...

11 October 2004: Exciting event of the day: my computer is finally set up and I figured out how to login to my laser account remotely! (ssh secure shell)...It's been exactly a month since I arrived in MA, although we spent two weeks getting 'oriented' to the H-way of life. I'm currently taking four courses: Mathematics (I'm learning about metric spaces and compact sets...immensely abstract but infinitely interesting - check out the course webpage here: Math 25a, Physics, Economic Models (which is watered down multivariable calculus) and French (the latter courses satisfy requirements). My plate of activities ranges from varsity fencing to the bach society orchestra, and I'm holding two jobs (that's two jobs more than I've held in my entire life!) - one in the science prep room and the other in the admissions office (sorry, I'm not making the major admissions decisions...). When I'm not occupied by this continual stream of activity, I'm in my dorm, Wigglesworth, G-32, a beautiful tri-story brick edifice (yes, it deserves that word) along Mass Ave. I have four fabulous roomates whose interests range from kendo to British historical fiction (there's even one who wanted to learn to play the violin her entire life!). In short, it's an eclectic mix and never will there be a shortage of conversation ammunition! I'm enjoying the freedom of the college lifestyle - over the weekend, I went to the Harvard Cornell football game (and was a part of the rallying tailgate!), played intramural ultimate frisbee for kicks, watched several movies with good friends, had scrumptious crumpets in Adams House (an upperclass dining hall that underclassmen are unable to eat in!) and accumulated an undeniably enormous amount of work for Monday night. THIS is college life (on the weekends) to the nth degree! On the weekdays, my day starts with a 7am run along the Charles in all its spledour, and rarely ends before 10 or 11 pm, at which point my brain has extracted all it can possibly hold for the day. It's a work hard, play hard environment that is encouraged greatly by the entryway system, which is simply a group of 6 to 10 rooms of first-year students who are advised together on matters of living. The environment has been much warmer and personal that I would have ever expected, mainly because I couldn't have anticipated the comforts of residential life. I'll be updating regularly here, because it feels more like my webpage than the new one...

On an interesting note: Prof Metcalf's notes on the prevalence of velocity dependent forces in college physics could have not been better confirmed by my experience here...see the problem sets: Physics 16.

21 July 2004: My magnetic moment seems to be off balance. Maybe it was something I ate...

16 July 2004: my last full day of being a kid.
cantaloupe + physics = loopy
Group, pronounced: groop
Cantaloupe, pronounced: canta*loop

15 July 2004: Ideas for Research -->

• Acousto Optical Modulator
• building a diode laser
• Fabry-Perot Interferometry
• Michelssohn Interferometers

14 July 2004: WHAT FRESHMAN SEMINAR TO TAKE? These are pass-fail, <12 student courses that are taken for interest in the field. I've narrowed it from 100ish to 50ish to 25ish (you get the idea) but these are all too yummy to pass up:

• Calculating Pi: focuses on the "mathematical, computational, and historical aspects of calculating pi...the participants modify and/or enhance existing C++ programs to implement algorithms for calculating pi or can use Mathematica...there will be a scope for a variet of interests and talents: people who enjoy reading Newton's or Euler's work in original form, or who excel at proofs, or who are skilled at user-interface or object-oriented programming, or who have a strong interest in the history of mathematics and the lives of great mathematicians..."
• Seeing By Spectroscopy (ohhhhhh!):
• The Simple Art of Murder
• Beethoven's String Quartets (specifically, Op. 18!)
• Mentality of Crime
• Undergraduate Physics Laboratory (REU type...)

13 July 2004: MANY TOURS (francium lab!)

12 July 2004: Interfering, counterpropagating beams with linear polarizations create a polarization gradient. Then where does circular polarization come in? The resounding answer seems to be in the "magneto" part of the MOT - the linear polarization persists until the cell...

• "Well, I may be vegetarian, but I don't eat glass..."
• My future dust is getting eutrophized by the sun~!

11 July 2004: AHHH...see dee to the backslash floppy and el s to see if it's...oh, of course, see P...(heard from lab @ 01:34am)...

11 July 2004: I was living at home this week and taught myself the Mendelssohn Violin Concerto - the last movement needs a bit more work on its velocity - yes, in terms of both its speed and direction. This past week in the lab was quite eventful...in particular, the talk given by Prof. Galvez, learning of an SPIE Meeting on Optical Tweezers, Prof. Metcalf's talk on MOTs, and Stony Brook's "how to get into graduate school lecture," to mention a few. Note that each of these events was accompanied by infinite quantities of fantastic food! I think that I should check off the "Recently Gained and/or Lost Large Amounts of Weight" box on my college health forms - moderation has no meaning to me when it comes to pleasures for the palate!

Overview of the Week (overview of theory I attempted to absorb):

• blackbodies, heat capacities, photoelectric effect, compton effect, atomic spectral wave/particulate nature of light, heinsenburg's uncertainty principle
• People: Schrodinger, Hamilton, Heinsenburg, Bohr
• Linear Motion: Potential Barriers, Tunneling, Particle in a box, two-dimensional square well, harmonic oscillator
• Rotational Motion: particle on a ring, particle on a sphere, atomic orbitals
• Operators:
• Angular Momentum:
• Atomic Spectra: Zeeman effect, Stark Effect
• (finish the list NOW)

