Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum optics of ultracold quantum gases: open systems beyond
  dissipation (habilitation thesis)   Quantum optics and ultracold gases are established fields, but they almost do
not overlap: the quantum nature of light is typically neglected in works on
ultracold atoms. In our work the quantumness of both light and ultracold matter
plays a key role. First, we show that light is a quantum nondemolition (QND)
probe of many-body phases: they can be distinguished by correlations and full
distribution functions (we consider bosons, fermions, and dipolar molecules).
Light is not only sensitive to densities, but also to the matter-field
interference. Second, we prove that the measurement backaction constitutes a
novel source of competitions in many-body systems, especially, for non-QND
cases. This leads to a plethora of new phenomena: oscillations of multipartite
entangled modes, protection and break-up of fermion pairs, antiferromagnetic
orders, long-range pair tunnelling and entanglement beyond Hubbard models. We
prove that feedback control induces phase transitions and tunes their
universality class. Third, the quantization of trapping potential (quantum
optical lattices) leads to novel phases, including both density orders
(supersolids, density waves) and bond orders of matter fields (superfluid and
supersolid dimers, trimers). Results beyond ultracold atoms include: We extend
the paradigm of feedback control from the state control to control of phase
transitions. We present the measurement backaction as a novel source of
competitions in many-body physics. We merge quantum Zeno dynamics and
non-Hermitian physics and show a novel type of Zeno phenomena with Raman
transitions beyond Zeno dynamics. We propose quantum simulators based on
collective light-matter interaction. Our models can be applied to arrays of
other systems (qubits). In general, quantum measurements and feedback produce
new phenomena untypical to both closed unitary systems and open dissipative
ones in many-body physics.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex