align:start position:0% hi everybody I'm rumen and today I will align:start position:0% hi everybody I'm rumen and today I will align:start position:0% hi everybody I'm rumen and today I will talk about three things optical trapping align:start position:0% talk about three things optical trapping align:start position:0% talk about three things optical trapping the Boltzmann constant and Brownian align:start position:0% the Boltzmann constant and Brownian align:start position:0% the Boltzmann constant and Brownian motion the goal of the lab is to extract align:start position:0% motion the goal of the lab is to extract align:start position:0% motion the goal of the lab is to extract Boltzmann's constant out of Brownian align:start position:0% Boltzmann's constant out of Brownian align:start position:0% Boltzmann's constant out of Brownian motion and there are two key components align:start position:0% motion and there are two key components align:start position:0% motion and there are two key components to think about first one is the align:start position:0% to think about first one is the align:start position:0% to think about first one is the Boltzmann constant which is prevalent in align:start position:0% Boltzmann constant which is prevalent in align:start position:0% Boltzmann constant which is prevalent in different types of science for example align:start position:0% different types of science for example align:start position:0% different types of science for example we can have it in biophysics where align:start position:0% we can have it in biophysics where align:start position:0% we can have it in biophysics where people use the Boltzmann constant to try align:start position:0% people use the Boltzmann constant to try align:start position:0% people use the Boltzmann constant to try to understand forces in a cellular level align:start position:0% to understand forces in a cellular level align:start position:0% to understand forces in a cellular level we have it in thermodynamics with the align:start position:0% we have it in thermodynamics with the align:start position:0% we have it in thermodynamics with the famous equipartition theorem how does align:start position:0% famous equipartition theorem how does align:start position:0% famous equipartition theorem how does this relate to the Brownian motion the align:start position:0% this relate to the Brownian motion the align:start position:0% this relate to the Brownian motion the key thing is to think about length align:start position:0% key thing is to think about length align:start position:0% key thing is to think about length scales Brownian motion is relevant in align:start position:0% scales Brownian motion is relevant in align:start position:0% scales Brownian motion is relevant in terms of microns and at the same time if align:start position:0% terms of microns and at the same time if align:start position:0% terms of microns and at the same time if we look at the cellular level for align:start position:0% we look at the cellular level for align:start position:0% we look at the cellular level for example if we look at our hair we have align:start position:0% example if we look at our hair we have align:start position:0% example if we look at our hair we have micron sized hair all right so there are align:start position:0% micron sized hair all right so there are align:start position:0% micron sized hair all right so there are different ways to measure the align:start position:0% different ways to measure the align:start position:0% different ways to measure the Boltzmann's constant some people measure align:start position:0% Boltzmann's constant some people measure align:start position:0% Boltzmann's constant some people measure the speed of sound in argon gas others align:start position:0% the speed of sound in argon gas others align:start position:0% the speed of sound in argon gas others do optical trapping in air we will do align:start position:0% do optical trapping in air we will do align:start position:0% do optical trapping in air we will do slightly different optical trapping as align:start position:0% slightly different optical trapping as align:start position:0% slightly different optical trapping as you will see but the consensus among the align:start position:0% you will see but the consensus among the align:start position:0% you will see but the consensus among the scientific community is that it is align:start position:0% scientific community is that it is align:start position:0% scientific community is that it is challenging our plan is to prepare align:start position:0% challenging our plan is to prepare align:start position:0% challenging our plan is to prepare Brownian particles and control their align:start position:0% Brownian particles and control their align:start position:0% Brownian particles and control their Brownian motion we take glass beads of align:start position:0% Brownian motion we take glass beads of align:start position:0% Brownian motion we take glass beads of their spherical glass beads of diameter align:start position:0% their spherical glass beads of diameter align:start position:0% their spherical glass beads of diameter of 3.2 microns and the main to is to align:start position:0% of 3.2 microns and the main to is to align:start position:0% of 3.2 microns and the main to is to concentrate a highly focused lasers on align:start position:0% concentrate a highly focused lasers on align:start position:0% concentrate a highly focused lasers on top of these beads there's interesting align:start position:0% top of these beads there's interesting align:start position:0% top of these beads there's interesting physics going on light carries momentum align:start position:0% physics going on light carries momentum align:start position:0% physics going on light carries momentum versa generates force we have that the align:start position:0% versa generates force we have that the align:start position:0% versa generates force we have that the net gradient force opposes the motion of align:start position:0% net gradient force opposes the motion of align:start position:0% net gradient force opposes the motion of the beam while the net scattering force align:start position:0% the beam while the net scattering force align:start position:0% the beam while the net scattering force goes along the motion of the beam and align:start position:0% goes along the motion of the beam and align:start position:0% goes along the motion of the beam and when these two forces balance each other align:start position:0% when these two forces balance each other align:start position:0% when these two forces balance each other we have a beat that is at the center align:start position:0% we have a beat that is at the center align:start position:0% we have a beat that is at the center when you push this beat a little bit to align:start position:0% when you push this beat a little bit to align:start position:0% when you push this beat a little bit to the left or to the right then we have align:start position:0% the left or to the right then we have align:start position:0% the left or to the right then we have that the gradient forces are pulling align:start position:0% that the gradient forces are pulling align:start position:0% that the gradient forces are pulling back in the center and essentially we align:start position:0% back in the center and essentially we align:start position:0% back in the center and essentially we observe a simple