An Overview of the Week (non-science aspects): Monday, 05 July 2004 was the observation of the Fourth of July (no lab). Tuesday, 06 July 2004 was the Laser Teaching Center's floor waxing day; the residual stench of the nasty chemicals was enough to keep me away from the lab all Tuesday and all Wednesday, 07 July 2004. Instead, we (Azure and myself) spent the better of the day reaping the benefits of our Student Activities Fees - or more specifically, at the SAC BBQ (Undergraduate IDs required! Ani tried to pass off as me!) getting picture perfect burgers, pickles and ice cream -- as well as on the world's most disjointed/cut-prone/crowd-esque line for spray painted t-shirts. At one point, the part of the line in front of me was getting wider and longer - and while this might have been a bad thing if we needed to get to class, it was quite helpful, as Azure was able to run to the computer lab and the LTC to get confirmation of: (at first, just) Maxwell's Equations, (and later) Schrodinger's Wave Equation, Kepler's Laws, Heisenburg's Uncertainty Equation, the Wave Equation...the list goes on. Too bad our plan for Schrodinger's Wave Equation and Cat were thwarted by an Earth Science Major scared of the greek letter psi (ψ - see! even I can write it in html!). Azure ended up with Heisenburg and I got Euler (initially with a terrible mistake, but fortunately, I was rescued from the fury of the mathematics gods by Dr. Noe). By the time the t-shirt business was over (and we were too sunburned and spray-paint-high to function properly!) it was time for Rita's talk about spatio-temporal chaos (in my state of delirum, I especially enjoyed watching the morphing movies!). Eventually, I got some MOT reading in at home. On Thursday, 08 July 2004 was the day Prof. Galvez visited, and talked about vortices, as well as (more to my personal interest) his experience with Optical Tweezers. Of particular interest was his comment an SPIE meeting on OT, August 2-6 -- I'd seriously sacrifice my wave function to go...On another exciting note, I received some much needed course advice from Alex Ellis for the upcoming semester. The golden formula is to take as many physics/math courses as possible because by then, they'll have abolished the accursed "core Curriculum" that waters down/prevents you from taking interesting, in-depth courses. Then again, knowing university bureaucracy, un-implementation of the core might not happen before the next ice age. In any case, we (Dr. Noé, Prof Koch, Prof. Metcalf, Prof Galvez, Alex Ellis, Azure, and myself) had a scrumptious dinner at Carnival. I ordered a platter of tubular pasta which turned out to be significatly larger than the lagest quantity of nanotube-esque pasta with eggplant I could have ever imagined. To write down all (or any!) of the amazing conversation topics would be too large for the server to handle, but all were physics related. [That makes me smile.] Friday, 09 July 2004 began with my fiasco at the doctor's office and getting too many shots in one arm...and nearly resulted in me missing Prof Metcalf's talk! In the end, I walked out of the doctor's office with a bill with too many digits to recont, four shots in my right arm, and a set of (finally!) completed health forms for college sports. I arrived at the lab to find my amazing peers had stalled the talk just for me (as well as the fact that you can die from meningitis within hours...this is a disease I got away with not being vaccinated through thirteen years of public school and six years of summer camp!). Anyway, the lecture was incredible --- it was was everything I had been reading about for the past four weeks in lay-physics-person's terms. I found his treatment of Phase Space Density really helpful - PSD is simply the six elements of V_x, V_y, V_z, S_x, S_y, S_z (position and velocity in three dimensions each that are changed by forces resulting from the Zeeman and Doppler shifts, respectively). I personally think that the best physicists can explain the most complicated theories to little children because truly understanding and knowing physics allows one to think, see, and explain clearly (remember the quick explanations of the bottle cap threads and projector interference?). Back to Friday: it ended with Azure and myself 'transporting' the AGEP wraps to the Keg Party in our spray-painted scientifc-hippie shirts.

More things Real Physicists Do:

• Spend Saturdays in the lab
• carry tupperware, toothbrushes, and silverware at all times
• Heat dinner (garlic pasta) in the nuclear structure laboratory
• Get excited by the prospect of seeing the Raisin Trap

Everyone always has 20/20 hindsight

A note on last week: I was in an optical vortex on friday, and got stuck in unaviodable optical molasses yesterday, and Tuesday was lost to the stink of the newly waxed floors. Since then, I've learned that MOTs are 'just apples' and Francium is just raisins.

01 July 2004: The earth is flat, waves travel through the aether, we are at the center of the universe, atoms are indivisible, blood-letting cures disease, and decelerating atoms cools them. You shouldn't believe everything in print, but...

page 83 of the 1999 Springer-Verlag edition of Laser Cooling and Trapping by H. J. Metcalf and P. van der Straten reads: "It is important to stress that deceleration is not the same as cooling: cooling requires a compression of the velocity distribution in phase space..."

Ouch...I've been working with that definition of laser cooling for weeks. What now?

More things I need to learn about:

• The optical Bloch equations: which are analogous to the Bloch equations for nuclear magnetic resonance (NMR!)
• The Stern Gerlach Magnet:
• The Faraday Effect (magneto-optical effect)
• The Fokker Planck Equation:
• The Ehrenfest Theorem: expectation value of an operator must correspond to the behavior of its classical counterpart (this seems to makes alot of sense - something like 'consistency in all reference frames')
• Fine Structure: splitting of states by spin orbit interaction
• Hyperfine Structure (HFS): usually smaller than fine structure because of smaller size of nuclear magnetic moment
• Sisyphus Cooling
• lin perp lin
• σ+ σ- Polarization Scheme
• Light pressure force = radiation pressure force = scattering force = dissipative force (I am clingling to my meager background in OT lingo!)
• Russel Saunders Notation
• Wigner Eckart Theorem
• Wave Functions/Hamiltonian/Lorentzian/
• Liouville Theorem
• Rydberg Atoms

More things I need to learn about that are not directly related to laser cooling:

• The partial electron - 1998 Nobel Prize
• Gyroscopes & theory
• Look up the deBye Lectures
• More about MAXWELL'S EQUATIONS!

On another note, while picking up garlic pizza and strawberries today, we saw a boat named "Boyd's Nest,' and learned from a rather unique periodic table at the farmstand that Fr = rasin, Rb = raspberry, and Be = blueberry. The streak of enlightenment continued through lunch: first, you tilt and maximize the path length of a carbonated beverage (from bottle to cup) to minimize the amount of foam; and second, the discontinuous bottle cap threads prevent pressurized drinks from exploding. Ah, the joys of receiving a well-rounded education in a physics lab! Interestingly, the bottle cap explanation came just as naturally as the projector remote control interference one. Prof. Metcalf claims that those are the simple joys of having a Ph. D. In that case, I have alot to learn.

