Light Meets Matter: Atoms and Lasers Martin Plenio - Clocks and Entanglement

Peter Knight - Quanta and Non-Classicality

Yaron Silberberg - Lasers and Microscopy

Paul Corkum - Attosecond ScienceSteve Brehmer - Mayo High School Rochester, Minnesota

What is light?In the late 1600s Newton explained many of the properties of light by assuming it was made of particles. Tis true, that from my theory I argue the corporeity of light; but I do it without any absolute positivenessThe waves on the surface of stagnating water, passing by the sides of a broad obstacle which stops part of them, bend afterwards and dilate themselves gradually into the quiet water behind the obstacle. But light is never known to follow crooked passages, nor to bend into the shadow.Im thinking waves.In 1678 Christian Huygens argued that light was a pulse traveling through a medium, or as we would say, a wave.Because of Newtons enormous prestige, his support of the particle theory of light tended to suppress other points of view.

In 1803 Thomas Youngs double slit experiment showed that, much like water waves, light diffracts and produces an interference pattern. Light must be waves!=2dsin

it seems we have strong reason to conclude that light itself is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.In the 1860s Maxwell, building on Faradays work, developed a mathematical model of electromagnetism. He was able to show that these electromagnetic waves travel at the speed of light.

E=hf+E=hfIn 1900 Max Planck was able to explain the spectrum of a blackbody radiator by assuming that light energy is quantized. That quantum of light energy was later named a photon.A few years later, in 1905, Einstein used Plancks idea to explain the photoelectric effect.I dont like that!That quantum of light energy seems particle-like!

In 1909 G.I. Taylor experimented with a very dim light source. His work, and many modern experiments show that even though only one photon passes through a double slit, over time, an interference pattern is still produced - one particle at a time.It would seem that the basic idea of the quantum theory is the impossibility of imagining an isolated quantity of energy without associating with it a certain frequency.=h/pLouis de Broglie, in 1923, reasoned that if light waves could behave like particles then particles should have a wavelength.Soon after, an experiment by C. J. Davisson and L. H. Germer showed that electrons could produce interference patterns just like those produced by light.n=2dsin

p=/hIf we know the wavelength we are certain about the momentum.But, because a wave is spread out in space, we are uncertain about its position.{If we add together many wavelengths...We are uncertain about the momentum.But, we are now more certain about position.{Heisenbergs Uncertainty Principle helps us examine the dual nature of light, electrons, and other particles.

Photons striking a double slit, one at a time, produce interference.If we observe which slit the photon choosesthe interference pattern disappears.A similar experiment can be done with beam splitters and mirrors.We can tell when someone is watching.

Eve may measure a classical signal without detection.We do not know how much Eve has learnt about the key!Eves measurements of a quantum signal causes perturbation and can be detected.When evolving freely, quantum systems exhibit wave character.When measured, quantum systems exhibit particle character.Measurements that acquire information perturb the quantum system.How can Alice and Bob know that their communications will remain private?Quantum KeysZUPMOS

Potential EnergyPositionPotential energy for a classical harmonic oscillator is continuous and can have a value of zero.Maxwell showed that oscillating electric charge produces an electromagnetic wave.Schrdinger's equation was published in 1926. The solution of this equation for a particular particle and the forces acting on that particle is called the wave function (). Quantized energy levelsUnlike the classic oscillator, this system has a minimum energy or zero-point energy. Zero-point energy

A vibrating rope between two fixed points can only produce standing waves that are a multiple of 1/2 .Because of the zero point energy even a complete vacuum is filled with waves of every wavelength but only certain wavelengths can exist between two closely spaced mirrors in the vacuum.In 1948 Hendrick Casimir predicted that these two mirrors would be pushed together because of the difference in energy.

diffraction still limits the size of objects we can resolve. The smallerthe object the shorter the wave-length required.Once you have designed optics to correct for aberrations caused by the lenses

Using Schrdinger's wave equation, can be calculated for electrons in the Coulombpotential of an atom. gives us the probability of finding an electron in a particular location.These calculations show discrete energy levels similar to the calculations for a harmonic oscillator.An electron is excited to a higher energy when a photon is absorbed and gives off a photon when it relaxes to a lower energy.An atom fluoresces when a short photon excites the atom and a longer photon is given off.

