arXiv subjects

Ludmila Praxmeyer

Publications and source records attributed to Ludmila Praxmeyer.

7 recordsLinked to original sources

arXiv2019

Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

The Wigner-Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean lifetime and decay constants of quantum systems do not necessarily take arbitrary values, but could become functions of energy eigenvalues and have a discrete spectrum. It is demonstrated also that a constraint upon mean lifetime and energy appears, which is used to derive the resonance conditions at which long-lived states occur. The latter indicate that quantum dissipative effects do not always lead to decay but, under certain conditions, can support stability of a system.

quant-ph↗

arXiv2016

Phase space representation of non-Hermitian system with $\mathcal{PT}$-symmetry

We present a phase space study of non-Hermitian Hamiltonian with $\mathcal{PT}$-symmetry based on the Wigner distribution function. For an arbitrary complex potential, we derive a generalized continuity equation for the Wigner function flow and calculate the related circulation values. Studying vicinity of an exceptional point, we show that a $\mathcal{PT}$-symmetric phase transition from an unbroken $\mathcal{PT}$-symmetry phase to a broken one is a second-order phase transition.

quant-ph↗

arXiv2015

Families of Orthogonal Schrodinger cat-like-states

We analyze condition of orthogonality between optical Schrodinger cat-like-states constructed as superposition of two coherent states. We show that the orthogonality condition leads to quantization of values of a naturally emerging symplectic form, while values of the corresponding metric form are continuous. A complete analytical solution of the problem is presented.

quant-ph↗

arXiv2015

Direct Measurement of Time-Frequency Analogues of Sub-Planck Structures

Exploiting the correspondence between Wigner distribution function and a frequency-resolved optical gating (FROG) measurement, we experimentally demonstrate existence of the chessboard-like interference patterns with a time-bandwidth product smaller than that of a transform-limited pulse in the phase space representation of compass states. Using superpositions of four electric pulses as realization of compass states, we have shown via direct measurements that displacements leading to orthogonal states can be smaller than limits set by uncertainty relations. In the experiment we observe an exactly chronocyclic correspondence to the sub-Planck structure in the interference pattern appearing for superposition of two Schödinger-cat-like states in a position-momentum phase space.

quant-ph↗

arXiv2009

Near-unit fidelity entanglement distribution using Gaussian communication

We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme, which even beats the coherent-state-benchmark for entanglement distribution based on error-free non-Gaussian measurements. This is achieved through two innovations: first, optical squeezed states are utilized instead of coherent states. Secondly, the amplitudes of the bright signal pulses are reamplified at each repeater station. This latter variation is a strategy reminiscent of classical repeaters and would be impossible in single-photon-based schemes.

quant-ph↗

arXiv2007

Time-frequency Domain Analogues of Phase Space Sub-Planck Structures

We present experimental data of the frequency resolved optical gating (FROG) measurements of light pulses revealing interference features corresponding to sub-Planck structures in phase space. For superpositions of pulses a small, sub-Fourier shift in the carrier frequency leads to a state orthogonal to the initial one, although in the representation of standard time-frequency distributions these states seem to have a nonvanishing overlap.

physics.optics↗

arXiv2005

Time and Frequency description of Optical Pulses

The connection between the time-dependent physical spectrum of light and the phase space overlap of Wigner functions is investigated for optical pulses. Time and frequency properties of optical pulses with chirp are analyzed using the phase space Wigner and Ambiguity distribution functions. It is shown that optical pulses can exhibit interesting phenomena, very much reminiscent of quantum mechanical interference, quantum entanglement of wave packets, and quantum sub-Planck structures of the time and frequency phase space.

physics.optics↗