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The Blume research group works on various quantum mechanical aspects of atoms, molecules, and photons. Quantum mechanics has been around for over a century and many of its predictions, starting with the spectral lines of atoms, have been confirmed with incredible accuracy. Yet, we are still spending endless hours trying to wrap our heads around the fact that an electron can be simultaneously a particle and a wave and that, bizarrely, a measurement changes the state of the very thing that we are trying to get information about…

But quantum mechanics is much more than a fundamental science that continues to inspire philosophical discussions, which — depending on personality and setting — may tremendously enrich or, possibly more likely, kill just about any party. Quantum mechanics has revolutionized our daily lives: Without quantum mechanics, we wouldn’t have LEDs, we wouldn’t have laser pointers, we wouldn’t have flat screen TVs, we wouldn’t have transistors,… This list goes on and on. Yet, the best of quantum mechanics lies still ahead of us…

Common applications such as the laser pointer take advantage of “quantization”, a concept unique to quantum mechanics and absent in classical physics. While “quantization” and “probability” play a role in many every-day-life devices and appliances, there is another aspect of quantum mechanics, namely quantum entanglement, that has not yet been put to use, as least not so widely. Simply put, entanglement means that one can know something about one object (say an atom) by looking at a different object that may be residing at a different location. This can be thought of as the quantum state storing information or having knowledge — it is exactly this aspect that is not only intriguing but also immensely useful. The potential practical implications of these quantum correlations are enormous: One might be able to manipulate something without ever touching it. Entanglement, and a variety of related concepts, play a key role in what is frequently referred to as the “second quantum revolution”. This second quantum revolution, which is expected to harness quantum resources such as entanglement, is expected to impact humankind in a variety of ways: it is expected to significantly improve imaging techniques, thereby changing biology and medical diagnosis; it is expected to allow us to uncover mysteries surrounding dark matter and the early Universe; it is expected to play a pivotal role in measuring time and space ever more precisely, leading to notably improved navigation capabilities; it is expected to provide secure communication channels; and it is expected to yield enhanced sensing technology, revolutionizing weather forecasting, early detection of earthquakes, and mapping of natural resources.

The theoretical research conducted by Blume’s group aims at understanding entanglement and correlations from the bottom up. As part of this quest, we aim to develop insights into what governs the transition from few to many: How many particles or degrees of freedom are needed to predict the behaviors of large systems? And how does this depend on the nature of the interactions, the dimensionality, and the temperature? What effective descriptions work in which regimes? And why? Under which circumstances do effective coordinate descriptions, such as the use of hyperspherical coordinates, provide a fruitful avenue for analyzing the system dynamics? When can we replace the full quantum evolution by an effective master equation? Can we devise, in collaboration with experimentalists, protocols that take maximal advantage of the quantum resources in, e.g., interferometer sequences? Can we characterize and understand exotic quantum states and quantum matter? And how can these systems be probed?

The questions raised in the previous paragraph are broad and wide-ranging. The Blume group tends to develop theory applicable to cold atoms; often times, the atoms are cooled to the quantum degenerate regime where the statistical properties of the particles come to the fore. We perform scattering and bound state calculations. Many of these calculations use Fermi-Huang zero-range pseudo-potentials, which — in the simplest form — are just one-dimensional delta-functions that students learn about in undergraduate quantum (they are really useful!). We also probe the time evolution in response to gentle or violent perturbations, including quantum quenches. Where possible, we perform full quantum calculations using a variety of numerical techniques such as Monte Carlo techniques and exact diagonalization using, e.g., explicitly correlated Gaussian basis states. Frequently, we combine paper-and-pencil derivations with Mathematica numerics or high-performance computing. We are also interested in mean-field theory, master equation approaches, statistical quantum mechanics, atom-light interactions, photonics crystals, and much more.