The 'fortune' function seems to know me quite well. Tonight, it came up with:

You need more time, and you probably always will.

30 June 2004: Journal Sorting!

What I learned in today's lecture: light is a wave-icle (notice it is a wave-icle and not a par-ve)! No, really, Prof. Metcalf's lecture on QM and its development was quite Feynman-esque --- it presented QM concepts understandably. I must admit that I am an adrent fan of physics in its qualitative form - the ideas are neat, logical and organized. Though I'm pretty sure the ideas of the lecture were similar to those of last year, the ideas seemed to be saying something different today, most likely because I was listening with laser cooling in mind. So just for the record, as we 'sat there like lumps,' we heard about:

• Physicists like to do two things - measure zero and find symmetry
• Maxwell (Equations unite Electricity, Magnetism & Optics), Planck (blackbody radiation), Einstein (photoelectric effect), Rutherford (Au foil & α paticle experiment), Bohr (atomic orbital model), deBroglie (matter waves)
• Maxwell added displacement current to makes his equations 'work' <-- I'd like to know more about this....
• Prof. Metcalf went totally non-linear on this one: angluar momentum is a highly misleading name in suggesting both geometry and motion; more accurate is the French for a. m., cinetique...
• Translational Invariance (Δ P = 0) <-- Newton's Three Laws
• Time-Reversal Invariance (Δ E = 0)
• Rotational Invariance (Δ L = 0)

From the basic premises in a textbook, I derived c = 1 / √ ( ε₀ μ₀ ) --> never before had I dealt with Maxwell outside the context of multivariable calculus. It was nice feeling...

After doing so, I was directed to several sites w/javascript that I'll have to visit later on...including Prof. Sprouse's Physics Page and MasteringPhysics.com, for book 11e. Around ten, Azure started shining the 532nm (that's green, for those of you who dont 'speak' the EM spectrum...have you ever wondered why the HTML color codes weren't simply the wavelength or frequency of the color?!) on random materials, and found that the fluorescent glasses turned the green spot yellow. That wasn't at all unexpected, but when 532nm was directed through a red, translucent waterbottle, both images of the spot on the waterbottle were yellow and the image of the spot after the waterbottle was 532nm again. Strange.

29 June 2004: I was able to clarify many concepts through the Nobel lecture readings and discussions with other people (actually, force-feeding MOTs down the throats of many unsuspecting people!). Explaining (or at least, attempting to explain!) cooling theory to random (i. e., non-science) people - from one of my best friends (who has not taken physics...) to my guidance counselor (who seemed to express a genuine interest!) has taught me more than anything else I've been doing. Thus my petit lecture on laser cooling & trapping has evolved into the following:

This summer, I am not 'building a Magneto-Optical Trap' as I had previously thought - Magneto-Optical Trap is the name of the physical effect I am hoping to observe - I am studying laser cooling and trapping. Because atomic temperatures are directly related to the square of atomic velocities, cooling atoms involves physically decreasing atomic velocities. Thus, laser cooling involves a veolcity dependent force; that is, by using atomic transitions and the Doppler Effect, an 'atomic braking force' that increases with increasing atomic velocity is observed. More speficially, a laser's wavelength is detuned (shifted to the redder end of the EM spectrum) with respect to atomic resonance levels, so an atom will absorb photons that are traveling in the direction opposite to its own travel direction. This can happen because from the viewpoint of the atom, the START HERE moving towards a laser beam will absorb (and later, scatter) photons due to the Doppler is introtuduced: (etc etc)...However, there is a Doppler Limit a temperature at which the absorption/emission has been saturated by the availble quanta. More specifcally, the atom is too cold (or slow) to make use of the doppler shift in order to absorb photons. Consequently, the Zeeman effect is introduced (by the addition of a magnetic field) to split the atomic transitions, precluding the need for continuously blue-tuning the laser as the atoms cool. Trapping of atoms involves increasing atomic densities by

Things I still need to look up: (the list is getting LONGER as I work harder)

• Ioffe Pritchard Configuration
• Pondermotive Force
• the Time Orbiting Potential
• Stern-Gerlach Magnet
• Ramsey's Separated Oscillatory Fields
• Earnshaw's Theorem (optical version)
• Mechanisms of PZTs
• Majorana Transition
• Lamb Shift
• Optical Pumping
• Helmholtz coil: consists of two loops of wire with current flowing in the same sense that creates a uniform/homogenous magnetic field when the loops share an axis.
• Anti-Helmholtz Coil: the Helmholtz coil with one of the currents reversed, so an inhomogeneous magnetic field is created along the loop axis that ranges from the maximum near the coils and drops to zero exactly between the coils, creating a magnetic quadrupole.
• Rabi Physics
• Spin Echo
• Optical Lattices
• Spherical quaadrupole vs. quadrupole (any difference?)
• Circular polarization (of the orthogonal beams)
• Polarization and the Zeeman Effect
• Laser Modes: LG = TEM₀₀; HG;
• and last but not least... Sisyphus Cooling

I was up at six this morning (courtesy of my neighbors who decided to rev up their motorcycles ~2am...) and spend most of the day reading in my *new favorite spot* (hint: its the Stony Brook equivalent of Guam). Highlight: today was PayDay - never in my life have I earned that much money from working...

28 June 2004 : I've been updating several days worth of journals tonight...starting with my Zeeman questions from last week. There seems to be an endless amount of information available, and BEC making seems to involve almost every branch of physics (that I have yet to encounter formally in class!). Ah, the quote I got in fortune today seems to sum it all up quite nicely:

You single-handedly fought your way into this hopeless mess.