harmonic motion in a align:start position:0% observe a simple harmonic motion in a align:start position:0% observe a simple harmonic motion in a more concrete example what we did is we align:start position:0% more concrete example what we did is we align:start position:0% more concrete example what we did is we took samples and we can find everything align:start position:0% took samples and we can find everything align:start position:0% took samples and we can find everything into a two-dimensional plane this is align:start position:0% into a two-dimensional plane this is align:start position:0% into a two-dimensional plane this is very important we have two directions align:start position:0% very important we have two directions align:start position:0% very important we have two directions the X direction in the Y direction for align:start position:0% the X direction in the Y direction for align:start position:0% the X direction in the Y direction for the beads we put them into water and align:start position:0% the beads we put them into water and align:start position:0% the beads we put them into water and source of Brownian motion comes from the align:start position:0% source of Brownian motion comes from the align:start position:0% source of Brownian motion comes from the collisions between our bead with the align:start position:0% collisions between our bead with the align:start position:0% collisions between our bead with the molecules into the water align:start position:0% molecules into the water align:start position:0% molecules into the water these are thermal collisions that align:start position:0% these are thermal collisions that align:start position:0% these are thermal collisions that generate Brownian motion as you can see align:start position:0% generate Brownian motion as you can see align:start position:0% generate Brownian motion as you can see this lonely beat has its Brownian motion align:start position:0% this lonely beat has its Brownian motion align:start position:0% this lonely beat has its Brownian motion what's interesting is when we shine align:start position:0% what's interesting is when we shine align:start position:0% what's interesting is when we shine light on top of a beat we trap this beat align:start position:0% light on top of a beat we trap this beat align:start position:0% light on top of a beat we trap this beat and we can find the Brownian motion so align:start position:0% and we can find the Brownian motion so align:start position:0% and we can find the Brownian motion so it's feasible to measure the motion and align:start position:0% it's feasible to measure the motion and align:start position:0% it's feasible to measure the motion and the theory behind this is very beautiful align:start position:0% the theory behind this is very beautiful align:start position:0% the theory behind this is very beautiful it's about the equipartition theorem align:start position:0% it's about the equipartition theorem align:start position:0% it's about the equipartition theorem which relates the kinetic energy coming align:start position:0% which relates the kinetic energy coming align:start position:0% which relates the kinetic energy coming from the simple harmonic motion on the align:start position:0% from the simple harmonic motion on the align:start position:0% from the simple harmonic motion on the left-hand side with the thermal energy align:start position:0% left-hand side with the thermal energy align:start position:0% left-hand side with the thermal energy of due to the degrees of freedom now let align:start position:0% of due to the degrees of freedom now let align:start position:0% of due to the degrees of freedom now let us recall that we have a two-dimensional align:start position:0% us recall that we have a two-dimensional align:start position:0% us recall that we have a two-dimensional confinement so we have a direction in X align:start position:0% confinement so we have a direction in X align:start position:0% confinement so we have a direction in X and direction in Y so it means that in align:start position:0% and direction in Y so it means that in align:start position:0% and direction in Y so it means that in each of the directions we have one align:start position:0% each of the directions we have one align:start position:0% each of the directions we have one degree of freedom which is correlated align:start position:0% degree of freedom which is correlated align:start position:0% degree of freedom which is correlated with this equipartition theorem now an align:start position:0% with this equipartition theorem now an align:start position:0% with this equipartition theorem now an interesting thing about the statistical align:start position:0% interesting thing about the statistical align:start position:0% interesting thing about the statistical motion of the molecules is that we have align:start position:0% motion of the molecules is that we have align:start position:0% motion of the molecules is that we have the simple harmonic motion however the align:start position:0% the simple harmonic motion however the align:start position:0% the simple harmonic motion however the things are moving into water so there is align:start position:0% things are moving into water so there is align:start position:0% things are moving into water so there is a drag force that dominates so we align:start position:0% a drag force that dominates so we align:start position:0% a drag force that dominates so we simplify the left hand side what is very align:start position:0% simplify the left hand side what is very align:start position:0% simplify the left hand side what is very interesting is the F factor which comes align:start position:0% interesting is the F factor which comes align:start position:0% interesting is the F factor which comes from the collisions between the beat align:start position:0% from the collisions between the beat align:start position:0% from the collisions between the beat with the molecules this generates align:start position:0% with the molecules this generates align:start position:0% with the molecules this generates forcing and driving of the simple align:start position:0% forcing and driving of the simple align:start position:0% forcing and driving of the simple harmonic motion I like to point out one align:start position:0% harmonic motion I like to point out one align:start position:0% harmonic motion I like to point out one thing about the scales of the forces we align:start position:0% thing about the scales of the forces we align:start position:0% thing about the scales of the forces we have Pico Newton's which is relevant for align:start position:0% have Pico Newton's which is relevant for align:start position:0% have Pico Newton's which is relevant for optical trapping and for Brownian motion align:start position:0% optical trapping and for Brownian motion align:start position:0% optical trapping and for Brownian motion this is the first observation that we align:start position:0% this is the first observation that we align:start position:0% this is the first observation that we did and actually Einstein this operation align:start position:0% did and actually Einstein this operation align:start position:0% did and actually Einstein this operation a long time ago he observed the white align:start position:0% a long time ago he observed the white align:start position:0% a long time ago he observed the white noise essentially the collisions they