupling can also be utilized where
the parallel and perpendicular are responsible
for making sure that the gmr can be utilized
very effectively so in general the parallel
and perpendicular current is sufficient to
make sure that the magnetization of the two
layers can be made either aligned or put in
the anti parallel mode small fields can produce
big effects the parallel and perpendicular
current is sufficient to make the magnetic
layers be parallel or be aligned in the opposite
way and therefore gaint magneto resistance
devices can be very effective in these kinds
of applications in more general cases of spintronics
the idea is to employ electronic spin in electronic
devices this as i mentioned earlier is important
to note the distinction from the usage of
nuclear spin which has been done in terms
of nmr in this particular case its the electron
spin which is the important aspects which
is being utilized for the electronic devices
the gaint magneto resistive effect is critical
in these cases where the two ferromagnetic
layer has been mentioned whether they are
parallel or they are counter or anti parallel
are going to effect as to having a low resistance
verses high resistance and that is the principle
behind this idea of using the spintronic concept
so these magnetic semiconductors are very
effective because they can be utilized for
processing or could be utilized in terms of
ferromagnetic materials as we just mentioned
in terms of data storage where the magnetic
fields that are induced as the result of the
applied changes in the relative orientation
can lead to data storage
so ferromagnetic semi conductors can be integrated
on a single chips and single chip computers
can be utilized for embedded applications
such as cell phones intelligent appliances
security which are all currently being utilized
for these kinds of technology so in effects
spintronics is basically a mixture of spin
with electronics is the electron spin and
electronics put together is the principle
of spintronics so the materials and the considerations
which are effective are metals which can act
in terms of this spin memory the other principle
would be the logic which is going to be the
charge
so in terms of the electronics its the charge
of the material which could be in terms of
semiconductor which give raise to the logic
aspects where as the memory part of it could
be in terms of the spin as we talked about
ferromagnetic materials which need the metal
alliance to do this job and therefore we have
the principle of the memory and the logic
on a same chip as a result of this combination
of the say the metal ion with respect to a
semiconductor with the charge species given
raise to the logic so all semiconductor or
hybrid structure is the question because we
could also use semiconducting substance which
could have spin property so we could have
both all semiconducting properties or materials
or hybrid structures for spintronic applications
spin quantum computation is the part which
we were looking at right here where the advantages
of spintronics lie in many particular areas
the spin interactions are small as compared
to coulomb interaction and there is lesser
interference which is there as a result they
can be miniaturize is here the spin current
can flow essentially without any dissipation
which means that there is a less heat to worry
about which is one of the major advantages
with respect to a miniaturization issues a
spin can be changed by polarized light which
cannot be by using the charge and so spin
has its advantage of interaction with light
to do or produce interaction which are effective
in terms of spin logic spin is a nontrivial
quantum degree of freedom
because we know that there is a spin quantum
member which is can be utilized for our quantum
states where as charge is not a quantum degree
of freedom that sense so a quantum computer
would therefore be utilizing the superposition
of spins and you can use the spin half as
a qubit which is our new functionary that
we have been discussing
so in terms of these molecular electronic
devices the spintronics place a major role
where the spin electronics of the magneto
electronics which can be utilized by this
is one of the area where this can be taking
to the next level it was discovered in nineteen
eighty eight by german and French physicists
and ibm commercialise the concept in ninety
ninety seven in terms of the spintronics idea
it exploits the spin of electrons rather than
charge information of the circuits the information
is stored into spins in particular spin orientation
whether its up or down and a spins being attached
to mobile electrons carrying information along
a wire this is one other very important aspects
of the spin which can be utilized in this
process the spin orientation of electrons
survive for a relatively long time which makes
spintronic devices attractive for memory storage
devices in computers and because of the long
range of time scales which the spin orientation
can provide there have been applications of
spintronics in computers in terms of the hard
drive which uses the magnetic spin to store
long term information and the information
is retained on power loss so that is a permanent
memory which is am storage which is which
is been utilized already in terms of computers
the ram in the cpu on the other hand does
not use these spintronic principle and essentially
uses the charge and as a result information
is lost on power loss so here is the example
of how the magnetic disk drives ah which have
been utilized on the basis of the micro drive
for instance utilize the spin of the system
and takes the advantage of spintronic to store
information on a permanent basis so ah let
us now explore a little bit on the aspects
of spintronic that we have been talking in