Let's just hope I can find my way out just as single-handedly! I'm stil holding fast to my outdoor reading philosophy - the air, the lighting, the breeze - but it seems too blissful a cure for my obstinate ignorance. Worse, the more I read, the less I know. Refer back to the quote for my sentiment on this topic...anyway, today's fare was largely a review of the 1997 and 2001 Nobel lectures (which I have yet to finish). On another note, the high school students arrived today for Simons...one REU seems very distressed by their arrival (points for guessing who!). Seminar today given by Tim Chupp of the University of Michigan/TRIMUF: "A Proposed Electric Dipole Moment Measurement with Radon." Some catch phrases from the EDM (electric dipole moment) lecture today): handedness = parity = chirality

• Baryon Asymmetry
• Higgs
• Super Symmetry (SUSY)
• Read more in Feynmann Lectures Vol.3
• Left-Right

Actually, what was really interesting was how the projector's remote control wasn't working - but when Prof. Metcalf turned off the lights, all was fine. The infrared radiation from the ceiling lights (!) were allegedly interfering with the infrared signal of the remote. I was quite impressed by how quickly and easily the physicists understood the "DON'T MOVE FOR A MINUTE, I'M TURNING ALL THE LIGHTS OFF!" to be the cause of projector remote failure!

More MOT Reading: From The National Physics Laboratory in the UK, the definition of a Magneto Optical Trap: The magneto-optical trap (MOT) consists of three orthogonal pairs of circularly polarized counter-propagating laser beams and an anti-Helmholtz magnetic field. Atoms are cooled down by exchange of momentum with the photons they absorb during their random motion. The lasers are detuned slightly from the resonance frequency to optimize both the absorption rate and the cooling. The magnetic field places in resonance the atoms which are moving away from the trap center with photons that are moving towards them. (In other words atoms interact more with the field that pushes them back into the trap than with the field that pushes them out.) Cooling is achieved because the atoms tend to acquire momentum (from the light field) that is directed opposite to their direction of travel, whereas they re-radiate the photons (with momentum) in a random direction. The number of trapped atoms and their temperature depends on several parameters including laser beam detuning and intensity. Typically a trap operates with up to 108 atoms in a cloud less than 1 mm in diameter and 1011 cm-3 density. Optical Molasses, unlike an MOT, is not strictly a trap. Here the atoms move in three orthogonal pairs of counter-propagating laser beams. The beams are most effective in cooling when linearly polarized such that the counter-propagating beams are orthogonal. The retarding force is proportional to velocity (a damping force) but there is no static magnetic field and no trap center. The atoms are slowed in the region of the beam overlap. Typically, a molasses contains ten times fewer atoms than an MOT for similar beam powers.

From what I know now, the Doppler shift provides for the velocity dependent 'braking force' that slows the atoms by discriminating through individual atomic speeds, while the Zeeman effect allows slowed atoms to continue being cooled by splitting the atomic transitions and allowing smaller quanta absorptions to further lower atomic speeds. However, this describes only a scheme for slowing atoms; the MOT allows the clumping of the slowed atoms. Using a position dependent force (which I have yet to fully understand...maybe after the actual coil design I'll get it) as generated by the magnetic field (will the Stark effect come into play here?!), atoms farther from the trap center (the intersection of the six laser beams) experience a greater restoring force into the center. From what I understand, there's a velocity dependent force to cool the atoms and a position dependent force to prevent them from scattering. Those two elements take care of the temperature part of the BEC idea, but how about adding a 'density dependent force'? One that will effectively 'clump' the atoms and increase the phase space density beyond 2.62 - and solve the problem too few atoms in the BEC. It seems that the MOT should be clumping the particles, but they simply prevent them from escaping...I feel that there should be a force that actually pulls atoms into the trap center based on atomic density. How that's to be accomplished...I am clueless as of yet.

I was quite happy to see this referenced in C. S. Adams and E. Riis' Laser Cooling and trapping of Neutral Atoms, Prog. Quant. Electr. 1997, Vol. 21, No. 1, pp. 12: "The principle of an optical dipole trap has its origins in the work by Ashkin on trapping and levitating transparent microscopic particles using light..."

More things to investigate:

• Helmholtz Coils:
• Circular Polarization:
• Spherical Quadrupole Magnetic Field:
• optical Earnshaw Theorem:
• The Stern-Gerlach Effect:

25 June 2004: Maxwell's Equations: Griffiths, David J. Introduction to Electrodynamics. Third Ed.; Pollack and Stump. Electromagnetism. 2002 Pearson Education Inc.

More on:

• The Stark Effect: the splitting of spectral lines observed when the radiating atoms, ions, or molecules are subjected to a strong electric field. The electric analogue of the Zeeman effect (i.e., the magnetic splitting of spectral lines), it was discovered by a German physicist, Johannes Stark (1913). Earlier experimenters had failed to maintain a strong electric field in conventional spectroscopic light sources because of the high electrical conductivity of luminous gases or vapors. Stark observed the hydrogen spectrum emitted just behind the perforated cathode in a positive-ray tube. With a second charged electrode parallel and close to this cathode, he was able to produce a strong electric field in a space of a few millimeters. At electric field intensities of 100,000 volts per centimeter, Stark observed with a spectroscope that the characteristic spectral lines, called Balmer lines, of hydrogen were split into a number of symmetrically spaced components, some of which were linearly polarized (vibrating in one plane) with the electric vector parallel to the lines of force, the remainder being polarized perpendicular to the direction of the field except when viewed along the field. This transverse Stark effect resembles in some respects the transverse Zeeman effect, but, because of its complexity, the Stark effect has relatively less value in the analysis of complicated spectra or of atomic structure. Historically, the satisfactory explanation of the Stark effect (1916) was one of the great triumphs of early quantum mechanics.
• The Zeeman Effect:the splitting of a spectral line into two or more components of slightly different frequency when the light source is placed in a magnetic field. It was first observed in 1896 by the Dutch physicist Pieter Zeeman as a broadening of the yellow D-lines of sodium in a flame held between strong magnetic poles. Later the broadening was found to be a distinct splitting of spectral lines into as many as 15 components. Zeeman's discovery earned him the 1902 Nobel Prize for Physics, which he shared with a former teacher, Hendrik Antoon Lorentz, another Dutch physicist. Lorentz, who had earlier developed a theory concerning the effect of magnetism on light, hypothesized that the oscillations of electrons inside an atom produce light and that a magnetic field would affect the oscillations and thereby the frequency of the light emitted. This theory was confirmed by Zeeman's research and later modified by quantum mechanics, according to which spectral lines of light are emitted when electrons change from one discrete energy level to another. Each of the levels, characterized by an angular momentum (quantity related to mass and spin), is split in a magnetic field into sub-states of equal energy. These sub-states of energy are revealed by the resulting patterns of spectral line components. The Zeeman effect has helped physicists determine the energy levels in atoms and identify them in terms of angular momenta. It also provides an effective means of studying atomic nuclei and such phenomena as electron paramagnetic resonance. In astronomy, the Zeeman effect is used in measuring the magnetic field of the Sun and of other stars.