align:start position:0% noise essentially the collisions they align:start position:0% noise essentially the collisions they generate uncorrelated forcing and we can align:start position:0% generate uncorrelated forcing and we can align:start position:0% generate uncorrelated forcing and we can think of it as something that is not align:start position:0% think of it as something that is not align:start position:0% think of it as something that is not biased with any distribution is just align:start position:0% biased with any distribution is just align:start position:0% biased with any distribution is just uniform as you can see on these slides align:start position:0% uniform as you can see on these slides align:start position:0% uniform as you can see on these slides we have the position plotted in terms of align:start position:0% we have the position plotted in terms of align:start position:0% we have the position plotted in terms of and it exhibits a uniform distribution align:start position:0% and it exhibits a uniform distribution align:start position:0% and it exhibits a uniform distribution of the spectrum another thing that I align:start position:0% of the spectrum another thing that I align:start position:0% of the spectrum another thing that I would like to point out is to look at align:start position:0% would like to point out is to look at align:start position:0% would like to point out is to look at this plot of fluctuations in X&Y and the align:start position:0% this plot of fluctuations in X&Y and the align:start position:0% this plot of fluctuations in X&Y and the power which is linear with the current align:start position:0% power which is linear with the current align:start position:0% power which is linear with the current of the lasers as you can see as the align:start position:0% of the lasers as you can see as the align:start position:0% of the lasers as you can see as the power becomes big this means that we are align:start position:0% power becomes big this means that we are align:start position:0% power becomes big this means that we are trapping more so we have less align:start position:0% trapping more so we have less align:start position:0% trapping more so we have less fluctuations which is something as align:start position:0% fluctuations which is something as align:start position:0% fluctuations which is something as expected all right so let's figure out align:start position:0% expected all right so let's figure out align:start position:0% expected all right so let's figure out what we want to do with this lab we have align:start position:0% what we want to do with this lab we have align:start position:0% what we want to do with this lab we have the equipartition theorem and align:start position:0% the equipartition theorem and align:start position:0% the equipartition theorem and essentially we have three components align:start position:0% essentially we have three components align:start position:0% essentially we have three components that we would like to measure in order align:start position:0% that we would like to measure in order align:start position:0% that we would like to measure in order to extract Kb we need to find the align:start position:0% to extract Kb we need to find the align:start position:0% to extract Kb we need to find the fluctuations which I just presented to align:start position:0% fluctuations which I just presented to align:start position:0% fluctuations which I just presented to you we need to find the stiffness align:start position:0% you we need to find the stiffness align:start position:0% you we need to find the stiffness coefficient alpha which is related to align:start position:0% coefficient alpha which is related to align:start position:0% coefficient alpha which is related to the spring constant of motion and then align:start position:0% the spring constant of motion and then align:start position:0% the spring constant of motion and then we need to measure the temperature T the align:start position:0% we need to measure the temperature T the align:start position:0% we need to measure the temperature T the apparatus that we use has two main align:start position:0% apparatus that we use has two main align:start position:0% apparatus that we use has two main components the two components are align:start position:0% components the two components are align:start position:0% components the two components are concerned with the two types of light align:start position:0% concerned with the two types of light align:start position:0% concerned with the two types of light that we use in our experiment we use a align:start position:0% that we use in our experiment we use a align:start position:0% that we use in our experiment we use a laser that shines on top of the confined align:start position:0% laser that shines on top of the confined align:start position:0% laser that shines on top of the confined two-dimensional samples and tries to align:start position:0% two-dimensional samples and tries to align:start position:0% two-dimensional samples and tries to trap a beat the scatter light from the align:start position:0% trap a beat the scatter light from the align:start position:0% trap a beat the scatter light from the laser goes into a QP D a quadrant photo align:start position:0% laser goes into a QP D a quadrant photo align:start position:0% laser goes into a QP D a quadrant photo detector which is an ultra-fast camera align:start position:0% detector which is an ultra-fast camera align:start position:0% detector which is an ultra-fast camera that manages to quickly digitalize the align:start position:0% that manages to quickly digitalize the align:start position:0% that manages to quickly digitalize the content and give us the position of the align:start position:0% content and give us the position of the align:start position:0% content and give us the position of the scattered light so when we trap the beat align:start position:0% scattered light so when we trap the beat align:start position:0% scattered light so when we trap the beat we know where it is by observing the align:start position:0% we know where it is by observing the align:start position:0% we know where it is by observing the feedback from the QPD the other align:start position:0% feedback from the QPD the other align:start position:0% feedback from the QPD the other interesting part of the apparatus is the align:start position:0% interesting part of the apparatus is the align:start position:0% interesting part of the apparatus is the LED light which illuminates the sample align:start position:0% LED light which illuminates the sample align:start position:0% LED light which illuminates the sample and then it brings it to the CCD camera align:start position:0% and then it brings it to the CCD camera align:start position:0% and then it brings it to the CCD camera and this is very important so the CCD align:start position:0% and this is very important so the CCD align:start position:0% and this is very important so the CCD camera is very slow it cannot measure align:start position:0% camera is very slow it cannot measure align:start position:0% camera is very slow it cannot measure Brownian motion what it can do is it can align:start position:0% Brownian motion what it can do is it can align:start position:0% Brownian motion what it can do is it can tell us where are the beats it can allow align:start position:0% tell us where are the beats it can allow align:start position:0% tell