terms of molecular or the termic states so
that we understand what we are actual discussing
so in terms of the level structures ah totally
filled shells will have a angular momentum
or the spin as zero and so the angular momentum
associated with the spin will be zero so the
magnetic ions required partially filled shells
so that the total angular momentum or the
total spin is non zero and that is why the
choice of the system depends on this property
which means that the as long as their transition
metals for example iron cobalt nickel which
have these nd shells where you can get them
partially filled or four f shells rare earths
like gadolinium or the five f actinides which
can also be utilized for these kinds of spintronic
devices it could also utilize the molecular
states for example two sp shell which are
found in organic radicals and others for example
nitrogen inside c sixty as long as ah hybridisation
it can always be utilized many particle states
require that we assume that partially filled
shell contains n electrons then there are
say two times two l plus one states corresponding
to the n th shell and the possible distribution
are over two times two over two l plus one
orbitals and these are the degeneracy of many
particle states and this is because for every
particular electrons there are are two possible
orientation that are possible
so with every orbital representation of an
electron there are two spin states which are
possible and that is why these numbers are
becoming in these kinds of terms so the irons
in the crystals are therefore going to interact
with a magnetic field in terms of the crystal
field effects they behave differently in a
crystal lattice than in vacuum for instance
the three d four d five d and four f five
f ions typically lose their outer most s two
shell electrons and sometimes some of the
electrons of outermost d or f shells ah for
example the three d and in terms of ion two
plus is partially filled and the partially
filled shell on the outside of the ion gives
rise to strong crystal filled effects which
can then interact ah strongly with a magnetic
field and the partially filled shell inside
of five sp shells have weaker effect and therefore
what we are essentially seeing are the effect
of how they are interacting
so for example the gadolinium plus ion a partially
filled shells inside of five s and five p
shells which have weaker effect whereas on
the other hand ion two which is the partially
filled shells outside of the iron have strong
crystal filled effects and therefore ion has
very strong magnetic effect as we all know
as a result of this kind of interactions so
depending on which states we are looking at
will be have a different interactions to look
at so the three d four d or five d states
which are on the d shell verses the f shell
which is four f and five f we have two different
conditions these are the ones which are transition
and the other ones are in a transition elements
which we are looking at so the transition
elements have strong overlap with d orbital
strong crystal filled effect stronger than
spin orbit coupling and these treats the crystal
field first spin orbit coupling as small perturbation
in a single ion picture is not applicable
so in these cases the single electronic states
orbital part ah sort of splits to look into
a tetragonal job of condition and the effect
of the field where as in these case the weak
field effect due to the four f leads to weak
overlap with f orbital weak crystal field
effects weaker than the spin orbit coupling
and these needs to be treat as spin orbits
coupling first crystal field partially lifts
the two j plus fold degeneracy and leads to
ah many electrons states which has multiplex
with fixed l s and j geometry and so when
they they have the two j plus one in the vacuum
state in the crystal lattices they have these
states which are getting separated out
so (Refer Time:18:00) the two effects whether
they are in terms of the transitional elements
or the or the others where we are using the
f orbital they have slightly different effects
but due to crystal field effect verses their
original conditions where they are considered
and and one of them is stronger than the other
and they can be utilized in different ways
so generally speaking what we have discussing
is with spins we have the rotation the almost
an ideal cubit because these are essentially
looking at the rotational status as we have
been talking about it is almost an ideal condition
because its separated and can be addressed
very easily
so we can consider its up upto actual but
typically this spin up is consider as the
zero th state for instance and spin down as
the defer state and quantum algorithm factoring
searching sincerely would require an input
of this array of state which output into some
superposition state which have been addressed
with unitary operations and they all work
simultaneously to produce the net result and
at the end of it when the final state is achieved
the measurement gives raise to the state that
is being measured simple quantum gets in terms
of spin would be just in terms of one qubit
spin rotations for instance a two qubit exchange
interactions which can go between the spin
spin interaction between them and the exchange
interaction give raise to say adamant operations
whereas the spin rotation can simply produce
super positions so the spin relaxation and
manipulation of localised states in semiconductors
can actually be utilized as we have discussed
earlier also ah in terms of quantum computing
architecture or the quantum dot architecture
for example is placed in between the different
condition of their states and then they have
been put together so for example here is a
silicon donor nuclear spin in the quantum
computing architecture where the phosphorus