Rubidium Facts 85Rb = 72.15% 87Rb = 27.855 Rb D2: 780.03nm Rb D1: 794.76nm

Things heard after our curry-less meal at the Curry Club:

• "...so some superior being must have sanctioned our taking of those signs..."
• "Would you buy a car with its hood welded shut?!"
• "We could say that you just had an "under the hood" experience...you're hired..."
• A notation of croque-ball. (pronounced like "croaky-ball")

24 June 2004: Conclusion: the best articles are the older ones. Good Sites: HowStuffWorks.com; HyperPhysics Site; Wikipedia;

• PZTs: Piezoelectric transducer/PbZrTi, or Lead Zirconate Titanates...the piezocermanic tube actuator operates by changing dimensions in response to an applied electric field. The magnitude of motion is proportional to the applied voltage. They also work in reverse; that is, the piezoelectric material generate charge when squeezed. In this case, the amplitude and frequency of the signal is directly proportional to START HERE
• The Zeeman Effect: an external magnetic field will exert a torque on a magnetic diople and the magnetic potential energy which results is

  U (θ) = - μ ⋅ B;

  in other words, in the presence of an external magnetic field, the state of an atom will have different energies due to having different orientations of the magnetic diloples in the external field. The net result is that the atomic energy levels are split into a larger number of levels (and consequently, the spectral lines also split). The pattern and amount of splitting are indicative of the presence and strength of an external magnetic field (respectively? I have yet to find this out). The splitting is associated with the orbital angular momentum quantum number L of the atomic level. This quantum number can take non-negative integer values and the number of split levels in the magnetic field is 2 L + 1. Remember that historically...

  s corresponds to L = 0 p corresponds to L = 1 d corresponds to L = 2 f corresponds to L = 3 g corresponds to L = 4

  It is common to precede the designation witht he integer principle quantum number n. So "2p" really corresponds to n = 2 and L = 1. In this example, the lowerst level is an "s" level, so L = 0 and 2 L + 1 = 1, so there is no splitting in the magnetic field. However, the first excited state is L = 1 (the "p" sublevel), so it is split into 2 L + 1 = 3 levels by the magnetic field. Here, a single transition is split into three transitions by the magnetic field. This is exactly why the Zeeman Effect is important to preserve the velocity-dependent force (The Doppler Effect) in laser cooling: by introducing a magnetic field into the system as Doppler Cooling runs its process, the transitions of 87Rb are split precisely to allow Doppler Cooling to persist as each atom is slowed, preventing early 'saturation' of the d-cooling. So the necessity of Zeeman is to prevent Doppler Cooling from stopping due to saturated transitions. I am not entirely sure of one aspect of the Zeeman Effect (more specifically, how it is integral to laser cooling processes) - the polarization effects. Polarization is related to the direction in which the electromagnetic fields are vibrating. This has an effect on whether the spectral light can be observed. I'll look more into this later.

• The "anomalous" Zeeman Effect: the magnetic field interacts with the electron spin magnetic moment and consequently contributes to the Zeeman Effect in many cases. Because electron spin had not been discovered at the time of Zeeman's original experiments, so the cases in which electron spin contributed were condsidered to be anomalous. In general, both orbital and spin moments are involved.
• The Stark Effect: the splitting of atomic spectral lines as a result of an externally applied electric field. This is NOT symemetric like the splitting of the Zeeman Effect. The splitting of the energy levels by an electric field first requires that the field polarize the atom and then interact with the resulting electric dipole moment. The Stark Effect has been of 'marginal' benefit in the analysis of atomic spectra, but a major tool in molecular rotational spectra (if I'm ever in need of 'light reading' on a rainy Saturday...)
• Fine Structure: (simple explanation) one of the first experiemtal evidences for electron spin, fine structure is the splitting of quantum levels of an atom when precisely observed (when the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely spaced doublets). This small splitting of the spectral line is attributed to an interaction between the electron spin S and the orgital angular momentum L, and is called the spin orbit interaction. (What is that?!)
• Spin Orbit Interaction: The energy levels of atomic electrons are affected by the interaction between the electron spin magnetic moment and the orbital angular momentum of the electron. It can be visualized as a magnetic field caused by the electron's orbital motion interacting with the spin magnetic moment. This effective magnetic field can be expressed in terms of the electron orbital angular momentum. The interaction energy is that of a magnetic dipole in a magnetic field and takes the form f(r) = S ⋅ L, where S is the Spin angular momentum and L is the Orbital angular momentum. When atomic spectral lines are split by the application of an external magnetic field, it is called the Zeeman effect. The spin-orbit interaction is also a magnetic interaction, but with the magnetic field generated by the orbital motion of an electron within the atom itself. It has been described as an "internal Zeeman effect."
• More on the Zeeman Effect: (from Websters) the widening and duplication, triplication, etc., of spectral lines when the radiations emanate in a strong magnetic field. First observed in 1896 by P. Zeeman, a Dutch physicist, it is now regarded as an important confirmation of the electromagnetic theory of light.

