so we have been looking at the temporal aspects
of interaction of light with matter which
is resulted in qubit manipulations and this
is the specific part of work that has been
going on in our particular area of research
and since it relates to all the various different
aspects of quantum computing that we have
been discussing throughout this course i thought
i will finish it off by looking at the other
interaction that also is very important in
this particular aspect which is a spatial
interaction concept
so as in terms with the ion trapped condition
where the spatial interaction part was utilized
to make sure that the qubits could interact
properly and the gates could be associated
in this manner here also we can do this saying
principle by having a spatial modulation being
applied by an optical field so in this regard
let me show you how this works ah in terms
of these spatial control the basics of optical
trapping is been shown here the trap essentially
is of a particle which happens because of
the laser being passing through the particle
undergoes bending due to the higher refractive
index of the particles in comparison to the
environment it is kept in
so typically a bead which is being trapped
in a liquid would be having the higher refractive
index and are of typical micron sizes are
lower and having a gaussian spatial beam would
essentially mean that the beam would interact
with the bead in such a way so that it is
drawn more towards this focus so the radiation
pressure from the proton flux is utilized
in this process of trapping the particle so
this can be thought in terms of the paraxial
gaussian mode the spatial mode of the beam
and if a gaussian beam is not available in
fact if it is a flat top ah or a square or
a rectangular beam specially ah it will not
be possible to trap a particular bead in this
particular fashion
because the gradient of the paraxial beam
would not be possible to balance the forces
so for single beam optical trap paraxial gaussian
beam is essential temporally however the laser
can be either c w or pulsed optical tweezers
use light to manipulate microscopic objects
the radiation pressure from a focussed laser
beam is able to trap small particles in biological
systems optical tweezers are used to apply
peco newton range forces and measure nanometre
range displacements in objects ranging in
size from ten nano meters to about hundred
millimetres so this as a lot of influence
in ah many areas of research and in this particular
case we have utilized the femtosecond lasers
for certain benefits
one of the benefit is the simultaneous detection
of two photon fluorescence and back scattered
light which is possible in this particular
case ah as long as the beats are coated with
the two photon die ah this enables bright
field video imaging and it could be used in
both continuous wave or mode locked laser
wave operations ah either by looking at this
scatter or by looking at the two photon fluorescence
since the visibility of the system becomes
much better because of the fluorescence it
is possible to have better signal to noise
of the trap particle and so smaller and smaller
particles can be visualized as a result of
this particular approach so we have manage
to show ah trapping for various range of particles
ranging from four microns to hundred nanometres
quite comfortably here is a ah slide picture
which shows ah four and one micron particles
which has stably trapped with femtosecond
eight hundred nanometre lasers and the principle
of trapping works easily with the two photon
fluorescence because the fluorescence ah comes
from only the focal point ah where the intensities
high enough to produce the two photon fluorescence
signal in every other place with photon fluorescence
signal is not possible to be generated and
so the focal plane where in the particle get
trapped is easily detected
so spatial trapping with the help of optical
pulses can be utilized towards trapping smaller
and smaller particles so we have gone to particle
sizes which are either in the range of wave
length of the light used or even smaller than
that under those conditions the force depends
on polarizability ah for example latex nano
particles are hard to trap high peak power
of an ultra short laser pulse ah helps however
the repetition rate is also critically the
pulses come after a very long time then the
stable trapping time will not be possible
to be maintained
so here is a cartoon of how these particle
trapping works and the ah particle is basically
put into a potential created by the optical
field under which the particle gets trapped
the when the pulse goes away particle experiences
no gradient force however when the pulse is
not present the particle experiences no gradient
force however the brownian motions or the
fluctuations within the beam base continue
as long as the next pulse comes before the
brownian motion takes the particle away from
the trapping zone the particle remains trapped
and so that is the reason of the reputation
rate of the laser to be sufficiently high
to make sure that the particle remains trapped
so here is a cartoon of how a microscope objective
essentially traps a particle in it's force
field and mostly this force field is thought
to be a modelled as a harmonic potential where
in the particle a sitting and the close to
the minima of the harmonic potential that
is how the model is being developed and what
we have found is that it is also possible
to have multiple particles come together because
as the particle size goes lower the zone in
which the particle trapping can happen can
be large enough to accommodate more than one
particle and that would enable multiple particle
trapping
so for instance with a hundred nanometre for
instance with a hundred nanometre latex bead
particle with eight hundred nanometre wave
length laser pulses we are under the condition
where the wave length of light is greater
than the diameter of the particle beam looked
at so it is in some sense better than the
diffraction limited condition this can be
observed through two photon much easily ah
once the cal system is calibrated by using
back scattering data of four and one micron
the particle aggregation can also be tagged
through the extremely sensitive technique
ah and so here is the case where we can see
ah a second particle coming in to the trapping
zone and seeing a two particle trap simultaneous
coupling pulse shows that these efficient
and sensitive ultrafast optical tweezers is
possible to let us reach our goal towards
spatial temporal control and spectroscopy
so that is one of the interesting parts of
having a trap which can enable the motion
of particles so this is in some sense analogous
to the condition which we have discussed earlier
where we have atoms in lattice so we would
imagine we can if you could produce ah traps
where we could put the qubit like objects
to be coupled by using optical particles ah
by using optics such that they could then
be make to interact and things however at
this point of time atom trapping is not really
out of word is out is reach in terms of the
conditions that we are using ah but the same
principle works for the atom lattice that
we have used before or discuss before in our
regular lectures for quantum computing here
so the back scattering technique ah can help
us set the problem and then using the fluorescence
coming from that two photon fluorescence coming
from the trap particle if they calibration
is made right it can help us go down to look
at smaller and smaller particles so that way
quantum dots of sixteen nanometre particles
of also been trapped you also seen ah multiple
trapping as we discuss before and so these
