Lecture30 - Physics 344 Foundations of 21st Century...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: on x-ray diffraction in section 25.2 of M&I Volume II, 3rd edition or on pages 847-850 in M&I Volume II, 2nd edition. Exam 2: Thursday, December 1 at 8:00pm in ARMS B061
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x y z Single-Photon States To test any definition of a single-photon state of the electromagnetic field, we must be able to specify a way to create the state and, then, compare the outcomes we predict for experiments that detect the photon to what we observe. The first experiment using a truly single-photon source was conducted by Aspect and Grainger in 1986. The concept is simple, in that a single excited atom is the source of the single photon emitted when it decays. We’ll discuss how they met the practical challenge of singling that particular photon out from other electromagnetic field excitations present in experimental situations when we examine their experiment a little later. For now, we simply analyze the single-photon state produced by the decay of a single excited atom within our cavity We’ve focused on field states within a cavity because the field’s discrete spectrum (only angular frequencies ω n = n π /a are allowed) helps us understand and represent the states and because they are analogous to the discrete energy states of other quantum systems.
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x y z First, consider a collection of excited atoms near the center of a long cavity, long so that we don’t have to worry about emitted photons reflected back from the mirrors for until after we’ve made measurements on photons propagating away from the atoms. We imagine exciting the atoms at t = 0 and counting photons that arrive at a detector located well away from the atoms in the direction toward the mirror at x = a. What do you expect to observe? Based on our experience with decays of radioactive nuclei, we would expect to see an emission rate (activity) from the source that decays exponentially with time. Remember, the only thing we had to assume to understand this behavior was that the individual decays are independent of each other. This is, in fact, essentially what is observed with typical state half-life values of 10 -8 or 10 -9 seconds. These are short by everyday standards, but long compared to the roughly 10 -15 second optical oscillation period of the emitted radiation.
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A graph of the electric field amplitude of a classical pulse of radiation as a function of x within our cavity would look something like this, at a time t well after the atoms were excited at t = 0 but before the resulting pulse of radiation reaches mirrors at t r = a/2c and is reflected back toward the atoms. Note, the “high-frequency” optical oscillation period is not
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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue University.

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Lecture30 - Physics 344 Foundations of 21st Century...

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