23 June 2004: MOT design - see below...

The more I learn about laser cooling, the more interesting the theoretical implications - and the more impressed I am with physicists in general. My favorite idea in all of physics (thus far) is the mechanism by which laser cooling is accomplished. The atoms must be cooled, and then clumped. Somewhere in there, there's a bit of physics. Cooling atoms involves decreasing their velocities, because temperature is related to the square of average atomic velocity. Hence, a velocity dependent force: an application of the Doppler Shift. The greater the velocity, the greater the retarding force. Once the atoms are slowed (i. e. cooled), they must be driven into a small area. Hence, the position dependent force: an application of the Zeeman Effect. The farther a cold atom is from its target position, the greater the force it will experience until it is in that precise position. At that point, all the cooled and congregated bosons will assume the same quantum state...and conquer the world! Well, not really. But the use of physical phenomena to basically "stick alot of little things into a little refrigerator" was genius. Absolute Genius.

Selected Lines: From the October 1990 issue of Physics Today, Claude Cohen-Tannoudji and William D. Phillips on New Mechanisms for Laser Cooling: "Another famous example of photon-atom interaction to control atoms is laser cooling. This technique relies on the resonant exchange of linear momentum between photons and atoms to control their external degrees of freedom and thus reduce their kinetic energy." From the 14 July 1995 Vol. 269 issue of Science Anderson, Ensher, Matthews, Wieman, and Cornell on Observation of a Bose-Einstein Condensation in a Dilute Atomic Vapor: "...the phenomenon of Bose-Einstein consensation requires a sample so cold that the thermal deBroglie wavelength, &lambda db, becomes larger than the mean spacing between particles. More precisely, the dimensionless phase-space density, &rhops - n(&lambdadb)3, must be greater than 2.612, where n is the number density. Fulfilling this stringent requirement has eluded physicists for decades. Certain well-known physical systems START HERE note: &lambda db = h/(2 &pi m k T)1/2, where

More things to be learned: (How to use "dict" and "fortune," that is!)

• General Question: why are atomic velocity distributions in the shape of a Maxwell-Boltzmann curve and NOT a Gaussian distribution? Are the two the same?
• Isotropic: invariant with respect to direction; having the same properties in all directions; more specifically, equally elastic in all directions
• Anisotropic: not invariant with respect to direction (NOT isotropic); specifically, "anisotropic crystals"
• ZOTs: the alter ego of MOT. go figure.
• Zeeman Shift:
• The Stark Effect:
• Phonons:
• Lamb Shift:
• PID: (NOT pelvic inflammatory disease, as I am perpetually reminded by my health teacher, but) the Proportional Integral Differential
• the AD 590: a battery-esque device that creates a current directly proportional to the Kelvin temperature of a system by using Fermi Levels... More Notes
• and other Heuristic Paradigms...

Papers I need:

• S. Chu, L. W. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985).
• S. Chu, M. Prentiss, A. Cable, J. Bjorkholm in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds., Springer-Verlag, Berlin (1987), p. 58.
• C. Wieman and S. Chu, eds., J. Opt Soc. Am B 6 (no. 11) (1989).
• E. Raab, M. Prentiss, A. Cable, S. Chu, D. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
• W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, D. E. Pritchard, ibid. 70, 2253 (1993).

Random things conversation snippets:

• "ahhh...can't wait for Fridays laser cooled keg..."
• {Prof. Metcalf's comment when I said that I wanted to make a BEC from scratch...me: after all, don't we have all the materials?} "...well, it's just like saying, here's some iron and steel, now go build a piano..."

22 June 2004: grad reh --> physics REU meeting --> van de graaff accelerator tour --> more MOT studies

I'm beginning to read repeats of the same information on laser cooling in different terms, just because of the sheer number of articles I've found in the past week. Some of these have made the principles incredibly clear...my favorites:

From Laser Cooling and Trapping of Neutral Atoms, 201-202: "...the atomic beam was to be slowed using the transfer of momentum that occurs when an atom absorbs a photon...am atomic beam with velocity v is irradiated by an opposing laser beam. For each photon that a ground-state atom absorbs, it is slowed by vrec = h &lambda / m (where &lambda is the wavelength of the light). In order to absorb again the atom must return to the ground state by emitting a photon. Photons are emitted in random directions, but with a symmetric average distribution, so their contribution to the atom's momentum averages to zero. The randomness results in a "heating" of the atom..." This clarifies my earlier questions on the randomness of the spontaneous emission. From Laser Cooling and Trapping of Neutral Atoms, 211: "The idea of magnetic trapping is that in a magnetic field, an atom with a magnetic moment will have quantum states whose magnetic or Zeeman energy increases with increasing field and states whose energy decreases, depending on the orientation of the moment compared to the field. The increasing energy states, or low-field seekers, can be trapped in a magnetic field configuration having a point where the magnitude of the field is a relative minimum...the requirement for stable trapping, besides the kinetic energy of the atom being low enough, is that the magnetic moment move adiabatically in the field. That is, the orientation of the magnetic moment with respect to the field should not change. From the proposal of Hansch and Schawlow: "A gas of atoms is irradiated from both sides by laser beams tuned slightly below the atomic resonance frequency. An atom moving toward the left sees that the laser beam opposing its motion is Doppler shifted towards the atomic resonance frequency. It sees that the laser beam directed along its motion is Doppler shifted further from its resonance. The atom therefore absorbs more strongly from the laser beam that opposes its motion, and it slows down. The same thing happens to an atom moving to the right, so all atoms are slowed by this arrangement of laser beams. With pairs of laser beams being added along the other coordinate axes, one obtains cooling in three dimensions. Because of the role of the Doppler Effect in the process, this is now called Doppler Cooling.