Labeling specific parts of the object with a substance that fluoresces helps bring out details in the image. A confocal microscope uses a point source (laser) to cause one small spot to fluoresce at a time. You create an image by scanning across the object.

Energy is pumped into the medium, exciting electrons to the metastable state.An electron drops to the ground state and produces a photon.That photon interacts with another excited electron causing it to drop.Meta-stable stateGround stateA second photon is produced by stimulated emission.Those photons reflect and continue to stimulate more photons.

If you have a very intense light, two photons can induce a single fluorescence.In single photon excitation, fluorescence is produced all along the path of the light. In two-photon excitation the light is only intense enough to produce fluorescence at the focal point.

Can we break the diffraction limit?Because of diffraction a molecule might look like this.But we would have a pretty good idea of its location.unless we can turn them on one molecule at a time.If we have many molecules in the same location we will not be able to resolve them

Eadweard Muybridge froze the motion of a horse in 1878 - a millisecond event.Harold Edgerton stopped a bullet at the microsecond time scale.If we wish to examine electrons we must take pictures at the attosecond level.One attosecond is to 1/2 second as 1/2 second is to the age of the universe.

The alternating electric field of laser beam can accelerate an electron out of an atom and then send it crashing back into the atom.The frequencies of light produced as the electron accelerates can interfere to produce a very short pulse of light.

These pulses of light, interfering with the electron itself, can tell you everything you can know about the electrons wave function.Now, movies of atoms moving and bonds breaking are possible.

Improved solar panelsImages that defy the diffraction limitUnderstanding the PhotonMolecular movies

Problem SetYoungs experiment is performed with blue-green light of wavelength 500 nm. If the slits are 120 mm apart, and the viewing screen is 5.40 m from the slits, how far apart are the bright fringes near the center of the interference pattern? 2.25 mmThe cosmic background radiation follows a black body curve. If the radiation peaks at a wavelength of 2.2 mm, what is our temperature? 2.6 K If the universe was 2970 K 379000 years after the big bang when the universe became transparent to electromagnetic radiation, what was the peak wavelength of the curve? 976 nmPhotoelectrons are ejected from the surface of sodium metal when illuminated. The stopping potential for the ejected electrons is 5.0 V, and the sodium work function is 2.2 eV. What is the wavelength of the incident light? 170 nmIf you double the kinetic energy of a nonrelativistic particle, what happens to its de Broglie wavelength? Cut by a factor of (1/2)0.5 What if you double its speed? Cut by a factor of 1/2 If we assume the suns emission rate is 3.9 X 1026 W and that all of its light has a single wavelength of 550 nm, at what rate does it emit photons? 1 X 1045 photons/sIn a tube television electrons are accelerated through a 25.0 kV potential difference. If they are nonrelativistic, what is their de Broglie wavelength? 7.75 pmHow far would a beam of light travel in 1 s? 900 m In 1 attosecond? 0.30 nm

8. Discuss M.C. Eschers print and its relationship to the dual nature of light and Heisenberg Uncertainty Principle.9. The Uncertainty in the position of an electron is 50 pm or about the radius of a hydrogen atom. What is the uncertainty in the measurement of the momentum for that electron? 2.1 X 10-21 kgm/s10. Starting with the idea that an electron is a wave, prove that En =n2h2/8mL2 for an electron trapped as a standing wave in a one-dimensional box. Assume the length of the box is L and that m is the mass of the electron (hint: use de Broglies equation and find momentum in terms of kinetic energy).What would be the smallest diameter object you might expect to resolve with a microscope if the wavelength of light being used is 500 nm, the index of refraction is 1.4 and the total angle seen by the lens is 5? 2 X 10-6 m = 2 mA pulsed laser emitting 694.4 nm light produces a 12 ps, 0.150 J pulse. What is the length of the pulse? 3.60 mm How many photons are emitted during each pulse? 5.24 X 1017 photons13. The diagram at the right shows the energy levels in a substance. What wavelength of light is required to excite the electron. 4.29 m What wavelength of light is emitted? 0.100 m

