Get Advances in Chemical Physics, Vol.119, Part 1. Modern PDF

By Myron W. Evans, Ilya Prigogine, Stuart A. Rice

ISBN-10: 0471389307

ISBN-13: 9780471389309

ISBN-10: 0471466131

ISBN-13: 9780471466130

The recent variation will give you the sole accomplished source on hand for non-linear optics, together with distinct descriptions of the advances during the last decade from world-renowned specialists.

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Extra resources for Advances in Chemical Physics, Vol.119, Part 1. Modern Nonlinear Optics (Wiley 2001)

Example text

11 we have shown the contour plots of the Q function for the fundamental mode (Fig. 11a) and the second-harmonic mode (Fig. 11b) for the initial mean number of photons of the fundamental mode Na ¼ 10. It is seen that the centroid of the distribution, in case of the fundamental mode, moves to the left along the Re a axis showing squeezing along this axis at initial stages of the evolution, and next it becomes a two-peak structure first noticed by Nikitin and Masalov [24]. Nikitin and Masalov [24] suggested that the two peaks appearing in the Q function indicated a macroscopic superposition of quantum states.

0 2 ð128Þ H I ¼ "hk pffiffiffi 2 0 the diagonalizing matrix U has the form   1 1 À1 U À1 ¼ pffiffiffi ð129Þ À1 1 2 1 1 pffiffiffi pffiffiffi and the two eigenvalues are l0 ¼ À 2 and l1 ¼ 2. We have two coefficients cn;k ðtÞ 1 U ¼ pffiffiffi 2  1 1  ; pffiffiffi c2;0 ðtÞ ¼ cos ð 2 ktÞ ; pffiffiffi c2;1 ðtÞ ¼ Ài sin ð 2 ktÞ ð130Þ and the resulting state has the form pffiffiffi pffiffiffi jcð2Þ ðtÞi ¼ cos ð 2 ktÞj2; 0i À i sin ð 2 ktÞj0; 1i ð131Þ The mean numbers of photons in the state (131) are given by pffiffiffi h^ aþ ^ aiðtÞ ¼ 2cos 2 ð 2 ktÞ ; pffiffiffi h^ bþ ^ biðtÞ ¼ sin 2 ð 2 ktÞ ð132Þ which are exact analytical formulas for these particular initial conditions.

4. The potential represents a well in which the particle will oscillate exhibiting fully periodic behavior. From Eq. (109) we get qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dnb ð110Þ ¼ 2 nb ð1 À nb Þ2 À nb E0 dt Comparing Eq. (110) with Eq. (66), we find that both equations have extra terms (the E or E0 terms) which make the solutions oscillatory, but the physical reason for oscillations is different in both cases. In Eq. (66) different from zero E comes from the nonzero initial value of the second-harmonic mode intensity, while in Eq.

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Advances in Chemical Physics, Vol.119, Part 1. Modern Nonlinear Optics (Wiley 2001) by Myron W. Evans, Ilya Prigogine, Stuart A. Rice

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