I will briefly overview a many-body theory that can rigorously identify particle clusters participating in diverse quantum processes. Using atomic Bose–Einstein condensates (BECs) and semiconductors as examples, I will explicitly show why such a capability offers lucrative perspectives for future experiments.
In semiconductors, this development has evolved to quantum spectroscopy which utilizes quantum fluctuations of light to select a desired quantum process among multiple excitation paths. I will demonstrate this concept through the recent experimental discovery of a dropleton.
Semiconductor experiments with extremely strong terahertz (THz) pulses can change electron’s potential landscape by 1 eV over a 1 A distance. Using the cluster identification, I will explain ° how THz experiments can access delicate quantum processes such as high-harmonic generation, dynamical Bloch oscillations, and electronic quantum interferences.
When atom–atom interactions become strong enough, a process called quantum depletion can eject BEC atoms to noncondensed ones. I will explain why the quantum depletion generates a sequential build up of clusters, identical to that observed in semiconductors after an ultrafast laser excitation. The quantum kinetics of BEC-generated clusters follows from the hyperbolic Bloch equations which quantitatively explain the first BEC experiment with the strongest possible atom–atom interactions.
 M. Kira and S. W. Koch, Semiconductor Quantum Optics, (Cambridge University Press, 2011).
 A.E. Almand-Hunter, H. Li, S.T. Cundiff, M. Mootz, M. Kira, and S.W. Koch, Quantum droplets of electrons and holes, Nature 506, 471 (2014).
 O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S.W. Koch, and R. Huber, Sub-cycle control of terahertz high- harmonic generation by dynamical Bloch oscillations, Nat. Photon. 8, 119 (2014).
 M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S.W. Koch, M. Kira, and R. Huber, Real-time observation of interfering crystal electrons in high-harmonic generation, Nature 523, 572 (2015).
 M. Kira, Hyperbolic Bloch equations: atom-cluster kinetics of an interacting Bose gas, Ann. Phys. 356, 185 (2015).
 M. Kira, Coherent quantum depletion of an interacting atom condensate, Nat. Comm. 6, 6624 (2015).
 P. Makotyn, C. Klauss, D. Goldberger, E. Cornell, and D. Jin, Universal dynamics of a degenerate unitary Bose gas, Nature Phys. 10, 116 (2014).