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22 The PCB Design Magazine • June 2016 avoid having a termination point inboard on the BGA (attempt to keep the connections lim- ited to the first two rows). And if you are truly pressed for real estate, consider a blind via ap- proach. Shaughnessy: When do we "hit the wall" with tol- erances? At what point is the piece just not manu- facturable? Thompson: Another great question. I used to say we have hit the mechanical wall at .0059" drill sizes and .003" traces and spaces. I have to amend that now to whatever you can reason- ably process at fab. If you can deal with .002" traces and spaces, this would allow for two tracks between BGA pads. This is good. Like- wise, previously when we said .0059" was the mechanical "wall," we see some folks are going down to .003" and .002" holes! I think if geom- etry dictates smaller holes and features, fabrica- tors must find a way to make that happen. Shaughnessy: Thanks for the good info, Mark. Thompson: My pleasure, Andy. PCBDESIGN FROM THE CAM SHOP: TIGHT TOLERANCE DESIGN TIPS The universe has been forget- ting its own initial state since the Big Bang, a fact linked to the unrelenting forward march of time. Systems that forget where they started are said to have thermalized, since it is often— but not always—an exchange of heat and energy with some other system that causes the memory loss. The opposite case is localization, where in - formation about the initial arrangement sticks around. Such a situation is rare, like an ice cube that never melts, but one example is Anderson lo- calization, in which particles or waves in a crystal are trapped near impurities. Now, researchers working with JQI and QuICS Fellow Christopher Monroe have directly observed this localization in a system of 10 interacting ions, trapped and zapped by electric fields and lasers. Their findings were published June 6 in Nature Physics. "The transition of quantum systems from ther - malized to localized represents a boundary be- tween states governed at long times by quantum mechanics and ones that follow classical physics," says Jake Smith, a graduate student at JQI and the first author of the pa - per. "It's important to know if a given quantum system will thermalize be- cause if it does you can use techniques from classical physics to pre- dict its long-time behavior." By focusing a powerful laser to a diameter of just over a micron, the team also applied a ran- dom shift to the magnetic environment of each spin, creating the necessary disorder. Then, they tuned the strength of the interactions relative to the size of this disorder and traced the emergence of localization. They performed many experiments with random amounts of disorder, preparing each spin to point either up or down and then measur - ing all of the spins after a certain amount of time to see where they pointed. "This work is a major advance in quantum sim- ulation as our platform can be scaled to dozens of ions, where detailed modeling becomes impossi- ble due to the complexity of many-body quantum states," Smith says. Disorder Grants a Memory to Quantum Spins

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