Quantum interference nonlinear optics

S. Mukamel I would like to make a comment regarding interference effects in quantum and classical nonlinear response functions [1, 2]. Nonlinear optical measurements may be interpreted by expanding the polarization P in powers of the incoming electric field E. To nth order we have... 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

N. Mulchan, D. Ducreay, R. Pina, M. Yan, and Y. Zhu. Nonlinear excitation by quantum interference in a Doppler-broadened rubidium atomic system. Journal of the Optical Society of America B 2000 May 17(5) 820-826. 

Fig. 3.11 (A) Single-photon interference in a Mach-Zender interferometer with equal arms. BSl and BS2 are beam-splitters with coefficients Ct and for transmission and reflectirai, respectively (ICrl = Cr = 1/2) Ml and M2 are mirrors (100% reflecting) and D and D2 are photoncounting detectors. The dependence of photon wavefunction If on time and the distance along the optical path is not indicated explicitly. If BS2 is removed, or if either path is blocked before BS2, photons are detected at D1 and D2 with equal probability but when BS2 is presem and both paths are open, photons are detected only at Dl. (B) Two-photon quantum interference. Short pulses of light with frequency v are focused into a crystal with nonlinear optical properties (XTL). This...

To summarize, the EOM-PMA considerably facilitates the computation of various optical signals and 2D spectra. With shght alterations, the EOM-PMA can also be applied to compute nonlinear responses in the infrared (IR). The three-pulse EOM-PMA can be extended to calculate the A-pulse-induced nonhnear polarization [51], which opens the way for the interpretation of fifth-order spectroscopies, such as heterodyned 3D IR [52], transient 2D IR [53, 54], polarizability response spectroscopy [55], resonant-pump third-order Raman-probe spectroscopy [56], femtosecond stimulated Raman scattering [57], four-six-wave-mixing interference spectroscopy [58], or (higher than fifth order) multiple quantum coherence spectroscopy [59]. 

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