No matter how clear theory is at this point, the MOT seems to be far from reality. My goal for tomorrow is to design the MOT, no matter how fated for failure such a design would be - I am plenty acquainted with theory; unfortunately, if theory was the only necessary component to the project, we would have been done last week! The power supply for the diode's voltage regulator broke and has consequently stalled the actual implementation of sat spec (according to James and Rita).

21 June 2004: I started listing terms I want to clarify...currently, these terms include:

• Piezoelectric Transducer (PZT):
• Penning Trap
• Zeeman Effect:
• Side Locking:
• Peak Locking:
• Peltier Effect:
• Littrow Configuration: Hyperfine Structure: some kind of splitting of quantum spin

A Sampling of Journals I found in the Physics Library today:

• K. G. Libbrecht and J. L. Hall, "A low-noise high speed diode laser current controller," Rev. Sci. Instrum. 64 (8), 2133-2135 (1993).
• G. D. Rovera, G. Santarelli, and A. Clairon, "A diode laser system stablized on the cesium D₂ line," Rev. Sci. Instrum. 65 (5), 1502-1505 (1994).
• A. S. Arnold, J. S. Wilson and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69 (3), 1236-1239 (1998)
• Yukiko Shimizu and Hiroyuki Sasada, "Mechanical Force in Laser Cooling and Trapping," Am. J. Phys. 66 (11), 960-967(1998).
• Daryl Preston, "Doppler-free saturated absorption: Laser Spectroscopy," Am. J. Phys. 64 (11), 1432-1436 (1996).
• Paul Feng and Thad Walker, "Inexpensive diode laser microwave modulation for atom trapping," Am. J. Phys. 63, 905-908 (1995).
• K. B. MacAdam, A. Steinbach and C. Weiman, "A narrow-band tunable diode laser system with grating feedback and a satruated absorption spectrometer for Cs and Rb," Am. J. Phys. 60 (12) 1098-1111 (1992).
• M. H. Andersen, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995)
• Carl Wieman, Gwenn Flowers, and Sarah Gilbert, "Inexpenseive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63 (4), 317-330 (1995).
• Philip Gould, "Laser cooling of atoms to the Doppler limit," Am. J. Phys. 65 (11), 1120-1123 (1997).

18 June 2004: Saturated Absorption...(demystified!)

When a laser beam passes through an atomic vapor cell, and frequency of the laser matches an allowed transition between a ground state and excited state of the atom, a photon can be absorbed by the atom. However, laser excitation causes random thermal excitation of atoms (because temperature α average kinetic energy) that results in a Doppler Shift of both the absorbed and emitted radiation. This occurs because the frequency of the absorbed and re-emitted radiation is dependent on atomic velocities. Thus, atoms are said to be Doppler Broadened when they absorb and emit radiation at different frequencies. Doppler Broadening conceals the details in the atomic hyperfine structure (which comes from the interaction of the nuclear moments with electric and magnetic fields and field gradients produced by the orbiting electrons) whose transition are closely paced. However, Doppler Broadening can be overcome by performing pump-probe saturation measurements.

Hyperfine structure of an atom's absorption spectrum can be seen by using pump and probe beams. In pump-probe saturated absorption measurements, two counter propagating laser beams interact with the same atoms in the region where they intersect. The probe beam causes an atom to experience a set of transitions and the pump beam creates another set of transitions in the same atoms. Therefore, the field that reaches the detector is a function of both Doppler Broadened Peaks and Hyperfine structure.

The pump and probe beams are created by splitting a single beam from a diode laser into two separate beams by using a 5% retarding plate. The weak 5% beam is called the probe beam and is directly sent through the beam. This beam causes transitions in the atoms that create Doppler-broadened peaks. The pump beam is the more intense beam, 95% of the original beam. Instead of going directly through the cell like the probe beam, the pump beam is redirected using two flat gold-coated mirrors to where it is precisely counter-propagating with respect to the probe beam. The mirrors deflecting the pump beam are aligned so that the pump and probe beams intersect through the entire length of the cell. The pump beam changes the density of atoms in the lower levels having particular velocity v _z, and then raise them to a higher energy level where the probe beam again interacts with those same atoms and cause Doppler broadened saturated absorption with hyperfine structure.

In order for the atoms to undergo energy level transitions the frequency of the laser must be equivalent to the energy of the transition energy of the atoms.

In past experiments, researchers have been successful with saturated absorption of 133-Cs and detection of cesium's Doppler-broadened peaks with hyperfine structure. In the atom cooling and trapping experiment, the saturated absorption tunes and locks the lasers to the proper transition of 87Rb. The laser beams from both the pumping and repumping lasers are split for saturated absorption, and the resultant saturated absorption spectra allows the lasers to be visually tuned to the right transitions in 87Rb.

Trapping and Re-pumping: Trapping Rubidium is simply confining the Rubidium atoms to a small area. Before this can be accomplished, the Rubidium atoms must be cooled. In theory, cooling atoms is a simple matter - it implies a decrease in atomic velocity. The average velocities of atoms at room temperature are in the neighborhood of 102 to 103 m/s. To retard atomic motion, an external force opposite to atomic motion must be applied. Once the atoms are cooled, the force provided by the lasers ceases to be a strong opposing force. To keep the atoms from escaping the confined area, a non-homogeneous magnetic field and a position dependent force are introduced. When the atoms are cooled to a certain point (zero velocity), the atoms are no longer affected by the trapping laser (the atoms feel an equal force from each beam). During this time, however, the atoms are colliding with other atoms still present in the confinement area that causes the Rubidium to be kicked out of the confinement area. This dilemma can be solved by introducing a position dependent force. By making the force zero in the confinement area and allowing the magnitude of this restoring force to increase radially, the cooled atoms will be trapped in a small area.