*The conference covered a wide range of topics centered on photons and their interaction with matter. I have selected ideas that I felt were most appropriate for a high school physics class and I have included background material that will help in explaining the phenomena. If you would like a more detailed discussion, the talks can be heard in their entirety at: http://online.itp.ucsb.edu/online/qcontrolt_c09/.*Newton did not specifically say that light had to be particles. He did describe many of the properties of light in terms of particles including refraction, and reflection. He did not see evidence for wave properties such as interference, and as in this quote, diffraction. This lead him to favor particles.Newtons reputation kept the physics community from seriously considering light as waves for about 100 years. It seems that very little research was done during that time to actually resolve the issue.*Young first experimented with a pin hole and sunlight and saw interference fringes. In 1816 Fresnel wrote a paper looking at light in terms of waves and predicting such effects as diffraction and interference. He was disappointed to hear that Young had already reported these effects. In 1818 the French Academys annual competition concerned diffraction and interference effects and hoped to obtain convincing evidence for a corpuscular theory. In response to the challenge Fresnel showed that the shadow behind a small sphere would have a bright spot at its center. Youngs original double slit experiment was done with double pin holes. The sketch of the production of the interference pattern was done by Young.This is a good time to get out the ripple tank if you have not already done so. I also like to demonstrate interference with microwaves and sound.*If light is a wave, then what is waving? In 1845 Faraday showed that light traveling through a thick piece of glass had its plane of polarization rotated by a magnetic field applied to the glass. This convinced Faraday that light was somehow related to electricity and magnetism. Faraday lacked the math skills needed to develop his theory of lines of force into a mathematical theory of electromagnetic waves. Maxwell went beyond the work of Faraday to present the new idea that an electric field that is changing in time must be accompanied by a magnetic field. It is not just currents in conductors that produce fields but changing electric fields in any medium, including empty space. Maxwell did not live to see the experimental verification of his theory by Hertz in 1888.

