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arXiv:1508.00342

Quantum Analysis of Subharmonic Generation Via First-Order Hamiltonian

Fesseha Kassahun

Published Aug 3, 2015• 1 citation
arXivHTMLPDF

Abstract

We have established that the mean photon number obtained employing the conventional Hamiltonian for the twin light beams with the same frequency, produced by a subharmonic generator, is half that of the twin light beams with different frequencies. In view of this, we have found it to be quite appropriate to describe the process of subharmonic generation by the same Hamiltonian regardless of whether the twin light beams have the same or different frequencies. Applying this Hamiltonian, we have calculated the photon statistics and quadrature squeezing for the signal-signal and the signal-idler modes. Obviously, this time the mean photon number of the signal-signal modes is exactly the same as that of the signal-idler modes. In addition, we have found that the maximum global quadrature squeezing of the signal-signal or the signal-idler modes is 50$\%$ below the vacuum-state level and the maximum local quadrature squeezing of the signal-signal modes is 74.9$\%$ below the same level.

DOI
10.48550/arxiv.1508.00342

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We have established that the mean photon number obtained employing the conventional Hamiltonian for the twin light beams with the same frequency, produced by a subharmonic generator, is half that of the twin light beams with different frequencies. In view of this, we have found it to be quite appropriate to describe the process of subharmonic generation by the same Hamiltonian regardless of whether the twin light beams have the same or different frequencies. Applying this Hamiltonian, we have calculated the photon statistics and quadrature squeezing for the signal-signal and the signal-idler modes. Obviously, this time the mean photon number of the signal-signal modes is exactly the same as that of the signal-idler modes. In addition, we have found that the maximum global quadrature squeezing of the signal-signal or the signal-idler modes is 50%\%% below the vacuum-state level and the maximum local quadrature squeezing of the signal-signal modes is 74.9%\%% below the same level.
We have analyzed the statistical and squeezing properties of the signal mode applying the solution of c-number Langivin equations for the combination of the twin signal light beams. We have found that the mean photon number to be twofold of that of a twin signal light beam. And a large part of the mean photon number is confined in a relatively small frequency interval. In addition, we have shown that the local quadrature squeezing of the signal mode is in general greater than the global quadrature squeezing and approaches to the global quadrature squeezing as increases. Moreover, the one-mode subharmonic light beams have a maximum amplified squeezing of 75% below the vacuum state level and occurs in frequency interval.
We have analyzed photon statistics and quadrature squeezing of the signal mode produced by one-mode subharmonic generator. It is found that the mean photon energy of the signal mode is twice of a twin signal light beam. And the energy fluctuations of the two signal light beams are four times that of one of the signal light beams. We have also shown that the photon energy quadrature squeezing of the output signal mode is exactly equal to that of the cavity signal mode. In light of this, the global quadrature squeezing of the signal mode is independent of the mean photon energy. On the basis of the above results, the quantum analysis of a one-mode sub-harmonic generating system should somehow be modified.
Abstract The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a singleport mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50 % maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50 % entangled.
A detailed photon statistics of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented. We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies. According to our study we have observed that the mean photon number of the cavity mode decreases with the cavity damping constant increase, which implies that the more photons are escaped from the cavity for the large damping constant and the mean photon number of residue pump mode increases with the amplitude of pump mode.
A detailed quantum entanglement of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented.We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies.According to our study we have the quadrature variance decreases with the amplitude of pump mode and it approaches to the value of the quadrature variance of a two-mode vacuum state as cavity damping constant approaches to 1.In addition to this the degree of entanglement of the cavity modes for the system under consideration increase with the amplitude of the pump mode and decrease with the cavity damping constant, which implies that the degree of entanglement of twin light beams decreases as quadrature variances approaches to that of a two-mode vacuum state.
It has been known for a while that coherent high-intensity photon number eigenstate fields can be generated through nonlinear optical parametric processes,1 the same ones that give rise to quadrature squeezing.2,3 In contrast to quadrature squeezing which is essentially a single-mode phenomenon, although it is widely misunderstood that it is a two-mode phenomenon, the generation of single-mode number states through three- or four-wave mixing depends on two separate signal and idler modes that are perfectly correlated in photon numbers, in other words a twin beam. The nature of such twin beams is elucidated in both the Schrodinger and the Heisenberg pictures. In particular, it is shown that strong photon number correlation in a twin beam can still be obtained in an amplifier rather than an oscillator configuration, another widely missed point.