Classic MOT systems utilize six beams: three beams from the laser and the retro-reflection of these 3 beams after passing through the confinement area. These beams cannot be reflected perfectly back into the laser, as doing so would harm the diode. To continue trapping the atoms, the design incorporates another laser that allows for atomic transitions from another state that is out of the range of the trapping laser. The trapping laser is tuned to the 5S (F=2) to the 5P3/2 (F��=3) transition, while the re-pumping laser is tuned to the transition that occurs every 1 out of every 1000 transitions: 5S (F= 1) to 5P3/2 (F��=2). The re-pumping laser prevents the atoms from being stuck in this state.

To keep the laser from wandering too far from the required wavelength, the trapping laser must be stable within a few megahertz. Additionally, because the number of atoms trapped is directly proportional to laser output, the laser output should be relatively high. Laser diodes are the best to use for this experiment because of its characteristic high output, low cost, and availability of wavelengths. Unfortunately, diodes have a single drawback - mode hopping. This occurs when one transition frequency overlaps another, i.e. the lasing mode of the frequency overlaps with another, and makes tuning very difficult, especially when attempting to lock the laser. The lack of a smooth transition between frequencies results in output jumps instead of an even background.

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On a non-research note...Dr. Noe took us out for sushi at Ichi's...maybe it's because it's only the beginning of the summer, or maybe it's because Sage and Allison aren't here...but I couldn't help noticing that lunch was very quiet! Between the six of us (Dr. Noe, Rita, James, Lidiya, Azure and myself), we covered every type of ice cream ( -, wasabi, ginger, green tea, green tea, and red bean, respectively). An improvement on last year: I enjoyed my first piece of eel, but didn't have enough courage for the tail. Maybe next year...

Post Lunch Antics - Dr. Noe, on an atom in a MOT: "It must feel very confined..."

17 June 2004: diode laser/MOT research day. I'm also interested in learning the specifics of Rb Spectroscopy. I think some of yesterday's ideas on sat spec were a bit muddled...the following is a summer of what I understand of BEC thus far...

Bose Einstein Condensation is the name for the behavior of bosons as they reach very low temperatures and begin to occupy the lowest quantum states; such behavior is impossible for fermions (note the Pauli exclusion principle!). To observe the 'quantum clustering' of bosons (a term I coined and felt descriptive of the cooling process), they must be cooled. One method for achieving temperatures low enough is called laser cooling.

Laser cooling utilizes laser beams to lower the temperature of a dilute atomic gas. Because the temperature of any material is a measure of the average kinetic energy of the atoms, we know from chemistry that

KE _(average) = 1/2 m v ² = 3/2 K T

To cool the gas, a velocity -dependent force must be applied to the atoms. Light can supply this force to the atoms in the form of photons for absorption. However, this can happen only if the photons carry a quanta of energy that corresponds exactly to an electron transition in the atoms; namely,

E = h f

f' = f^o (1 + v/c)

Once the atoms are cooled, they must by trapped so that they will not wander out of the vicinity of the cell due to the random collisions (I hear a call for optical tweezers!). Trapping requires a position-dependent (or restoring) force, and Zeeman splitting with polarized light is the phenomenon that allows for trapping of cooled atoms. Zeeman splitting states that when an atom is under a magnetic field B, the quantum energy levels of its electrons split:

Δ E = u m B,
where
u = Bohr Magneton
m = 1, 0, -1 (magnetic quantum number)
B = magnetic field

Because a circularly polarized photon has angular momentum, LH or RH polarization dictate the specific transition that it can make (either m = 1 or m = -1). Thus, if a magnetic field varies linearly as a function of distance from the center of the cell, x, then

B = A x

Before trapping two isotopes of Rubidium, it is evaporated from a source into a trapping cell. The apparatus is in a vacuum (on the order of 10^-9 Torr) because higher pressures allow for background gas. Background gas is unwanted because it presents an opportunity for collision increase of the cooled vapor. Additionally, some sources note that the collision rate between the background gas and the cooled gas is actually higher than the trapping rate.

This represents the amount of laser cooling info I was able to effectively absorb and process from gibberish into 'plain English' for today...more to come later.

16 June 2004: Today was quite productive, as I started researching sat spec and laser cooling. I'm finding that resources are infinite and more painfully, that time is finite. A chat with Rita was very helpful in clearing up some of the laser cooling basics in terms of theory. I'll have to work on experimental methods some more.

I gained alot from the chat: from what I know now, the 'sat spec' (or Saturated Spectroscopy) process involves maintaining the frequency of the diode laser constant. The wavelength of the laser light is the factor that determines the amount of energy per quanta imparted to the Rubidium atoms in each collision. Usually, a very specific frequency must be produced for absorption by the Rubidium; however, because there are two different isotopes of Rubidium in the cell and due to the temperature (or velocity) distribution of the Rubidium atoms within the cell, each atom will "see" a different wavelength of the laser dependent on its velocity. Consequently, a range of wavelengths can be absorbed. However, this range is hard to reach: the diode laser's wavelength is sensitive to small physical variants including factors like temperature fluctuation, convection currents in the air and vibrations of the optical breadboard. Thus, the process of sat spec seeks to feed the laser back into itself in the pursuit of a feedback loop that forces the diode laser's frequency to "lock."

I saw some of the pictures of Rabi dips (representing the transitions when the two isotopes of Rubidium absorb the laser light) on James' page and I'm still learning about each dip in the graph. The more I learn, the less I know.

The next step: designing and constructing a magneto optical trap.

Dr. Noe posted some pictures from last year: check them out here...and here

15 June 2004: Investigations of theoretical properties of BEC; overview of experimental approaches to BEC formation. I've been reading ALOT on BEC and this was a particularly helpful BEC Link. Something else I came across was this site: NASA/ISS Microgravity Site.

14 June 2004: Day ONE of REU Physics...more to come later!

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