Cross-phase modulation

The EPS experiments were carried out according to the procedure described in Ref. [20], The sample, used in experiments, was a 0.6 M solution of HDO molecules in heavy water at room temperature (maximal OD-O.6). The solution was pumped through a sapphire nozzle to form 100-pm thick, free-standing jet, that was positioned at the intersection of the laser beams. Use of the free-standing jet instead of a sample cell allowed us to avoid unwanted complications such as temporal broadening of the ultrashort pulses, their adverse scattering, and cross-phase modulation. The excitation pulses were -70 fs in duration and centered around -3 tm [19]. The excitation pulse spectra and the absorption spectrum of the OH-stretch vibration of HDO molecules in D2O are shown in the inset to Fig.lb. 

Equations (16) and (17) describe second-harmonic generation (SHG) and third-harmonic generation (THG) of one laser beam with a single polarization. Self-phase modulation (SPM) of a single laser beam is described in Eq.(18) as e.g. employed in z-scan experiments [6]. Equation (19) is the cross-phase modulation (XPM) process between two laser beams and Eq.(20) describes the four wave mixing with degenerate frequencies (DFWM). 

For all-optical signal processing (based on pure y nonlinearities) the important quantity is the nonlinear refractive index n2. The resulting refractive index change can be induced either by the beam at the frequency co1 itself (self-phase modulation) or by a beam at another frequency to2 (cross-phase modulation). 

These processes are directly proportional to the imaginary part of the third-order susceptibility y of the self- and cross-phase modulation process. 

We have thus seen that the behavior of weak quantum fields is remarkably different from that of classical fields, as in the quantum regime the nonlinear phase shift is bounded between 27t tv2(i) 2/(L Sq). This fact severely limits the usefulness of weak coherent states for QI applications. Only in the limit of weak cross-phase modulation 9 [Pg.86]

Figure 2. Realization of optical CPHASE logic gate between two single-photon qubits, using polarizing beam-splitters (PBS), A/4 plates and 7r cross-phase modulation (XPM) studied here.

Besides the phase of the fundamental mode, strictly speaking, the preferred phase, many other characteristics have been studied in [226]. Because a large mismatch was chosen, they have lacked any trend, but an interesting oscillatory behavior has been discovered for the initial two-mode coherent state. Within each period, the phase-matched second-harmonic and second-subharmonic generation processes can be prepared. The model of an ideal Kerr-like medium [223] have been considered for a comparison with cascaded quadratic non-linearities. It follows that these nonlinearities exhibit not only self-phase modulation in the fundamental mode but also a cross-phase modulation of the modes that can be considered for a nondemolition measurement. 

We propose an asymmetric double AlGaAs/GaAs quantum well strueture with a eommon continuum to generate a large cross-phase modulation (XPM). The basie idea is to combine resonant tuimeling induced constructive interference in eross-phase modulation (XPM) and tunneling-induced transparency (TIT). The band structure is shown in Fig. 11, whieh is designed with small electron decay rates, which can reduce the linear absorption effectively. A... 

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu. Low-light-level cross-phase-modulation based on stored light pulses. Physical Review Letters 2006 Feb 2 96(4) 043603(4). 

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang. Enhanced Cross-Phase Modulation Based on a Double Electromagnetically Indueed Transparency in a Four-Level Tripod Atomic System. Physical Review Letters 2008 Aug 13 101(7) 073602(4). 

Z. B. Wang, K. P. Marzlin, and B. C. Sanders. Large cross-phase modulation between slow copropagating weak pulses in 87Rb. Physical Review Letters 2006 Aug 9 97(6) 063901(4). 

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