are interesting developments which have been
utilized one of the things which we notice
while this particular work has been developed
is the fact that the fluorescence the two
photon fluorescence coming from these chalk
particles also show a decay property which
is not quite expected and these decay occurred
not for the very small particles for example
the hundred nanometre particle doesn't show
any decay even when they aggregate
however the larger particles for example one
micron or four micron they show decay and
once these smaller particle say five hundred
nanometre particle individually even if they
don't show any decay when they start aggregating
they start showing decay essentially indicating
the fact that as the size of the particle
getting trapped is increasing to a size which
is beyond certain limit then there is a decay
feature which appears in at least the fluorescence
signal that we are using so when we looked
at this particular process so we had to understand
as to how this was happening we did not see
any of this kind of a decay feature to appear
in the back scattering signal for these kinds
of micro spheres
however the decay was always evident from
the fluorescence signals so one of the ways
that we understood this problem was to realized
that these particles are essentially undergoing
some sort of energy transfer when they reach
a condition where part of the particle is
not able to see all the light because when
the particle size is smaller then the particle
is always emerged in the photon flux however
has the particles size gets larger like one
micron two micron four micron because our
this is the wavelength is eight hundred nanometre
all of these particles are larger then the
zone in which the light is getting focus in
terms of diffraction limited conditions and
as a result of that the these larger particles
are not getting illuminated all through
that is one of the reasons why this can undergo
ah energy transfer within the illuminated
versus the non illuminated zone and that can
lead to a decay of the fluorescence that's
been observed and we did a very simple model
to rectify our conjecture and then it was
interesting to note that even with the very
simple approach of assuming a cone of the
beam coming in and a circle to just represent
the size of the bead by just taking the ratio
of the illuminated versus the non illuminated
part a simple model could be developed where
the decay was quite well correlating to the
size of the particle that was being used
so we were able to use this idea to easily
understand how the size of the bead was affecting
the way the trapping was going on once we
detected that it will also brought up an interesting
concept that has the particle size increased
which is what we had noticed earlier that
a for a five hundred nanometre particle which
is embedded within the eight hundred nanometre
wavelength light in the focal spot as the
particle size is increasing because of aggregation
we will also see the same affect that there
is a decay in the multiple particles fluorescence
and this is our observation in terms of linear
polarization of light first use no decay in
the t p f signal up to two particle trapping
t p f intensity decay in three particles with
some time scale and four particle with another
time scale of decay up to two particles the
whole microsphere system stays within the
focal region so there is no decay seen this
indicates that the two particles position
along the z axis and not along the radial
axis and that has been shown earlier with
some theoretical studies so this is one of
the interesting ah experimentally proofs of
the fact that the particle essentially is
aligned in the direction of the laser beam
for the linearly polarized light however when
circularly polarize light is used for trapping
there is a decay which is again evident for
even the two particle case and that is possible
because the for the circularly polarized light
the the dimmer undergoes tumbling motion and
as such it could be either aligned along the
axis or along the equator
so in circularly polarized beam due to rotation
of the cluster some area of the cluster remains
outside the illuminated zone and so the decay
can have now the experimentally spikes that
are often seen in these kinds of trapping
experiments are due to the ah biased diffusion
of large size clusters which are experimentally
difficulties which happen sometimes and as
they go through the focal region this kinds
of a spurious features may come so these can
be minimized as the concentration of the system
is reduced so the overall story correlated
very well to the theoretical prediction which
was earlier done based on the interaction
of the laser with dipolar particle assumptions
and our experiment essentially proves the
fact that when we do have this kind of a scenario
where particles are getting trapped and the
if they lose their symmetry because they are
going to become a dimmer then they are going
to align along the direction of ah propagation
to laser rather than in perpendicular to a
direction of propagation of laser
so we ah found several different aspects of
application of this particular spatio temporal
control of systems that we have developed
until now we have been also looking at how
interaction in time can change the property
of the system that we discussed in the previous
ah studies and ah one of the ways of development
of a quantum computer in this particular aspect
will definitely be involving and interaction
with both time and space as we have been showing
here
so ah with this i would like to actually ah
conclude our understanding and study of quantum
computation implementation and other aspects
that's we have been dealing with in this course
i have tried my best in explaining all the
different aspects which have come in to this
field over the years of development initially
the development of this field has been extremely
rapid with a lot of input and then there was
a period where a lot of questions was raised
and lot of understanding needed to be developed
so the initial years which were also fuelled
by the fact that feynman realized that quantum
systems need quantum computers to have the
best results ah brought in the entire principle
of ah interest in this area of quantum computing
for a while there was a there was a lot of
development and because universally t was
established by dovish then after there was
a period where a lot of questions were raised
on the viability and the error aspects of
the problem which were ah built on and the
first important development came when ah shor
was able to show the algorithm which works
exponentially in speed which is what is the
expectation of this ah realization of the
fact of quantum computing in reality and there
after grovers algorithm and many processes
and many other developments has happened ah
many important people have ah many important
developments have made contributions to this
field which are ah ah which are very critical
and it is still a very growing field
so many many aspects that we have discussed
here are still being explored and ah many
habit is perhaps going to change over the
next few years as we realize much better ways
of dealing with a these kinds of ideas so
with that i would expect that this particular
kind of course would need to get upgraded
ah in some years because a lot more new information
will come in and a lot more interesting results
will be there to be presented in such a ah
evolving developing course but i there is
a lot of interest and i hope you all enjoyed
the course and i look forward to having interacting
with you in the years to come in the future
thank you
