Dr Igor Mekhov

Quantum optics of ultracold quantum gases: Studying the ultimate quantum limit of the light-matter interaction

Both quantum optics and many-body physics of the lowest achievable temperatures are very active fields of modern research. However, the interaction between them is far from being complete.

In the most theoretical and experimental works on ultracold atoms, the role of light is reduced to a classical tool for preparing intriguing atomic states. In contrast, the main goal of my research is to develop a theory of phenomena, where the quantum natures of both ultracold matter and light play equally important roles.

This research will close the gap between quantum optics and physics of ultracold quantum matter, considering the ultimate quantum regime of the light-matter interaction. The experiments on this regime became possible just several years ago, which makes the interaction between theory and experiment promising.

Open quantum systems beyond dissipation: quantum measurements and feedback

We have proved that the backaction of fundamentally quantum measurement constitutes a novel source of competitions in many-body systems.

We demonstrated the novel type of phase transitions beyond the dissipative ones: feedback-induced phase transitions (FPT).

We shifted the paradigm of feedback control from the quantum state control to the control of quantum phase transitions by tuning the universality class of phase transitions.

Phys. Rev. Lett.-1 (2015), Phys. Rev. Lett.-2 (2015), New J. Phys. (2015), Phys. Rev. A (2015), Atoms (2015), Scientific Reports (2016), New J. Phys.-1 (2016), Phys. Rev. A-1 (2016), Phys. Rev. A-2 (2016), Phys. Rev. A-3 (2016), Phys. Rev. A-4 (2016), arXiv:1601.02230, New J. Phys.-2 (2016), Optica (OSA) (2016), Scientific Reports (2017).

A REVIEW PAPER is available at Journ. Phys. B 45, 102001 (2012) (arXiv:1203.0552).

RECENT RESULTS:

• We show that applying feedback to a quantum system induces phase transitions beyond the dissipative ones: the feedback-induced phase transitions (FPT). Feedback enables controlling essentially quantum properties of the transition, i.e., tuning its universality class via the critical exponents. Feedback provides the non-Markovianity and nonlinearity to the hybrid quantum-classical system, and enables simulating effects similar to spin-bath problems and Floquet time crystals with tunable long-range (long-memory) interactions.

• We develop a concept of "quantum optical lattices," where the quantized light creates fully quantum and dynamical trapping potential for ultracold bosons and fermions.

• We have introduced the quantum measurement into a many-body system. We have shown that the quantum backaction of weak (non-projective) measurement can efficiently compete with unitary dynamics, thus, constituting a novel source of the competitions in many-body systems. This leads to a plethora of novel effects such as the giant oscillations at single quantum trajectories, long-range correlated pair tunneling, Raman-like virtual transitions in quantum Zeno subspaces, measurement-induced protection and break-up of fermion pairs, and measurement-induced antiferromagnetic orders.

• We have suggested quantum simulations based on the collective enhancement of light-matter interaction. We demonstrated the emergence of not only density orders (e.g., density waves and supersolids), but also the orders of matter-wave coherences (bond orders). This is well beyond predictions of standard Dicke and Bose-Hubbard models.