us where are the beats it can allow us to look at the water and like find align:start position:0% us to look at the water and like find align:start position:0% us to look at the water and like find the beats we want to trap so these two align:start position:0% the beats we want to trap so these two align:start position:0% the beats we want to trap so these two components in combination are crucial align:start position:0% components in combination are crucial align:start position:0% components in combination are crucial for the success of our research there is align:start position:0% for the success of our research there is align:start position:0% for the success of our research there is interesting electronics coming behind align:start position:0% interesting electronics coming behind align:start position:0% interesting electronics coming behind this essentially the signals from the align:start position:0% this essentially the signals from the align:start position:0% this essentially the signals from the QPD and from the stage position where we align:start position:0% QPD and from the stage position where we align:start position:0% QPD and from the stage position where we put our sample are align:start position:0% put our sample are align:start position:0% put our sample are given in terms of volts so a natural align:start position:0% given in terms of volts so a natural align:start position:0% given in terms of volts so a natural question that arises is how are we going align:start position:0% question that arises is how are we going align:start position:0% question that arises is how are we going to remember what is important there are align:start position:0% to remember what is important there are align:start position:0% to remember what is important there are two important things that would like to align:start position:0% two important things that would like to align:start position:0% two important things that would like to keep track of two positions the first align:start position:0% keep track of two positions the first align:start position:0% keep track of two positions the first one is the position of the stage that align:start position:0% one is the position of the stage that align:start position:0% one is the position of the stage that gives us a relative point of align:start position:0% gives us a relative point of align:start position:0% gives us a relative point of consideration and the second one is the align:start position:0% consideration and the second one is the align:start position:0% consideration and the second one is the position of the QPD which as you can align:start position:0% position of the QPD which as you can align:start position:0% position of the QPD which as you can recall it measures the place of the beat align:start position:0% recall it measures the place of the beat align:start position:0% recall it measures the place of the beat that we have trapped these inputs are align:start position:0% that we have trapped these inputs are align:start position:0% that we have trapped these inputs are given in terms of volts so the natural align:start position:0% given in terms of volts so the natural align:start position:0% given in terms of volts so the natural thing to do is to find a calibration align:start position:0% thing to do is to find a calibration align:start position:0% thing to do is to find a calibration that converts these volts into actual align:start position:0% that converts these volts into actual align:start position:0% that converts these volts into actual distances here you can see how we do align:start position:0% distances here you can see how we do align:start position:0% distances here you can see how we do this we plot the stage X or position you align:start position:0% this we plot the stage X or position you align:start position:0% this we plot the stage X or position you can we can plot the stage Y it's align:start position:0% can we can plot the stage Y it's align:start position:0% can we can plot the stage Y it's completely analogous to the to the QPD align:start position:0% completely analogous to the to the QPD align:start position:0% completely analogous to the to the QPD positions here and the conversion factor align:start position:0% positions here and the conversion factor align:start position:0% positions here and the conversion factor hides along these slopes here well as align:start position:0% hides along these slopes here well as align:start position:0% hides along these slopes here well as you can see we have two different slopes align:start position:0% you can see we have two different slopes align:start position:0% you can see we have two different slopes here with different absolute values so align:start position:0% here with different absolute values so align:start position:0% here with different absolute values so this type of measurement is prone to align:start position:0% this type of measurement is prone to align:start position:0% this type of measurement is prone to errors how we approach this problem is align:start position:0% errors how we approach this problem is align:start position:0% errors how we approach this problem is that we fought by choosing more data align:start position:0% that we fought by choosing more data align:start position:0% that we fought by choosing more data points and trying to increase the align:start position:0% points and trying to increase the align:start position:0% points and trying to increase the statistic thus hopefully reducing the align:start position:0% statistic thus hopefully reducing the align:start position:0% statistic thus hopefully reducing the systematics of this measurement the align:start position:0% systematics of this measurement the align:start position:0% systematics of this measurement the second step is to start getting the align:start position:0% second step is to start getting the align:start position:0% second step is to start getting the components that we need in order to align:start position:0% components that we need in order to align:start position:0% components that we need in order to extract KB is to measure the stiffness align:start position:0% extract KB is to measure the stiffness align:start position:0% extract KB is to measure the stiffness coefficient alpha now the main idea is align:start position:0% coefficient alpha now the main idea is align:start position:0% coefficient alpha now the main idea is to take the equation of motion and to align:start position:0% to take the equation of motion and to align:start position:0% to take the equation of motion and to make a Fourier transform in order to get align:start position:0% make a Fourier transform in order to get align:start position:0% make a Fourier transform in order to get the positions in terms of frequencies align:start position:0% the positions in terms of frequencies align:start position:0% the positions in terms of frequencies there is mathematics behind this and align:start position:0% there is mathematics behind this and align:start position:0% there is mathematics behind this and essentially the power spectral align:start position:0% essentially the power spectral align:start position:0% essentially the power spectral distribution and as the distribution of align:start position:0% distribution and as the distribution of align:start position:0% distribution and as the distribution of this motion here that we expect obtains align:start position:0% this motion here that we expect obtains