Photon distribution function, tomograms and entanglement in stimulated Raman scattering

Intermodal entanglement in Raman processes

“…Interestingly, we have observed intermodal entanglement between i) pump mode and anti-Stokes mode, and ii) Stokes mode and anti-stokes mode. These two intermodal entanglement was not observed in the earlier analytic studies [24,25]. The beauty of the present study lies in the fact that analytic expressions for separability criterion are obtained by a completely quantum mechan-ical treatment where all four modes are considered quantum mechanical.…”

“…As our solution is valid for all times and hence the entanglement parameters are free from this particular problem which is generally a characteristic of short-time solutions. Another earlier effort to study the intermodal entanglement in the Raman processes by S. V. Kuznetsov [24] was restricted to the study of intermodal entanglement between Stokes mode and the vibration mode as they had considered a simplified two-mode Hamiltonian. Thus the use of a completely quantum mechanical description of the Raman process, our solution, and the strategy to use more than one inseparability criterion have helped us to obtain a relatively more complete picture of the intermodal entanglement in the Raman processes.…”

“…They have followed an independent approach and have numerically computed the time dependence of a measure of entanglement. Earlier S V Kuznetsov et al [24] studied the entanglement in the stimulated Raman process considering only two modes (Stokes mode and phonon mode) and taking the pump mode as the classical light source. Naturally Kuznetsov et al's work illustrated an incomplete scenario and failed to observe intermodal entanglement involving anti-Stokes mode and pump mode.…”

Probability Representation of Quantum States

“…The extension of the tomographic maps to the quantum case and a Weyl-Wigner quantization in the classical case were considered in Reference [ 42 ]. The methods of star-product, tomography, and probability representation of quantum mechanics were applied to different problems of quantum phenomena in References [ 43 , 44 , 45 , 46 , 47 , 48 ]…”

Probability Representation of Quantum Observables and Quantum States

“…We derive the evolution equation for quantum observables (Heisenberg equation) in the probability representation and give examples of the spin-1/2 (qubit) states and the spin observables. We present quantum channels for qubits in the probability representation.developed to obtain the formulation of quantum states more similar to the formulation of the states in classical statistical mechanics.Recently, the tomographic probability representation of quantum states was suggested [12]; in this representation, the quantum states are identified with fair probability distributions connected with density matrices in its phase-space representations by integral transforms; e.g., the Radon transform [13] of the Wigner function provides the optical tomogram [14,15], which is a standard probability distribution of continuous homodyne quadrature of photon depending on an extra parameter called the local oscillator phase, which can be measured [16].The probability distributions determining the spin states were considered in [17,18,19,20,21,22,23,24], and the tomographic probability representation of quantum states was studied in [25,26,27,28,29,30,31,32,33,34].The tomographic probabilities identified with quantum states can be associated with density operators, in view of the formalism of star-product quantization [35,36,37,38,39] analogous to the procedure where the phase-space quasidistributions of quantum states, like the Wigner function, are presented within the star-product framework in [40] (see also recent reviews [41,42]). On the other hand, quantum observables associated with Hermitian operators are presented within the star-product framework by symbols of the operators, which are some functions on the phase space, say, in the Wigner-Weyl representation or the functions of discrete variables in the spin-tomographic description of qudit states.The ...…”