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Phon(t)on-induced phase transitions

Periodic Reporting for period 4 - Phonton (Phon(t)on-induced phase transitions)

Reporting period: 2020-03-01 to 2021-08-31

One of our dreams for the future is to control and manipulate complex materials and devices at will.
This progress would revolutionize technology and influence many aspects of our everyday life. A
promising direction is the control of material properties by electromagnetic radiation leading to photo-
induced phase transitions. An example of such a transition is the reported dynamically induced
superconductivity via a laser pulse. Whereas the theoretical description of the coupling of fermions to
bosonic modes in equilibrium has seen enormous progress and explains highly non-trivial phenomena
as the phonon-induced superconductivity, driven systems pose many puzzles. In addition to the
inherent time-dependence of the external driving field, a multitude of possible excitation and
relaxation mechanisms challenge the theoretical understanding. Recently in the field of quantum
optics, a much cleaner realization of a photo-induced phase transition, the Dicke transition, has been
observed for bosonic quantum gases loaded in an optical cavity. Above a critical pump strength of an
external laser field, the ensemble undergoes a transition to an ordered phase.
We aim to advance the general theoretical understanding of photo-induced phase transitions both in
the field of solid state physics and quantum optics. In particular, we will focus on the design and
investigation of photo-induced transitions to unconventional superconductivity and non-trivial
topological phases. Our insights will be applied to fermonic quantum gases in optical cavities and solid
state materials. In order to treat these systems efficiently, we will develop new variants of the
numerical density matrix renormalization group (or also called matrix product state) methods and
combine these with analytical approaches.
So far, we have proposed an experimentally realistic setup in order to dynamically generate and stabilize non-trivial topological states. This setup uses a quantum gas coupled in a novel way to an optical resonator. By the novel coupling a cavity-assisted movement of the atoms occurs which leads to the topologically non-trivial phases. The topologically non-trivial state is stabilized by the dissipative attractor dynamics due to cavity losses.
Further, we design a setup which would enable the dynamic generation of superconducting and charge density wave states and quantum devices which filter different kinds of particles.
We find interesting dynamics, e.g. critical dynamics or aging, in dissipative systems signaled by two-time correlations functions.
We have developed several novel methods which can treat the coupling of a bosonic mode (photons or phonons) to an interacting many body system (atoms or electrons). In particular, we devised a novel numerical method based on the matrix product states which has proven to be efficient in treating these complex hybrid systems.
We expect that we will design ways in order to generate and control dynamically complex states, such as unconventional superconductivity. We plan to investigate the dynamics and the stabilization of these states following different schemes of control.
These might be used in order to design materials with dynamically controllable functionalities which could lead to technical applications.