with thirty one is going to have with the
additional advantage of electron and that
is why this electron donor from the silicon
is going to act like the device where it can
be utilized for doing this work this is how
the solid state device have been done here
is some of the implementation aspects which
had been taken care of the gallium arsenide
quantum dots for the instance where first
shown in the work by divincenzo in nineteen
ninety eight where they had proposed this
simple idea of the electrons being provided
by the silicon
so consideration of the solid state quantum
computer architecture both quantum dot structure
as well as silicon donor nuclear spin quantum
computer architecture has been utilized in
quantum dot architecture the electron transition
have been manipulated while the other structure
involves the silicon donor nuclear structure
architecture from from this particular case
where the phosphorus is utilized along with
the silicon donor so here are the more details
of these ideas that have been utilized
so the gaas quantum dots structure was first
shown by divincenzo and others in nineteen
ninety eight where they placed the quantum
dots acting like a single electron system
in between the device where they could apply
the field to make them interact where as in
the other case it was the silicon and phosphorous
called the silicon and germanium which were
put together for doing these kinds of similar
aspects where these junctions were been addressed
at different levels
so the typical experiments for these cases
for instances required the few electron dots
to interact at close enough distance in this
case for example the gallium arsenide case
the neighbouring quantum dots were being interacted
the single electron in each dot was been utilized
and the question is they were able to address
were whether this model was able to reproduce
the heisenberg model where the electron jumped
and the electron transition could be reached
by utilizing the same quantum mechanical concepts
that have been addressed earlier so the magnetic
field that was been utilized to make the interaction
occur because of this spin of the electron
was based on principle that the hamiltonian
involved ah the momentum part and the interaction
was due to the spin spin conditions of these
(Refer Time 23:00) electrons and when these
two states were being put together they were
going to interact and give raise to multiple
conditions instead of having just a single
minimum point and it almost look like that
they were able to separate out and form into
different conditions and it was almost like
they were forming homo polar binding in an
artificial molecule based on their interaction
with applied magnetic field however the applied
field was quite high in these cases and the
apply magnetic field in these cases were about
nine tesla where the two hole could be completely
separated out on the other hand ah so these
kinds of experiments required a devices and
energy which were not possible under normal
conditions so for instance this particular
work have require cyclotron radiation ah where
the energy was in terms of very high and magnetic
field which were possible from cyclotron energies
wided and the confinement was then able to
be achieved because of the interaction at
those high intensities with a application
of modified magnetic length the separation
could be worked on and could be utilized in
this principle
so this was the idea of the how this was bieng
applied so depending on the amount on magnetic
field applied the principle spin hamiltonian
interaction whether they had small exchange
or they had vortex mixing or they were level
crossing is a result of that which were mean
being looked at and depending on whether they
were able to be in individual states or they
were having some coupling or they were separated
out was been looked at by these utilizing
these principle so depending on the energy
provided for instance this particular cases
the level crossing was achieved when the energy
was greater than the spin spin coupling so
by utilizing magnetic field in consumption
with these energy levels that we talked about
this particular system was been applied and
with higher and higher energies other levels
of mixing was possible which gave raise to
this particular principle so these concepts
were very easily forwarded into cases where
three electrons for example were available
when there were three dots and their interactions
could be looked at in terms of how their energies
were being looked at
so the two spins and two quantum dots for
example b two the quantum the quantum gates
put together in this these considered them
as single spin qubits where the heinsenberg
hamiltonian essentially had this spin spin
coupling parts which have been looked at the
quantum gets were based on the rotations available
from the spin hamiltonian and the interaction
of the local magnetic field gives raise to
universal set of quantum gates and this is
how the two qubits were being connected and
been looked at the heinsenberg exchange hamiltonian
was validated for the spin based quantum dot
quantum computers in the example system of
couple two two d ah quantam dots the applied
field direction in the z direction was able
to produce the gate energy that was necessary
and it was possible to create these levels
of interactions by using these splitting and
the amount of magnetic field necessary to
do these kinds of activities the validity
of the exchange hamiltonian for six electron
dot was also shown in these kinds of experiments
where six electron double dot was been utilized
and they were able to show that interactions
were able to be controlled by using the magnetic
field of the applied system in most of these
cases these experiments were able to address
the idea that the heinsenberg exchange Hamiltonian
