typos fixed, thanks to Dean

1 files changed, 15 insertions, 11 deletions

diff --git a/single-photon-interference.tex b/single-photon-interference.tex
index 2e0db92..7680c6a 100644
--- a/single-photon-interference.tex
+++ b/single-photon-interference.tex
@@ -5,7 +5,7 @@
 
 \noindent
  \textbf{Experiment objectives}: Study wave-particle duality for photons by measuring
- interference pattern in the Young double-slit experiment using conventional light source (laser) and a
+ interference patterns in the Young double-slit experiment using a conventional light source (laser) and a
  single-photon source (strongly attenuated lamp).
 
 
@@ -16,7 +16,8 @@ There is a rich historical background behind the experiment you are about to per
 separated white light into its colors, and, in the 1680's, hypothesized that light was composed of `corpuscles',
 supposed to possess some properties of particles.  This view reigned until the 1800's, when Thomas Young first
 performed the two-slit experiment now known by his name.  In this experiment he discovered a property of
-destructive interference, which seemed impossible to explain in terms of corpuscles, but is very naturally
+destructive interference, which seemed impossible to explain in terms of
+corpuscles, but was very naturally
 explained in terms of waves.  His experiment not only suggested that such `light waves' existed; it also
 provided a result that could be used to determine the wavelength of light, measured in familiar units. Light
 waves became even more acceptable with dynamical theories of light, such as Fresnel's and Maxwell's, in the 19th
@@ -58,7 +59,7 @@ upward by about $2$~cm, but then ensure that it's returned to its fully down pos
 to confirm, on the detector box, that the toggle switch in the HIGH-VOLTAGE section is turned off, and that the
 10-turn dial near it is set to $0.00$, fully counter-clockwise.
 
-To inspect the inside of the apparatus open the cover by turning four latches that hold it closed. The details
+To inspect the inside of the apparatus, open the cover by turning the four latches that hold it closed. The details
 of the experimental apparatus are shown in Fig.~\ref{tsifig1.fig}. Take time to locate all the important
 components of the experiment:
 \begin{itemize}
@@ -76,7 +77,7 @@ the rotary scale is $0.01$~mm.
 
 \item Two distinct light detectors at the right-hand end of the apparatus: a \emph{photodiode}
 and a \emph{photomultiplier tube} (PMT for short). The photodiode is used with the much brighter laser light;
-it's mounted on light shutter in such a way that it's in position to use when the shutter is closed (pushed
+it's mounted on light the shutter in such a way that it's in position to use when the shutter is closed (pushed
 down). The photomultiplier tube is an extremely sensitive detector able to detect individual photons (with energy
 of the order of $10^{-19}$~J, and it is used with the much dimmer light-bulb source. Too much light can easily
 damage it, so \textbf{PMT is safe to use only when the cover of the apparatus is in place, and only when the
@@ -92,7 +93,7 @@ The experiment consists of three steps:
 distribution of a laser beam on a viewing screen.
 \item Using the photodiode you will accurately measure the intensity distribution after single- and two-slit interference patterns,
 which can be compared to predictions of wave theories of light. \\
-These two steps recreate original Young's experiment.
+These two steps recreate Young's original experiment.
 \item Then using a very weak light source you will record the two-slit interference pattern one photon at a time.
 While this measurement will introduce you to single-photon detection technology, it will also show you that
 however two-slit interference is to be explained, it must be explained in terms that can apply to single
@@ -164,7 +165,7 @@ convenience, have the slit-blocker set to that previously determined setting whi
 to emerge and interfere.
 
 The shutter of the detector box will still be in its closed, or down, position: this blocks any light from
-reaching the PMT, and correctly position  a 1-cm$^{2}$ photodiode, which acts just like a solar cell in actively
+reaching the PMT, and correctly positions  a 1-cm$^{2}$ photodiode, which acts just like a solar cell in actively
 generating electric current when it's illuminated. The output current is proportional to total power
 illuminating the detector area, so it is important to use a narrow slit allow only a selected part of the
 interference pattern to be measured. Make sure that a detector slit mask (with a single narrow slit) on a
@@ -179,14 +180,15 @@ thin coaxial cable to the INPUT BNC connector of the photodiode-amplifier sectio
 converted to \emph{voltage} signal at the OUTPUT BNC connector adjacent to it. Connect to this output a digital
 multimeter set to 2 or 20-Volt sensitivity; you should see a stable positive reading. Turn off the laser first
 to record the ``zero offset'' - reading of the multimeter with no light. You will need to subtract this reading
-from all the other reading you make of this output voltage.
+from all the other readings you make of this output voltage.
 
 Turn your laser source back on, and watch the photodiode's voltage-output signal as you vary the setting of the
 detector-slit micrometer. If all is well, you will see a systematic variation of the signal as you scan over the
 interference pattern. Check that the maximum signal you see is about 3-8 Volts; if it is much less than this,
 the apparatus is out of alignment, and insufficient light is reaching the detector.
 