*In 1900 Lord Rayleigh and James Jeans realize, based on their understanding of Maxwells equations, that light energy in a blackbody should be distributed equally among all the wavelengths that will fit inside the black body. This assumption lead them to propose that most of the light should be short wavelengths - thus the ultraviolet catastrophe.To solve the problem Planck made the unprecedented (and ad hoc) move of making the energy of a wave related to its frequency and not its amplitude as in classical theory. He also stated that light was released in bundles of energy that Gilbert Lewis, in 1926, called a photon. Planck never liked the idea. He said, My futile attempts to fit the elementary quantum of action somehow into the classical theory continued for a number of years, and they cost me a great deal of effort.Hertz discovered the photoelectric effect in 1887. It was shown that the energy of the electrons emitted did not depend on the brightness of the light but the frequency. Taking a cue from Planck, Einstein used his idea of a light quantum to explain the effect and was later awarded the Nobel Prize for his work. Einstein and Planck seemed to bring us back to a particle nature for light. Another example that might be considered at this time is Compton Scattering.*G.I. Taylor, one of the most distinguished physical scientists of this century, used his deep insight and originality to increase our understanding of phenomena such as the turbulent flow of fluids. His interest in the science of fluid flow was not confined to theory; he was one of the early pioneers of aeronautics, and designed a new type of anchor that was inspired by his passion for sailing. His experiment with photons resulted in his first paper. It leads us to understand that even though one photon encounters the double slits, wave properties still appear, but are displayed in a particle fashion.Prince Louis De Broglies proposed the idea that particles can also be thought of as waves for his PhD thesis. It was a difficult sale and required the intervention of Einstein.By 1920 it was shown that crystals produce diffraction patterns if struck by x-rays. In 1923 de Broglies ideas were verified by experiments like that of Davisson and Germer who bombarded crystals with electrons and got similar patterns. It has been shown that experiments similar to Taylors can be done with electrons, giving the same results. The Young double slit experiment was first done with electrons by Claus Jonsson in 1961. His experiment was voted most beautiful by the readers of Physics World in 2002. In 1989 Akira Tonaomara did the experiment with one electron at a time.*So what is light, particle or wave? Heisenbergs idea lets us think about a particle as a sum of waves. The more you know about the particle properties, because it is a sum of waves, the less you know about its waviness and visa versa. It is sometimes instructive to have students add waves using a graphing calculator or computer graphing program. I often do this first when talking about beats in my unit on sound.*This can be discussed in terms of the Heisenberg Uncertainty principle. If you dont know the actual location of the photons they produce wave behavior but as soon as you know the location (one slit or the other) the particle properties appear and the interference pattern disappears. In the second set of diagrams each red lines represent one photon that arrives at a photo-detector. In the top diagram it is set up so that the waves destructively interfere for the top detector and constructively interfere for the bottom. In the lower diagram on the right, because you know which path the photon has followed it behaves like a particle and follows one of the two paths. Thus, you can tell if someone is eves dropping on the system by the output of the system. *One application of this quantum weirdness is in securing communications. Sending a secret communication involves transmission of a key that both Bob and Alice will have in common and can use to decode their messages (whats up and mother over shoulder). If the key is intercepted in the process of transmission then all of their messages can be decoded. If you are using a quantum signal to send the key then you will know if there has been eavesdropping because the signal will change much like in the last slide.*More quantum strangeness comes when we consider an harmonic oscillator. If you think of a spring in a classical sense, it can have zero spring potential energy when it stops vibrating. Erwin Schrdinger, in a attempt to explain the waves associated with the electron, developed his wave equation. Given the mass of the particle, and the forces to which it is subjected - the spring for the harmonic oscillator - Schrdinger's equation gives us all the associated waves and in turn, the possible energies. Applying the equation to the harmonic oscillator we find that there is a lowest possible energy or zero-point energy and that the system cant go below that energy. *The zero-point energy means that even in a vacuum there will be fluctuations in the fields. Casimir predicted that if you place two mirrors close together (nm) then only waves that can exist between the mirrors as standing waves will fit, where-as all waves can exist outside of the mirrors. This means that there will be a difference in energy between inside and outside of the mirrors that will cause the mirrors to be forced together. In 1997 S. K. Lamoreaux measured the force using a torsion balance. The effect was confirmed the following year by U. Mohideen and Anushree Roy, using an atomic force microscope similar to the diagram above.*We can apply what we know about light to help us build a better microscope. Chromic and spherical aberrations have been corrected in modern lens with coatings and combinations of lenses made out of materials with different indexes of refraction. After making those corrections you still need to deal with diffraction. Because of lights wave nature there is a limit to what an optical microscope can resolve. Ernst Abbe found that the limit for resolving an object because of diffraction was described by the formula shown above. A modern microscope, like the one pictured that uses fluorescence (see next slide), can not overcome this limit.

*To understand how fluorescence can be used to enhance an image we need to discuss the structure of an atom. Schrdinger's wave equation is used to describe the possible electron waves that can exist inside the Coulomb field of the atom, not unlike the allowed vibrations for an harmonic oscillator. Each allowed wave represents a different energy level the electron can occupy. In a hydrogen atom, as in any atom, the electron jumps between those levels give rise to the spectrum for that atom.Because of Heisenberg's Uncertainty relationship we cant know exactly where the electron will be but the square of the wave function tells us the probability of finding an electron in a particular location in the atom. These are probability spaces are the orbitals we have come to know from chemistry.In a fluorescent molecule a photon my excite an electron to a higher energy level, that electron relaxes to a slightly lower level, then drops back to the ground state giving off a lower energy photon. The color of the emitted light is characteristic of the substance fluorescing.*Hundreds of different fluorescent stains have been developed that can be used to label different parts of and object like a cell. The confocal microscope, invented by Marvin Minsky, takes this a step further. Light is focused to a particular point in the object being examined and a pinhole is used to eliminate all the light not coming from that point. An imaged is produced by scanning the object as in this view of pollen from a Lily of the Valley.Sectioning an object can be achieved by focusing at different depths. The last picture shows 12 different cross-sections of a pollen grain made by scanning an the pollen at different depths.

