Okay, my understanding on this topic has developed quite a bit this evening, and below are the posts I made documenting that development.
Skip to the bottom to see my most recent remarks on the topic.Post #1-
lbrits said:
With regards to your other question, I'm not sure what you mean by coherent state in this context.
I suppose I was referring to the definition as used in these articles,
http://en.wikipedia.org/wiki/Coherent_state
http://webphysics.davidson.edu/Projects/AnAntonelli/node46.html
It's not clear to me why we could ever assume that by shining light on an atom, the electron would assume a coherent state - unless what I said about it being a superposition of states corresponding to a certain energy is true - in which case I can see how one might tune the incident laser light to force a coherent state.
But then, why would this be at all useful in ionizing electrons? Perhaps it's not, but it's useful in controlling the location of the electron, should you wish to "videotape" it, as the authors of this paper are trying to do (referring to my original post).
I suppose I'm mostly confused on why coherent states are ever "useful" for anything. Sure, they correspond in some sense to classical harmonic oscillators - but in the world of quantum mechanics, where we don't think about trajectories, etc, and just probabilities and observables, how does this simplify things? I don't expect anyone to really answer these questions (they're mostly ramblings at this point), but they hint at the source of my confusion.
Post #2-
Okay, after a bit more online research (and a little thinking), I've compiled all of this into the example of the Hydrogen atom. Below I've restated some conclusions from the above posts, and what I've just learned about coherent states.
A Hydrogen atom contains a nucleus (proton) and a bound electron. The electron is in a stationary state, where its probability distribution does not evolve with time. This is because the electron is bound by the Coulomb potential, which gives rise to a number of discrete energy levels. Occupation of any of these energy levels corresponds to a stationary state.
If the electron absorbs a photon, its state will change depending on the energy of the absorbed photon. If the photon’s energy exactly corresponds to the distance to a higher allowed energy level of the electron, then there is a certain finite probability that the electron will jump to that higher energy state. If the photon’s energy is anything else, then the electron will assume a superposition of energy eigenstates. Certain (special) superpositions correspond to “coherent states.”
A free electron wave packet will spread out over time because the different momentum components move at different speeds. When an electron is in a coherent state, it is because the potential (in this case, the Coulomb potential) is somehow keeping the wave packet together, that is, keeping it a minimum uncertainty wave packet at all times. Physically, a coherent state is left unchanged by the particle’s detection. This is why it is experimentally useful.
Post #3-
An excerpt from the article of interest is given below, followed by at least one question I have from the text:
"...Further control of the electron dynamics requires that the creation and acceleration of the electron wave packets (EWPs) are decoupled; this is not possible using tunneling ionization since the same laser field governs both events. Decoupling can be achieved by using extreme UV (XUV) attosecond pulses to create temporally localized EWPs through single photon ionization at a well defined phase of a synchronized IR field which drives the dynamics from that point forward. These attosecond EWPs are distinctly different from their tunnel ionization counterparts. They are born at the center of the potential well with properties that are directly inherited from the XUV pulses, which can be tailored in time and frequency. They can also have a nonzero velocity, and their subsequent dynamics can be controlled by choosing the phase and amplitude of a synchronized IR field appropriately. In particular, the laser field needed to drive these EWPs back to the potential is usually weaker than the laser field needed to form tunnel EWPs, leading to much less distortion of the properties to be studied.
Here, we demonstrate an attosecond quantum stroboscope capable of capturing electron motion on a subfemtosecond time scale. This technique is based on a sequence of identical atttosecond pulses which are synchronized with an IR laser field. The pulse to pulse separation in the train is tailored to exactly match the optical cycle of the laser field, and the electron momentum distributions are detected with a velocity map imaging spectrometer (VMIS).
This technique has enabled us to image the coherent scattering of electrons that are driven back to the ion by the laser field following their ionization. We envision that coherent electron scattering from atoms, molecules, and surfaces captured by the attosecond quantum stroboscope will complement more traditional scattering techniques since it provides high temporal as well as spatial resolution."
-J. Mauritsson, et al, “Coherent Electron Scattering Captured by an Attosecond Quantum Stroboscope”, Physical Review Letters 100, 073003
Question: Any ideas on what might be meant by “coherent scattering” in this case? Am I to imagine that we are only interested in electrons that are “bounced” off of the ion-core and that exit the atom with energy equal to the XUV laser (i.e., coherent scattering)?
Post #4-
Further, here is an excerpt from a summary of the article in February 2008's edition of
Physical Review Focus:
"...The pulses in the train were just three hundred attoseconds (10-18 seconds) long. The researchers synchronized the pulse train with the oscillations of a relatively weak infrared laser, so that their cloud of helium atoms received a strong, ionizing "kick" at a precise time during each laser cycle. Each attosecond pulse released a few electrons, some of which were thrown back against their atoms before being pushed sideways and detected."
The question here is:
what is important about throwing the electron back against the atom before it is whisked away for detection?Post #5, Final-
My interpretation of the excerpt shown above:
1. A weak IR-frequency laser is shown on a cloud of atoms. This causes the electrons to "wiggle" back and forth in the direction of the laser's E-field at at the laser's frequency, but is not enough to ionize the atoms or excite the atoms to higher states.
2. A train of evenly-spaced XUV attosecond laser pulses are directed at the cloud of atoms.
3. The pulse-spacing is matched to the frequency of the IR laser so that an electron in a given atom will be ionized (via single photon ionization) at a crest or trough of the E-field oscillation.
4. Depending on the timing in part (3), the electron will be driven back through the ion-core and towards a detector.
5. The electron's initial momentum after being ionized is well-defined and based on parameters of the XUV laser, and the electron's momentum is also recorded on a detector after ejection from the atom.
Anything seem wrong or missing in that analysis?