align:start position:0% this motion here that we expect obtains this form here from where we can extract align:start position:0% this form here from where we can extract align:start position:0% this form here from where we can extract the characteristic frequency F naught align:start position:0% the characteristic frequency F naught align:start position:0% the characteristic frequency F naught and F naught gives us alpha which is align:start position:0% and F naught gives us alpha which is align:start position:0% and F naught gives us alpha which is what we really need this is a log-log align:start position:0% what we really need this is a log-log align:start position:0% what we really need this is a log-log plot as you can see here another thing I align:start position:0% plot as you can see here another thing I align:start position:0% plot as you can see here another thing I would like to mention is look at the align:start position:0% would like to mention is look at the align:start position:0% would like to mention is look at the proportionality here as we increase the align:start position:0% proportionality here as we increase the align:start position:0% proportionality here as we increase the power we also increase the stiffness align:start position:0% power we also increase the stiffness align:start position:0% power we also increase the stiffness coefficient alpha because we trap more align:start position:0% coefficient alpha because we trap more align:start position:0% coefficient alpha because we trap more closely so it means that F nost has to align:start position:0% closely so it means that F nost has to align:start position:0% closely so it means that F nost has to increase and indeed when we increase the align:start position:0% increase and indeed when we increase the align:start position:0% increase and indeed when we increase the power we are shifting F naught to the align:start position:0% power we are shifting F naught to the align:start position:0% power we are shifting F naught to the right having all these components align:start position:0% right having all these components align:start position:0% right having all these components we can put this into the big picture and align:start position:0% we can put this into the big picture and align:start position:0% we can put this into the big picture and the big picture is the extraction of KB align:start position:0% the big picture is the extraction of KB align:start position:0% the big picture is the extraction of KB over here I showed you x squared the align:start position:0% over here I showed you x squared the align:start position:0% over here I showed you x squared the fluctuations I showed you alpha we can align:start position:0% fluctuations I showed you alpha we can align:start position:0% fluctuations I showed you alpha we can measure the temperature T and then we align:start position:0% measure the temperature T and then we align:start position:0% measure the temperature T and then we can get Kb the essence of this align:start position:0% can get Kb the essence of this align:start position:0% can get Kb the essence of this measurement is to look at the inverse align:start position:0% measurement is to look at the inverse align:start position:0% measurement is to look at the inverse proportionality between fluctuations and align:start position:0% proportionality between fluctuations and align:start position:0% proportionality between fluctuations and trap stiffness then we can make a fit align:start position:0% trap stiffness then we can make a fit align:start position:0% trap stiffness then we can make a fit with a reasonable chi-square probability align:start position:0% with a reasonable chi-square probability align:start position:0% with a reasonable chi-square probability and from here we can extract Kb the align:start position:0% and from here we can extract Kb the align:start position:0% and from here we can extract Kb the result is presented on the slide we also align:start position:0% result is presented on the slide we also align:start position:0% result is presented on the slide we also show you the measurement that we extract align:start position:0% show you the measurement that we extract align:start position:0% show you the measurement that we extract from literature our result is within two align:start position:0% from literature our result is within two align:start position:0% from literature our result is within two sigma of the accepted value of KB align:start position:0% sigma of the accepted value of KB align:start position:0% sigma of the accepted value of KB actually we're very close to 1 Sigma align:start position:0% actually we're very close to 1 Sigma align:start position:0% actually we're very close to 1 Sigma from the accepted value of KB what is align:start position:0% from the accepted value of KB what is align:start position:0% from the accepted value of KB what is driving this like unfortunate outcome align:start position:0% driving this like unfortunate outcome align:start position:0% driving this like unfortunate outcome the thing that drives this unfortunate align:start position:0% the thing that drives this unfortunate align:start position:0% the thing that drives this unfortunate outcome is the systematic errors on our align:start position:0% outcome is the systematic errors on our align:start position:0% outcome is the systematic errors on our picture this is our starting error this align:start position:0% picture this is our starting error this align:start position:0% picture this is our starting error this is the uncertainty in KB and there are align:start position:0% is the uncertainty in KB and there are align:start position:0% is the uncertainty in KB and there are different factors that contribute it to align:start position:0% different factors that contribute it to align:start position:0% different factors that contribute it to this as you saw the calibration is very align:start position:0% this as you saw the calibration is very align:start position:0% this as you saw the calibration is very difficult align:start position:0% difficult align:start position:0% difficult we have error from the laser hitting the align:start position:0% we have error from the laser hitting the align:start position:0% we have error from the laser hitting the water and changing the temperature we align:start position:0% water and changing the temperature we align:start position:0% water and changing the temperature we have systematic error of the electronics align:start position:0% have systematic error of the electronics align:start position:0% have systematic error of the electronics which we safely ignore because the first align:start position:0% which we safely ignore because the first align:start position:0% which we safely ignore because the first two factors dominate this our align:start position:0% two factors dominate this our align:start position:0% two factors dominate this our electronics were very precise and then align:start position:0% electronics were very precise and then align:start position:0% electronics were very precise and then we have the statistical uncertainties align:start position:0% we have the statistical uncertainties align:start position:0% we have the statistical uncertainties that we use which correspond to some align:start position:0% that we use which correspond to some align:start position:0% that we use which correspond to some error propagating tricks okay now let's