Intermodal entanglement in Raman processes

The operator solution of a completely quantum mechanical Hamiltonian of the Raman processes is used here to investigate the possibility of obtaining intermodal entanglement between different modes involved in the Raman processes (e.g. pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode). Intermodal entanglement is reported between a) pump mode and anti-Stokes mode, b) pump mode and vibration (phonon) mode c) Stokes mode and vibration phonon mode, d) Stokes mode and anti-stokes mode in the stimulated Raman processes for the variation of the phase angle of complex eigenvalue $\alpha_{1}$ of pump mode $a$. Some incidents of intermodal entanglement in the spontaneous and the partially spontaneous Raman processes are also reported. Further it is shown that the specific choice of coupling constants may produce genuine entanglement among Stokes mode, anti-Stokes mode and vibration-phonon mode. It is also shown that the two mode entanglement not identified by Duan's criterion may be identified by Hillery-Zubairy criteria. It is further shown that intermodal entanglement, intermodal antibunching and intermodal squeezing are independent phenomena.Comment: 11 pages, 4 figure

A prospective study on placental migration in mid trimester low lying placenta

Background: Objectives of the study were: to assess migration of low-lying placenta diagnosed by ultrasound around 20 weeks of gestation and to evaluate the factors influencing placental migration as well as to reduce feto-maternal morbidity and or mortality by excluding placenta previa and placenta accreta early.Methods: All antenatal mothers undergoing routine transabdominal congenital anomaly scan around 20 weeks of gestation were subjected to transvaginal ultrasonography to confirm low lying placenta. Every 4 weekly transvaginal ultrasonography was repeated until the lower edge of placenta migrated beyond 3 cm of internal cervical os or the patient had delivered, which one was earlier.Results: Out of total 686 cases, only 56 (8.16%) mothers had low-lying placenta in mid trimester. Follow up of these 56 cases showed that 33 (58.93%) cases placenta had migrated at term and 23 (3.35%) cases persist as placenta previa. The rate of migration of placenta was 80.76%, 39.13% and 42.86% in mothers following previous vaginal delivery, caesarean section or prior history of MTP/suction and evacuation. Placental migration was 80% and 47.39% where the distance between the internal cervical os and lower edge of placenta was between 2.1-3 cm and between 1.5-2 cm respectively. No placental migration was noted where the initial distance was less than 1.5 cm. Placental migration was more common in anteriorly situated placenta (65.85%) than the posterior one (40%).Conclusions: The rate of placental migration at term was 58.93%. However, factors like previous caesarean section, previous history of MTP or suction and evacuation, posteriorly situated placenta and placenta lying 1.5 cm from the internal cervical os may interfere with placental migration

Exact dynamics and squeezing in two harmonic modes coupled through angular momentum

We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.Facultad de Ciencias ExactasInstituto de Física La Plat

Exact dynamics and squeezing in two harmonic modes coupled through angular momentum

We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.Facultad de Ciencias ExactasInstituto de Física La Plat

Squeezing, mixed mode squeezing, amplitude squared squeezing and principal squeezing in a non-degenerate parametric oscillator

The Hamiltonian and hence the equation of motion of the field operators of a nondegenerate parametric oscillator (NDPO) under the influence of classical pump are formulated. The coupled operator differential equations involving the signal and idler modes are decoupled at the expense of fourth order differential equations involving the c-numbers. Without using the rotating wave approximation, the analytical solutions of the field operators are obtained. These solutions are approximated up to the second orders in dimensionless coupling constant. We investigate the squeezing, mixed mode squeezing, amplitude-squared squeezing, and the principal squeezing of the thermal and coherent light coupled to the NDPO. By using the input composite number state, we establish that the percentage and the range (interaction time) of squeezing is considerably increased with the increase of the signal photon number. For initial composite number state, the amplitude squared squeezing for Ys quadrature is obtained at the cost of canonically conjugate Zs quadrature. The percentage of amplitude squared squeezing increases significantly with the increase of signal excitation (photon). The so-called normal squeezing and the principal squeezing are also indicated for the NDPO coupled with the initially prepared composite coherent states not in the composite number states. In spite of the shortcomings of the analytical solutions, we obtain squeezing, amplitude squared squeezing and other nonclassical effects which are unavailable under the rotating wave approximation. In order to give the feelings about the analytical results (expressions), we give some symbolic calculations relevant to the possible experimental situations

Quantum phase fluctuations of coherent and thermal light coupled to a non-degenerate parametric oscillator beyond rotating wave approximation

The essence of the rotating wave approximation (RWA) is to eliminate the non-conserving energy terms from the interaction Hamiltonian. The cost of using RWA is heavy if the frequency of the input radiation field is low (e.g. below optical region). The well known Bloch-Siegert effect is the out come of the inclusion of the terms which are normally neglected under RWA. We investigate the fluctuations of the quantum phase of the coherent light and the thermal light coupled to a nondegenerate parametric oscillator (NDPO). The Hamiltonian and hence the equations of motion involving the signal and idler modes are framed by using the strong (classical) pump condition. These differential equations are nonlinear in nature and are found coupled to each other. Without using the RWA, we obtain the analytical solutions for the signal and idler fields. These solutions are obtained up to the second orders in dimensionless coupling constants. The analytical expressions for the quantum phase fluctuation parameters due to Carruther's and Nieto are obtained in terms of the coupling constants and the initial photon numbers of the input radiation field. Moreover, we keep ourselves confined to the Pegg-Barnett formalism for measured phase operators. With and without using the RWA, we compare the quantum phase fluctuations for coherent and thermal light coupled to the NDPO. In spite of the significant departures (quantitative), the qualitative features of the phase fluctuation parameters for the input thermal light are identical for NDPO with and without RWA. On the other hand, we report some interesting results of input coherent light coupled to the NDPO which are substantially different from their RWA counterpart. In spite of the various quantum optical phenomena in a NDPO, we claim that it is the first effort where the complete analytical approach towards the solutions and hence the quantum phase fluctuations of input radiation fields coupled to it are obtained beyond rotating wave approximation. To have the feelings of the analytical solutions, we give few numerical estimates of the quantum phase fluctuation parameters relevant to a real experimental situation