Anna Kowalewska-Kudlaszyk

In this work, we investigate the influence of the internal interactions within the nonlinear oscillatory system on its ability to lead to the violation of the Leggett-Garg inequality when performing a set of projective measurements. We emphasize the crucial role in selecting an appropriate time interval between the consecutive projections and show that, for some types of internal interactions that effectively confine the system's dynamics to only a few states, there are entire ranges of parameters characterizing the system for which the inequality cannot be violated.

We investigate the hierarchy of quantum correlations in a quadratic bosonic parity-time-symmetric system (PTSS) featuring distinct dissipation and amplification channels. The hierarchy includes global nonclassicality, entanglement, asymmetric quantum steering, and Bell nonlocality. We elucidate the interplay between the system physical nonlinearity (which serves as a source of quantumness) and the specific dynamics of bosonic PTSSs, which are qualitatively influenced by their damping and amplification characteristics. Using a set of quantifiers (including local and global nonclassicality depths, negativity, steering parameters, and the Bell parameter) we demonstrate that the standard PTSS typically exhibits weaker quantumness than its counterparts affected solely by damping or solely by amplification. Both the maximum values attained by these quantifiers and the speed and duration of their generation are generally lower in the standard PTSS. A comparative analysis of three two-mode PTSSs (standard, passive, and active) with identical eigenvectors and real parts of eigenfrequencies, but differing in their damping and amplification strengths, reveals the crucial role of quantum fluctuations associated with gain and loss. Among them, the passive PTSS yields the most strongly nonclassical states. Nevertheless, under suitable conditions, the standard PTSS can also generate highly nonclassical states. The supremacy of the passive PTSS is further supported by its fundamental advantages in practical realizations.

Jan Perina Jr, Adam Miranowicz, Grzegorz Chimczak, and Anna Kowalewska-Kudlaszyk, Quantum 6, 883 (2022). Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding eq…

Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabolical points and their degeneracies are explicitly discussed for the case of two modes. Quantum hybrid diabolical exceptional points (inherited, genuine, and induced) and hidden exceptional points, which are not recognized directly in amplitude spectra, are observed. The presented approach via the Heisenberg-Langevin equations paves the general way to a detailed analysis of quantum exceptional and diabolical points in infinitely dimensional open quantum systems.

SPIE Digital Library Proceedings

We consider a quantum nonlinear Kerr-like oscillator externally pumped by a series of ultrashort coherent pulses to analyze the quantum time-correlations appearing while the system evolves. For that purpose, we examine the violation of the Leggett–Garg inequality. We show how the character of such correlations changes when the system’s dynamics correspond to the regular and chaotic regions of its classical counterpart.

Inspired by the recent experiment of Hamsen et al. [ Phys. Rev. Lett. 118, 133604 (2017)], which demonstrated two-photon blockade in a driven nonlinear system (composed of a harmonic cavity with a driven atom), we show that two-photon blockade and other nonstandard types of photon blockade and photon-induced tunneling can be generated in a driven harmonic cavity without an atom or any other kind of nonlinearity, but instead coupled to a nonlinear (i.e., squeezed) reservoir. We also simulate these single- and two-photon effects with squeezed coherent states and displaced squeezed thermal states.

We study the problem of the influence of one-sided different noisy channels to the quantum correlations decay in a symmetric bosonic system. We concentrate on one type of these correlations—the entanglement. The system under consideration is composed of two nonlinear oscillators coupled by two-boson interactions and externally driven by a continuous coherent field. Our low-dimensional system can be treated as 2-qutrit one. Two different noisy channels (the amplitude and the phase-damping reservoirs) are applied to both of the system’s modes. We show that there is a noticeable difference in the quantum entanglement in 2-qubit subspaces of the whole system decrease after swapping the reservoirs between the modes of the considered symmetric system. It appears also that the degree of obtained entanglement depends crucially on the position of the appropriate type of reservoir. The origin of the observed asymmetry is also explained.