*Another development important to modern microscopes is the laser. Some energy levels inside the atom are metastable. Normally the average life time of an excited atom is about 10-8 s. In a metastable state the electrons may remain excited for 105 times longer before spontaneously emitting a photon. This allows time to get many atoms into a metastable state and create a population inversion where there are more excited atoms than ground state atoms.In 1917 Einstein introduced the concept of stimulated emission, meaning that a photon can stimulate another atom to emitt an identical photon. Laser is an acronym for light amplification by the stimulated emission of radiation.There is a mirror at each end of the laser. One mirror is close to 100% reflective, and the other allows a small amount of light to escape. As the photons bounce back and forth between the mirrors they are amplified by causing stimulated emissions from other atoms. Because of this process, all the photons in the light emitted have the same energy, phase, polarization, and direction of travel.*To improve the confocal microscope two-photon excitation is used. A laser is pulsed to provide a very intense beam of light with many photons. The photon energy is half the energy needed to excite the fluorescent molecule so two photons are needed to do the excitation. This can only happen because of the intensity of the beam. A disadvantage to the confocal microscope is the fact that the light tends to be dispersed as it travels through the object. This makes it hard to see deeper layers. Fluorescent markers also tend to bleach or fade under illumination. The two-photon method eliminates that problem because the beam is only intense enough to get excitation at the focal point so no other molecules fluoresce. This also eliminates the need for the pinhole because light only comes from the one point. Scanning gives you images such as these neurons.

*To break the diffraction limit described by Abbe we must go one step further. Diffraction will make a molecule look blurred out. Even so, we have a good idea where the molecule is. If you have many molecules in one small area it will be difficult to locate individual molecules. Chemical compounds have been developed that can be turned on and off. A laser activates them, giving them the ability to fluoresce. These molecules are attached to the structure of interest, are activated and then when excited tell us the location of that structure. The trick is to illuminate the sample with a very weak excitation beam so that only a few photons strike the sample at a time. In this way only one molecule fluoresces at a time and its location can be inferred. These marker bleach out quickly, turning the fluorescence off again.Using this technique we can use visible light to see things smaller then the typical 2 m diffraction limit for visible light. In these pictures we see fibers in a sample, first with a conventional microscope and then using this process. Different structures can be seen by using different labeling compounds.*Light can also be put to work to help us look at events that take place in very short time intervals. Muybridge was motivated to take photos of a running horse to settle the question of whether or not all four hoofs are off the ground at the same time. Edgerton became famous for his stop action photos, but if we wish to freeze the motion of atomic or subatomic particles we need to deal with attosecond flashes of light. It is fun to have students work out their own comparisons for the size of an attosecond.*One way to make these incredibly short pulses is to rock an electron back and forth inside an atom. If we are thinking of light as an electromagnetic wave, the alternating electric field of an intense laser beam can push an electron away from the nucleus and out of an atom and then as the field reverses, send the electron crashing back into the nucleus, much like a ball on a see-saw. The accelerating electron will produce a new electromagnetic wave. This wave will change frequency depending on where the electron is in its oscillation. If done properly all of these wavelengths will add up to make a very short pulse of light.*These very short pulses of light can then interfere with the wave that is the electron and tell you all about the electrons place in an atom or molecule. If this is done frame by frame movies of chemistry in action will soon be possible.*Where do we go from here? Measurements that are made routinely today were unimaginable even ten years ago. It is not unlikely that we will be watching molecular movies, that quantum noise will be applied to problems like creating better solar panels, and new techniques will be developed to look into an optical world we never thought possible.**