align:start position:0% error propagating tricks okay now let's align:start position:0% error propagating tricks okay now let's do our investigation the first one is align:start position:0% do our investigation the first one is align:start position:0% do our investigation the first one is about the calibration as you can see all align:start position:0% about the calibration as you can see all align:start position:0% about the calibration as you can see all of these slopes should be valid but align:start position:0% of these slopes should be valid but align:start position:0% of these slopes should be valid but they're actually not so what we do is we align:start position:0% they're actually not so what we do is we align:start position:0% they're actually not so what we do is we take them into account we average them align:start position:0% take them into account we average them align:start position:0% take them into account we average them then we take more data points we average align:start position:0% then we take more data points we average align:start position:0% then we take more data points we average again and then we propagate the errors align:start position:0% again and then we propagate the errors align:start position:0% again and then we propagate the errors in order to reduce the systematics the align:start position:0% in order to reduce the systematics the align:start position:0% in order to reduce the systematics the second one is due to the heating of the align:start position:0% second one is due to the heating of the align:start position:0% second one is due to the heating of the laser essentially what happens is when align:start position:0% laser essentially what happens is when align:start position:0% laser essentially what happens is when the laser hits the water it starts align:start position:0% the laser hits the water it starts align:start position:0% the laser hits the water it starts heating the vicinity and this is align:start position:0% heating the vicinity and this is align:start position:0% heating the vicinity and this is unfortunate because yes we can measure align:start position:0% unfortunate because yes we can measure align:start position:0% unfortunate because yes we can measure the room temperature by using the therm align:start position:0% the room temperature by using the therm align:start position:0% the room temperature by using the therm but actual uncertainty on the align:start position:0% but actual uncertainty on the align:start position:0% but actual uncertainty on the temperature is much bigger because we align:start position:0% temperature is much bigger because we align:start position:0% temperature is much bigger because we have extra heating due to the laser we align:start position:0% have extra heating due to the laser we align:start position:0% have extra heating due to the laser we tried elegantly to to avoid this by align:start position:0% tried elegantly to to avoid this by align:start position:0% tried elegantly to to avoid this by moving the laser constantly so that it align:start position:0% moving the laser constantly so that it align:start position:0% moving the laser constantly so that it doesn't stay in one place and heat up a align:start position:0% doesn't stay in one place and heat up a align:start position:0% doesn't stay in one place and heat up a lot but it's very hard to quantify how align:start position:0% lot but it's very hard to quantify how align:start position:0% lot but it's very hard to quantify how exactly it heats up the water and the align:start position:0% exactly it heats up the water and the align:start position:0% exactly it heats up the water and the third one is it's concerned with our fit align:start position:0% third one is it's concerned with our fit align:start position:0% third one is it's concerned with our fit with fluctuations in terms of the trap align:start position:0% with fluctuations in terms of the trap align:start position:0% with fluctuations in terms of the trap stiffness initially when we did the fit align:start position:0% stiffness initially when we did the fit align:start position:0% stiffness initially when we did the fit we with the PhD method we get a align:start position:0% we with the PhD method we get a align:start position:0% we with the PhD method we get a probability of chi-square equals 0 and align:start position:0% probability of chi-square equals 0 and align:start position:0% probability of chi-square equals 0 and then we quickly realize that essentially align:start position:0% then we quickly realize that essentially align:start position:0% then we quickly realize that essentially what we need to do is take into account align:start position:0% what we need to do is take into account align:start position:0% what we need to do is take into account the horizontal errors and here what we align:start position:0% the horizontal errors and here what we align:start position:0% the horizontal errors and here what we do is we transform the horizontal errors align:start position:0% do is we transform the horizontal errors align:start position:0% do is we transform the horizontal errors into the vertical errors and this thing align:start position:0% into the vertical errors and this thing align:start position:0% into the vertical errors and this thing we can do by using adding addition in align:start position:0% we can do by using adding addition in align:start position:0% we can do by using adding addition in quadrature and propagation of the errors align:start position:0% quadrature and propagation of the errors align:start position:0% quadrature and propagation of the errors which gave us a reasonable realistic align:start position:0% which gave us a reasonable realistic align:start position:0% which gave us a reasonable realistic chi-squared of 0.33 in conclusion I'll align:start position:0% chi-squared of 0.33 in conclusion I'll align:start position:0% chi-squared of 0.33 in conclusion I'll start with limitations as you saw it's align:start position:0% start with limitations as you saw it's align:start position:0% start with limitations as you saw it's very hard to distinguish between align:start position:0% very hard to distinguish between align:start position:0% very hard to distinguish between systematic errors and statistical align:start position:0% systematic errors and statistical align:start position:0% systematic errors and statistical uncertainties the reason for this is as align:start position:0% uncertainties the reason for this is as align:start position:0% uncertainties the reason for this is as you saw is that we are fighting with the align:start position:0% you saw is that we are fighting with the align:start position:0% you saw is that we are fighting with the systematics by introducing more align:start position:0% systematics by introducing more align:start position:0% systematics by introducing more statistics and everything mixes up in align:start position:0% statistics and everything mixes up in align:start position:0% statistics and everything mixes up in the propagation of errors the second align:start position:0% the propagation of errors the second align:start position:0% the propagation of errors the second thing that it was very difficult in this align:start position:0% thing that it was very difficult in this align:start position:0% thing that it was very difficult in this lab is that we need to move the laser align:start position:0% lab is that we need to move the laser