Black Holes and Blackboards: What Theory Research Looks Like

Using math to understand how the universe works has always excited me beyond measure. Before coming to UCSB, however, I had absolutely no idea what research in theoretical astrophysics actually looks like. Would my days consist of aimlessly scribbling equations? Would I spend my time reading stacks of dense papers? Would my hair somehow turn white and disheveled like Doc Brown’s from Back to the Future? As it turns out, some of these are closer to the truth than others. Here is what I actually do as a theoretical astrophysicist studying simulations of black hole accretion disks in Professor Omer Blaes’s Accretion Group.

In “The Lab”

Being a theorist means that my “lab” is pretty much anywhere that grants access to a laptop and plenty of hot coffee. In other words, I essentially wake up already “in the lab”. My day typically begins with a review of the work I did the night before, which means flipping through my notebook and going through whatever code I wrote the previous day. If I have the time, I also make my way through some of the recent literature and write down any technical questions for my advisor.

Next Step: Collaboration

The lack of physical lab space means that in order for me and my advisor to collaborate, we have to specifically set aside time to spend in front of the blackboard discussing the physics and working through problems and questions. These meetings are usually the second portion of my typical research day, and they are possibly the most important.

Our meetings usually have the following progression:

  1. Discuss plots and figures generated from the code since our last discussion
  2. Further develop the context of these problems and explore next steps
  3. Decide what trends we want to investigate more deeply
  4. Address any questions I have about the project/literature

During the meeting, I am always sure to jot equations or vocabulary that I want to explore on my own when I revisit the literature later.

Coding and Calculation

“The Lab”

This aspect of my research is both the most challenging and the most rewarding. After meeting with my advisor, I usually take time to reflect on the ideas we discussed and write details in my notebook. I may even consult the literature again to fill in any gaps in my knowledge or to revisit a concept we discussed. Additionally, I spend time deriving any relevant equations to get a deeper feel for the mathematics, and I begin to work on the code.

The main function of these codes is to calculate and graph solutions to the derived equations. This is the real “meat and potatoes” of my research: deriving equations and then finding the proper way to visualize their solutions so that they reveal the relationships we want to investigate. I then document the method I used to generate these graphs, and I make a note of any issues or difficulties I encounter along the way.

Summary

Although most people immediately associate research with working in a lab, research in theory heavily reflects all of the methodology and collaboration one expects to find in an experimental setting. This unique dynamic is actually one of the things that draws me to theoretical physics: the semisweet balance of independence and collaboration. Although the days vary greatly – sometimes with much more time spent meeting with colleagues, and others spent buried in the literature – I learn more about the universe every single day. That is ultimately what I think makes research so great.

EUREKA  Posted by 30 Jul 2019 / 0 comments

Wait a minute… Don’t Lasers Heat Things Up? A Laser Cooling Primer for the Uninitiated

Classical mechanics is the study of macroscopic objects and how they react to forces, and it works well. Really well. But when it comes to small particles, the same rules don’t apply. Quantum mechanics is the underlying theory that all particles can behave like waves, and vice versa.

We can’t see quantum effects in our day to day lives because things are too hot and heavy. Even though all particles behave likes waves, the amalgamation of the sheer number of them that it takes to make anything macroscopic cancels out any ambiguity. To see the effects of quantum theory in the lab, we have to cool lithium atoms down to just microKelvin away from absolute zero and pack them all together, where they will begin to show quantum interactions.

Unfortunately, I can’t buy ultra-cold lithium at Costco (you need a gold membership), so how do we make it ourselves? Cue the lasers. Laser cooling takes advantage of the interaction between atoms and light to slow them down. Since temperature is a measure of average kinetic energy, they are now ‘colder’.

“I hate to break it to you Max, but you’ve really lost it this time. We’re talking about lasers here. LASERS. Lasers heat things up. I saw this video of a laser blowing up a balloon.”

Ok fine. You got me. I saw that video too and it’s cool. Lasers usually heat things up. They are good at doing this because of how tightly packed the energy in a laser beam is. To put it in perspective, the average person probably puts out about 250 Watts while running. A horsepower is almost 800 Watts, and engines can put out many hundreds of horsepower. So, it may be a bit of a shock that even a 0.2 Watt laser beam is actually pretty powerful, sometimes even enough to permanently blind you. Yikes. Even with less than 1/1000th of the power that you can put out just by running, a laser can do some serious damage.

