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[1] 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[2].

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[3], and electronic quantum interferences[4].

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[5], identical to that observed in semiconductors after an ultrafast laser excitation. The quantum kinetics of BEC-generated clusters follows from the hyperbolic Bloch equations[5] which quantitatively explain[6] the first BEC experiment[7] with the strongest possible atom–atom interactions.

**References**

[1] M. Kira and S. W. Koch, Semiconductor Quantum Optics, (Cambridge University Press, 2011).

[2] 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).

[3] 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).

[4] 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).

[5] M. Kira, Hyperbolic Bloch equations: atom-cluster kinetics of an interacting Bose gas, Ann. Phys. **356**, 185 (2015).

[6] M. Kira, Coherent quantum depletion of an interacting atom condensate, Nat. Comm. **6**, 6624 (2015).

[7] P. Makotyn, C. Klauss, D. Goldberger, E. Cornell, and D. Jin, Universal dynamics of a degenerate unitary Bose gas, Nature Phys. **10**, 116 (2014).