align:start position:0% lab is that we need to move the laser constantly so one of the one of the align:start position:0% constantly so one of the one of the align:start position:0% constantly so one of the one of the people working on this topic has to keep align:start position:0% people working on this topic has to keep align:start position:0% people working on this topic has to keep track of where the laser is and whether align:start position:0% track of where the laser is and whether align:start position:0% track of where the laser is and whether you're trapping things that you may not align:start position:0% you're trapping things that you may not align:start position:0% you're trapping things that you may not want to trap the third thing is to the align:start position:0% want to trap the third thing is to the align:start position:0% want to trap the third thing is to the need to find better ways of calibration align:start position:0% need to find better ways of calibration align:start position:0% need to find better ways of calibration and there are people who are actively align:start position:0% and there are people who are actively align:start position:0% and there are people who are actively working on this on this topic here as align:start position:0% working on this on this topic here as align:start position:0% working on this on this topic here as you saw the main source of error came align:start position:0% you saw the main source of error came align:start position:0% you saw the main source of error came from the calibration actually but the align:start position:0% from the calibration actually but the align:start position:0% from the calibration actually but the process is that we can give a reasonable align:start position:0% process is that we can give a reasonable align:start position:0% process is that we can give a reasonable estimate to the Boltzmann constant and align:start position:0% estimate to the Boltzmann constant and align:start position:0% estimate to the Boltzmann constant and at the same time we can have a lot of align:start position:0% at the same time we can have a lot of align:start position:0% at the same time we can have a lot of fun while doing so I would like to thank align:start position:0% fun while doing so I would like to thank align:start position:0% fun while doing so I would like to thank to my partner Emma and I think align:start position:0% to my partner Emma and I think align:start position:0% to my partner Emma and I think collaboration is very important for align:start position:0% collaboration is very important for align:start position:0% collaboration is very important for Jayla and more specifically for this align:start position:0% Jayla and more specifically for this align:start position:0% Jayla and more specifically for this particular experiment this experiment is align:start position:0% particular experiment this experiment is align:start position:0% particular experiment this experiment is impossible to be done without a partner align:start position:0% impossible to be done without a partner align:start position:0% impossible to be done without a partner because it's very difficult it's very align:start position:0% because it's very difficult it's very align:start position:0% because it's very difficult it's very difficult to keep track of where you align:start position:0% difficult to keep track of where you align:start position:0% difficult to keep track of where you want to put align:start position:0% want to put align:start position:0% want to put and also what is going on around the align:start position:0% and also what is going on around the align:start position:0% and also what is going on around the laser well one of the people who is align:start position:0% laser well one of the people who is align:start position:0% laser well one of the people who is moving the laser the other one should be align:start position:0% moving the laser the other one should be align:start position:0% moving the laser the other one should be looking looking at the CCD camera and align:start position:0% looking looking at the CCD camera and align:start position:0% looking looking at the CCD camera and like telling where are we going on like align:start position:0% like telling where are we going on like align:start position:0% like telling where are we going on like what are we actually trapping like what align:start position:0% what are we actually trapping like what align:start position:0% what are we actually trapping like what do we want to avoid like we don't want align:start position:0% do we want to avoid like we don't want align:start position:0% do we want to avoid like we don't want these guys in our picture I also like to align:start position:0% these guys in our picture I also like to align:start position:0% these guys in our picture I also like to thank the staff of this class for their align:start position:0% thank the staff of this class for their align:start position:0% thank the staff of this class for their useful feedback and their valuable help align:start position:0% useful feedback and their valuable help align:start position:0% useful feedback and their valuable help and finally for your attention yeah so align:start position:0% and finally for your attention yeah so align:start position:0% and finally for your attention yeah so we have a lot of this should be trap align:start position:0% we have a lot of this should be trap align:start position:0% we have a lot of this should be trap stiffness versus the this is the current align:start position:0% stiffness versus the this is the current align:start position:0% stiffness versus the this is the current and here actually I haven't shown that align:start position:0% and here actually I haven't shown that align:start position:0% and here actually I haven't shown that it's like the trap stiffness defers align:start position:0% it's like the trap stiffness defers align:start position:0% it's like the trap stiffness defers whether you look in the X direction or align:start position:0% whether you look in the X direction or align:start position:0% whether you look in the X direction or the Y direction the actual measurements align:start position:0% the Y direction the actual measurements align:start position:0% the Y direction the actual measurements are analog is because the mathematics is align:start position:0% are analog is because the mathematics is align:start position:0% are analog is because the mathematics is the same but as you can see here we have align:start position:0% the same but as you can see here we have align:start position:0% the same but as you can see here we have different data points for the two cases align:start position:0% different data points for the two cases align:start position:0% different data points for the two cases we account this into our considerations align:start position:0% we account this into our considerations align:start position:0% we account this into our considerations yes yes align:start position:0% align:start position:0% mmm align:start position:0% align:start position:0% well I mean the air case well I mean align:start position:0% well I mean the air case well I mean align:start position:0% well I mean the air case well I mean everything boils down to this this align:start position:0% everything boils down to this this align:start position:0% everything boils down to this this consideration here okay let me just find align:start