Piotr Szańkowski

Oscillating Solitons in a Three-Component Bose-Einstein Condensate

We investigate the properties of three component BEC systems with spin exchange interactions. We consider different coupling constants from those very special ones leading to exact solutions known in the literature. When two solitons collide, a spin component oscillation of the two emerging entities is observed. This behavior seems to be generic. A mathematical model is derived for the emerging solitons. It describes the new oscillatory phenomenon extremely well. Surprisingly, the model is in fact an exact solution to the initial equations. This comes as a bonus.

Parameter estimation in memory-assisted noisy quantum interferometry

We demonstrate that memory in an

Spectroscopy of cross-correlations of environmental noises with two qubits

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The dynamics of two entangled qubits exposed to classical noise: role of spatial and temporal noise correlations

-qubit system subjected to decoherence, is a potential resource for the slow-down of the entanglement decay. We show that this effect can be used to retain the sub shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.

Cauchy-Schwarz inequality and particle entanglement

A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to reconstruct the spectrum of cross-correlations of noises acting at various locations. When the qubits are driven by the same sequence of pulses, real part of cross-correlation spectrum can be reconstructed, while applying two distinct sequence to the two qubits allows for reconstruction of imaginary part of this spectrum. The latter quantity contains information on either causal correlations between environmental dynamics at distinct locations, or on the occurrence of propagation of noisy signals through the environment. We illustrate the former case by modeling the noise spectroscopy protocol for qubits coupled to correlated two-level systems. While entanglement between the qubits is not necessary, its presence enhances the signal from which the spectroscopic information is reconstructed.

Class of compact entities in three-component Bose-Einstein condensates

We investigate the decay of two-qubit entanglement caused by the influence of classical noise. We consider the whole spectrum of cases ranging from independent to fully correlated noise affecting each qubit. We take into account different spatial symmetries of noises, and the regimes of noise autocorrelation time. The latter can be either much shorter than the characteristic qubit decoherence time (Markovian decoherence), or much longer (approaching the quasi-static bath limit). We express the entanglement of two-qubit states in terms of expectation values of spherical tensor operators which allows for transparent insight into the role of the symmetry of both the two-qubit state and the noise for entanglement dynamics.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

The Glauber-Sudarshan

Bogoliubov theory for atom scattering into separate regions

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Four-wave mixing in a parity-time (PT)-symmetric coupler

-representation is used in quantum optics to distinguish between semi-classical and genuinely quantum electromagnetic fields. We employ the analog of the

Cauchy---Schwarz inequality for general measurements as an entanglement criterion

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