worked for this kinds of systems and they
could be put to the applications as has been
discussed when the system Hamiltonian was
changed adiabatically the system wave function
was possible to be expanded in instantaneous
wave functions and the process were better
explained in that condition and the system
evolution was then governed by the schrodinger
equations where the instantaneous eigen values
and eigen states are needed to integrate the
schrodinger equations
so a by application of adiabatic condition
it was possible to ah make sure that the system
wave function was interacted in a way and
under that condition it was possible to provide
all the quantum correlation however due to
the non adiabatic interactions in the exchange
gate of double dots there were cases where
the interaction was lost and as long as the
adiabaticity was maintained it was possible
to get the interactions work in the heinserberg
in the quantum mechanical principle and computing
could be achieved
so in this particular case the principle of
adiabobaticity was important when the quantum
dots who had been made to interact in multiple
ways the extreme sensitivity of the exchange
coupling to the relative positioning of the
substitutional donor pair in the silicon is
entirely due to the six fold degeneracy of
the silicon condition band is minimum and
that led to the idea that the dipolar spin
coupling and dipolar gates could perhaps be
the reason for this extreme sensitivity in
order to ensure that that adiabaticity is
maintained it was important to make sure the
coupling and dipolar nature was maintained
in very careful manner for the qubits that
are dipolar coupled single electron spins
could be utilized and this work had also been
done in terms of the silicon phosphorus spin
dipolar gate quantum architecture where the
silicon and germanium mixed semi conductor
was having these states being addressed by
the control gates in single spin mechanism
and the applied magnetic field was the way
how these orientation of these spins were
being addressed the control gates where ah
controlled by the single spin measurement
properties and the in perfections in the presence
of the exchange was possible to be addressed
by using the principle that the long range
dipolar interaction is much smaller than the
short range exchange for large inter donor
separations how large should be the separation
so that the interaction or the rotation parameter
can be neglected is one of the problems which
was lead to these interactions and studies
in that area were done
and it was found that the criterium for the
gate error to be within the given study that
was done was a particular parameter which
was defined in this particular form and based
on that the gate times on the donor separation
was found to be on the order of three hundred
angstrom which allows easier lithography which
was experimentally necessary the gates are
ten to the power six times slower than the
exchange coupling however there is no need
for exchange control and donor positioning
with atomic precisions in these cases therefore
using silicon twenty eight the expected time
constants were found to be about the order
of the applied magnetic field ab about a one
tesla and that was one of the issues that
was been used ah using different donors for
example antimony phosphorus arsenic and dismac
the values which were found to be the most
effective was the one which was phosphourus
and because that is the one which has the
separation of about three hundred angstrom
and the antimony also was reasonable in its
applications so these are the ones which were
the better ones for utilization of these techniques
for the silicon dipolar quantum computer long
range couplings are corrected with no overhead
in gate time in order to provide the ability
to pi pulses within three five microseconds
that is required the dipolar implementation
is reliable its advantages and disadvantages
should be compared with other proposals without
exchange
so for example the earlier work ah in these
directions where in reported in these cases
which require electron shuttling between donors
the dipolar coupling insensitive to electronic
structure was also useful and no inter valley
interference interstitial defects were also
good qubits the top down construction schemes
based on ion implementation could be used
though they lack atomic precision in donor
positioning and they can be scaled up all
these work were done by the kane group in
the early two thousand and a lot of efforts
have been put in this area ah the electron
spin coherence in semiconductor quantum computing
ah required the usage of the bound orbital
states such that they had about the millisecond
of their electronic decay times which is the
gallium arsenide in quantum dots ah whereas
it was about ten seconds in terms of silicon
phosphide so the decoherence is dominated
by the spin spin interactions and that was
understood from the spectral diffusion the
in the electrons spins were the ones which
got coupled into the nuclear spins and therefore
they have to be careful the electrons Zeeman
frequency fluctuates due to nuclear dipolar
flip flops and as a result de coherence times
scale fifty two about fifty microseconds were
seen for gallium arsenide quantum dot whereas
it was greater than ten thousand microseconds
for the silicon phosphide so depending on
the applied conditions they used to have different
results so these were all based on ah blocks
equation where the important times scales
were due to the magnetic interactions could
be understood in terms of the t two stars
these are the different time scales of the
t m magnetization terms or the t one which
is the lifetime parts so the spin orbit on
the photon combination was one of the aspects
and there are hyperfine with phonons and spin