position:0% consideration here okay let me just find align:start position:0% consideration here okay let me just find my explanation it boils down to the the align:start position:0% my explanation it boils down to the the align:start position:0% my explanation it boils down to the the viscosity that dominates so in our case align:start position:0% viscosity that dominates so in our case align:start position:0% viscosity that dominates so in our case we have the viscosity of water that align:start position:0% we have the viscosity of water that align:start position:0% we have the viscosity of water that dominates when you look in different align:start position:0% dominates when you look in different align:start position:0% dominates when you look in different mediums you might have different types align:start position:0% mediums you might have different types align:start position:0% mediums you might have different types of viscosity which would change the align:start position:0% of viscosity which would change the align:start position:0% of viscosity which would change the motions so I have the paper I I didn't align:start position:0% motions so I have the paper I I didn't align:start position:0% motions so I have the paper I I didn't actually read through the whole details align:start position:0% actually read through the whole details align:start position:0% actually read through the whole details of the how exactly the mathematics align:start position:0% of the how exactly the mathematics align:start position:0% of the how exactly the mathematics changes probably does also probably and align:start position:0% changes probably does also probably and align:start position:0% changes probably does also probably and other issues that are that may not arise align:start position:0% other issues that are that may not arise align:start position:0% other issues that are that may not arise or may arise is the laser like in this align:start position:0% or may arise is the laser like in this align:start position:0% or may arise is the laser like in this case like laser like heats up the the align:start position:0% case like laser like heats up the the align:start position:0% case like laser like heats up the the water but I don't know how exactly the align:start position:0% water but I don't know how exactly the align:start position:0% water but I don't know how exactly the laser would react with the air maybe align:start position:0% laser would react with the air maybe align:start position:0% laser would react with the air maybe it's going to heat up a little bit but align:start position:0% it's going to heat up a little bit but align:start position:0% it's going to heat up a little bit but how is this heat by going to be align:start position:0% how is this heat by going to be align:start position:0% how is this heat by going to be distributed in space I'm not very align:start position:0% distributed in space I'm not very align:start position:0% distributed in space I'm not very knowledgeable of this as it now align:start position:0% align:start position:0% so the equipartition theorem it breaks align:start position:0% so the equipartition theorem it breaks align:start position:0% so the equipartition theorem it breaks into components it breaks into the align:start position:0% into components it breaks into the align:start position:0% into components it breaks into the component of X where we have one degree align:start position:0% component of X where we have one degree align:start position:0% component of X where we have one degree of freedom and it breaks into the align:start position:0% of freedom and it breaks into the align:start position:0% of freedom and it breaks into the component of Y where have another degree align:start position:0% component of Y where have another degree align:start position:0% component of Y where have another degree of freedom align:start position:0% of freedom align:start position:0% of freedom each of these considerations is align:start position:0% each of these considerations is align:start position:0% each of these considerations is concerned only with in one movement so align:start position:0% concerned only with in one movement so align:start position:0% concerned only with in one movement so for the okay well you can think about it align:start position:0% for the okay well you can think about it align:start position:0% for the okay well you can think about it in this way we have two degrees of align:start position:0% in this way we have two degrees of align:start position:0% in this way we have two degrees of freedom in total but in the actual align:start position:0% freedom in total but in the actual align:start position:0% freedom in total but in the actual directions that are useful for our align:start position:0% directions that are useful for our align:start position:0% directions that are useful for our considerations we have only one degree align:start position:0% considerations we have only one degree align:start position:0% considerations we have only one degree of freedom so yeah well I think this is align:start position:0% of freedom so yeah well I think this is align:start position:0% of freedom so yeah well I think this is for this this is 3.2 microns and this align:start position:0% for this this is 3.2 microns and this align:start position:0% for this this is 3.2 microns and this like later on like you might you saw the align:start position:0% like later on like you might you saw the align:start position:0% like later on like you might you saw the 1 microns align:start position:0% 1 microns align:start position:0% 1 microns I think our data is concerned with the align:start position:0% I think our data is concerned with the align:start position:0% I think our data is concerned with the 3.2 microns we didn't I like my results align:start position:0% 3.2 microns we didn't I like my results align:start position:0% 3.2 microns we didn't I like my results are not related with the micron 1 micron align:start position:0% are not related with the micron 1 micron align:start position:0% are not related with the micron 1 micron we just played with it and try this we align:start position:0% we just played with it and try this we align:start position:0% we just played with it and try this we also tried the trapping cells from align:start position:0% also tried the trapping cells from align:start position:0% also tried the trapping cells from onions it was very fun to play with but align:start position:0% onions it was very fun to play with but align:start position:0% onions it was very fun to play with but unfortunately we couldn't get any like align:start position:0% unfortunately we couldn't get any like align:start position:0% unfortunately we couldn't get any like valuable quantitative results there so align:start position:0% valuable quantitative results there so align:start position:0% valuable quantitative results there so even though it's quite a lot of fun we align:start position:0% even though it's quite a lot of fun we align:start position:0% even though it's quite a lot of fun we have some clips it's not worth for this align:start position:0% have some clips it's not worth for this align:start position:0% have some clips it's not worth for this presentation which concentrates on the align:start position:0% presentation which concentrates on the align:start position:0% presentation which concentrates on the KB align:start position:0% align:start position:0% [Applause]