This is partially due to the fact that laser light is coherent, effectively meaning it is all the same color. However, this combination of homogeneity and power ‘density’ actually also makes it perfect to cool atoms down. But how do you do it?

The answer is very clever: using the doppler shift. Most people have experienced an ambulance siren dramatically changing pitch as soon as it passes you. This is because the motion of the car changes the spacing of the sound waves travelling towards you, and so they hit your ear more or less frequently if the car is moving towards or away from you, respectively. We interpret this increased or decreased frequency as a change in pitch. Atoms ‘see’ light in exactly the same way. Light also has wavelike properties, and the motion of the atom will change the perceived frequency of the light depending on its velocity (see picture).

Another important piece of the puzzle that we need to use is the fact that a given atom can absorb or emit light only at specific frequencies. This is another quantum phenomenon, and although it is strange, it is true. A frequency of light corresponds to a color, so think of these specific frequencies as a specific color of light. For lithium, it is 671 nm, which is a deep red.

We’ve got the ingredients. How do we get the cool? Well, throw out your Ray-Bans. Imagine sending out light that has a frequency that is a little less than the one we need for the transition. If we send this beam into a cloud of gaseous atoms, then only the atoms that are moving towards the beam will see an increase in frequency, and therefore the right color light for the transition. The other atoms will see frequencies that are too low.

Even though photons do not have any mass, they do have momentum. When the atom moving towards the photon absorbs it, it gets a kick back in the opposite direction, and it is now slower! Over many cycles, we kick more and more of the atoms until they are cool enough to confine.

Although this is only the first step of many to get temperatures that are low enough to explore quantum interactions, it is amazing that massless light can cool atoms with real mass. Under the right conditions, lasers aren’t just a way to pop balloons and remove tattoos that you thought you wouldn’t regret.

EUREKA  Posted by 25 Oct 2018 / 0 comments

Guiding Waves

Photonic devices are the future of data transfer. Compared to conventional electronics, photonics offer the advantages of being lower power, and having a longer range and larger bandwidth. Fiber optics transmit data over vast distances with minimal loss. However, when it’s time to connect the cable to a waveguide, there are significant losses. As much as 90% of the energy put into the cable is lost at the connection point. I’m working on simulating this coupling loss at the fiber-waveguide interface.  Using specialized software, I’m designing a tapered waveguide which will focus more of the energy to and from the optical fiber. It requires a huge amount of energy to process all the data being generated by the internet. We can therefore cut down on the internet electricity usage by designing more efficient waveguides.

Waveguides are used to guide an electromagnetic wave over short distances where it will be modulated and converted from a light signal to a purely electrical one. My task is to use a CAD software called RSoft BeamPROP to design a waveguide structure that would minimize losses. Photonic design is basically applied physics; in order to efficiently construct and test the design, knowledge of classical electromagnetic theory is essential. To understand how the allowed energy states of the structure form, Maxwell’s equations must be matched along the boundary of the material. The solutions to Maxwell’s equations in waveguides are analogous to the quantum mechanical solutions to the finite-square-well.

Many undergraduate researchers that I know work on simulations. Simulations are very important because they allow scientists to better visualize the structure they are looking at and work out any design flaws before the device is fabricated. Manufacturing devices can be very expensive; a single wafer of certain semiconductors materials can cost up to $10000. BeamPROP uses solutions to Maxwell’s equations to model an electromagnetic wave propagating through different materials. By simply defining the structure geometry and specifying its index of refraction, the software can predict which solutions are permitted.

If anyone is interested in doing simulation work related to waveguides, I have a few suggestions. If you have time to read and comprehend how the physics simulation is programmed, you will vastly increase your efficiency. The greatest difficulty I faced was trying to understand where the software went wrong when it gave me a solution that didn’t make sense. By understanding the machinery behind the program, you can much better tailor your simulation to work with the software rather than against it. It will also give you a greater appreciation of how the physical principles of electromagnetism are coded into the program. Simulation software isn’t perfect. My PI has noticed that many people will place overconfidence in the software. This is why one must never turn off their intuition when performing simulations. Just because the software outputs a certain value, it doesn’t mean it is physical. A good way to reason out which solutions are legitimate is to run the same simulation using two different pieces of software. Until both are in agreement, it’s safe to assume that one or both programs aren’t giving you physical solutions.

References:

https://www.oc2me.com/products/rf-solutions/microwave-waveguides/

AIM  Posted by 30 Aug 2018 / 0 comments