orbit photons were the other ah parts
so the spin orbit phonon hyperfine phonons
spin orbit and photons are the ones which
are responsible for these time scales the
spectral diffusion parts with are interacting
due to nuclear spins and the time dependent
magnetic fields the dipolar or the exchange
coupling between like spins are also contributing
to some of these time scales the unresolved
hyperfine structure are the ones which give
raise to other decays and different g factors
and inhomogeneous fields and dipolar exchange
between unlike spins are the ones which are
often used in terms of the different time
scales which have been looked at when these
are looked at and therefore they are ordering
in terms of which goes in effect towards the
advantageous at the ones which have to be
addressed when these processes are being looked
at the spectral diffusion of a silicon phosphorus
spin had mainly based on the idea that the
applied magnetic field ah the phosphorus spin
can interact with the neighbouring silicon
twenty nine and the silicon twenty eight ah
particles and the electron spin of the system
would can be resulting as a result of this
process and the nuclear induced spectrum diffusion
arises because of the fact that the spins
can interact the nuclear spin flip flop due
to their dipolar interaction the nuclear spins
flip flop due to their dipolar interactions
the electrons Zeeman frequency fluctuates
in time due to nuclear hyperfine field and
as a result this particular approach is been
measured the theory behind this is based on
the nuclear pairs that are described by the
Poisson random variables whereas the flip
flop rates are calculated using the methods
of moments at high temperature and that is
possible due to high temperature expansion
the hamiltonian for these kinds of interactions
can be looked at in terms of the spin coordinates
of the coupling and the system together whereas
the other parts are due to the other coordinates
which arise as the result of the coupling
between the nuclear spins and the electron
and these are the areas where a lot of theoretical
work has gone in to make sure that these can
be understood in a way so there it becomes
better and better in terms of this spintronic
applications of the electrons which can then
be preserved and applied in a proper manner
the electrons in silicon beyond the ah the
magnetic field and the applied electric field
can basically be utilised also in terms of
the real space where the advantage of these
can be utilised so for instance the diamond
structure of the silicon can look like in
the reciprocal space in terms of giving raise
to the brillouin zone which can then be ah
looked at in the conduction band minimum which
will give rise to anisotropic and six fold
degeneracy so this anisotropic and six fold
degeneracy as a result of ah the real space
structure being subjected to the magnetic
field would give raise to the structures of
the anisotropic which are of the appropriate
degeneracy which can be utilized for further
applications
so the theoretical understanding of all these
processes is being utilized for the study
or the applications into the spintronic concept
and here is the review article which was mostly
based on these developments and was presented
a lot more work after these were also been
done which is mostly to do with the phosphorus
stone as in silicon which concerned with the
donors positioning where each of the phosphorus
stone as in silicon which concerned with the
donor positioning where each of the phosphorus
in the array must be exactly under the gate
that have been looked at this particular proposal
the initial ones you know based on the work
done by kane from australia where they proposed
that the quantum computers which promise to
exceed the computational efficiency of ordinary
classical machines ah can be practically implemented
by using quantum mechanical processing where
the information is encoded into the nuclear
spins of the donor atoms in dope silicon electronic
devices the logical approaches are individual
spins are performed using externally applied
electric spins and spin measurements are made
using currents of spin polarised electrons
the realization of such a computer is dependent
on the future refinement on conventional of
conventional silicon electronics and this
particular work from the university of new
south wales sidney was one of the important
development which as we know has been later
on utilised as i mentioned earlier in many
of the efforts coming from commercial areas
also the computation in this particular case
was possible due to the phosphorus thirty
one array in insis inside the silicon the
strength of the hyperfine interaction of this
interaction of the phosphorus thirty one is
propositional to the probability density of
the electron wave function at the nucleus
in semi conductors the electron wave functions
extends over the distances through the crystal
lattices to nuclear spins can consequently
interact with a same electron leading to electron
mediated or indirect nuclear spin coupling
because the electron is sensitive to externally
applied electric field the hyperfine interactions
are the ones which give raise to these principle
and the idea of this nuclear spin mediated
ah electron being interacted is over which
was done by these people and that is the part
of one of the areas of spintronics which has
been aspected very heavily so with this i
would like to end todays lecture which was
mostly focused on principle of how spin of
electrons can be looked at or interacted or
made to interact be a other methods of interactions
either with a nuclear principle or magnetic
principles so that they can be utilized simultaneously
with other applications and can be put together
with quantum inform
thank you