-\textbf{Initial tests of wave theory of light:} If we assume that the light beam is a stream of particle, we
+\textbf{Initial tests of wave theory of light:} If we assume that the light
+beam is a stream of particles, we
 would naively expect that closing one of two identical slits should reduce the measured intensity of light at
 any point on the screen by half, while the wave theory predicts much more dramatic variations in the different
 points in the screen. Which theory provides a more accurate description of what you see?
@@ -233,7 +235,9 @@ Fit your data with Eqs.~(\ref{1slit}) and (\ref{2slit_wDif}). You will need to a
 
 \subsection*{Single-photon interference}
 
-Before you start the measurements you have to convince yourself that the rate of photons emitted by the weak filtered light bulb is low enough to have in average less than one photon detected in the apparatus at any time. Roughly estimate the number of photons per second arriving to the detector. First, calculate the number of photons emitted by the light bulb in a 10~nm spectral window of the green filter (between $541$ and $551$~nm), if it runs at 6V and 0.2A, only 5\% of its electric energy turns into light, and this optical energy is evenly distributed in the spectral range between 500~nm and 1500~nm. These photons are emitted in all directions, but all of then are absorbed inside the box except for those passing through two slits with area approximately $0.1\times 10~\mathrm{mm}^2$. Next, if we assume that the beam of photons passing through the slits diffract over a $1~\mathrm{cm}^2$ area by the time they reach the detector slit, estimate the rate of photons reaching the detector. Finally, we have to adjust the detected photon rate by taking into account that for PMT only 4\% of photons produce output electric pulse at the output. That's the rate of event you expect. Now estimate the time it takes a photon to travel through the apparatus, and estimate the average number of detectable photons inside at a given moment of time. \emph{You may do this calculations before or after the lab period, but make sure to include them in the lab report.}
+Before you start the measurements you have to convince yourself that the
+rate of photons emitted by the weak filtered light bulb is low enough to
+have on average less than one photon detected in the apparatus at any time. Roughly estimate the number of photons per second arriving to the detector. First, calculate the number of photons emitted by the light bulb in a 10~nm spectral window of the green filter (between $541$ and $551$~nm), if it runs at 6V and 0.2A, only 5\% of its electric energy turns into light, and this optical energy is evenly distributed in the spectral range between 500~nm and 1500~nm. These photons are emitted in all directions, but all of then are absorbed inside the box except for those passing through two slits with area approximately $0.1\times 10~\mathrm{mm}^2$. Next, if we assume that the beam of photons passing through the slits diffract over a $1~\mathrm{cm}^2$ area by the time they reach the detector slit, estimate the rate of photons reaching the detector. Finally, we have to adjust the detected photon rate by taking into account that for PMT only 4\% of photons produce output electric pulse at the output. That's the rate of event you expect. Now estimate the time it takes a photon to travel through the apparatus, and estimate the average number of detectable photons inside at a given moment of time. \emph{You may do this calculations before or after the lab period, but make sure to include them in the lab report.}
 
 Now you need to change the apparatus to use the light bulb. Open the cover and slide the laser source to the side (do not remove the laser from the stand). Now set the 3-position toggle switch to the BULB position and dial the bulb adjustment up from 0 until you see the bulb light up. (\emph{The flashlight bulb you're using will live longest if you minimize the time you spend with it dialed above 6 on its scale, and if you toggle its power switch only when the dial is set to low values}). If the apparatus has been aligned, the bulb should now be in position to send light through the apparatus. Check that the green filter-holding structure is in place: the light-bulb should look green, since the green filter blocks nearly all the light emerging from the bulb, passing only wavelengths in the range 541 to 551 nm. The filtered light bulb is very dim, and you probably will not be able to see much light at the double slit position even with room light turned off completely. No matter; plenty of green-light photons will still be reaching the double-slit structure -- in fact, you should now dim the bulb even more, by setting its intensity control down to about 3 on its dial.
 
@@ -257,7 +261,7 @@ convenient count rate ($10^3 - 10^4$ events/second) at the central maximum.
 %you are counting substantially all true photon events, but minimizing the number of ``dark events''.
 
 \textbf{Single-photon detection of the interference pattern}. Most likely the experimental results in the
-previous section has demonstrated good agreement with the wave description of light. However, the PMT detects
+previous section have demonstrated good agreement with the wave description of light. However, the PMT detects
 individual photons, so one can expect that now one has to describe the light beam as a stream of particles, and
 the wave theory is not valid anymore. To check this assumption, you will repeat the measurements and take the
 same sort of data as in the previous section, except now characterizing the light intensity as photon count
@@ -355,7 +359,7 @@ The intensity is proportional to the square of the amplitude and thus
 I_P \propto \frac{(\sin (\frac{\pi a}{\lambda}\sin\theta))^2}{(\frac{\pi a}{\lambda}\sin\theta)^2}
 \end{equation}
 The minima of the intensity (``dark fringes'') occur at the zeros of the argument of the sin function:
-$\frac{\pi D}{\lambda}\sin\theta=m\pi$, while the maxima (``bright fringes'') are almost exactly match
+$\frac{\pi D}{\lambda}\sin\theta=m\pi$, while the maxima (``bright fringes'') almost exactly match
 $\frac{\pi D}{\lambda}\sin\theta=(m+\frac{1}{2})\pi$  for $m = 0, \pm1, \pm2, \cdots$.
 
 Let us now consider the case of interference pattern from two identical slits separated by the distance $d$, as