Stokes pulse

In time domain, the CARS signal, 5cars( ) can be described mathematically as a function of the delay, z, between pump/Stokes pulse, E (t), and probe pulse, 2(1) ... 

Because the Stokes pulse precedes but overlaps the pump pulse, initially Up and all population initially in field-free state 11) coincides with flo(0)- At the final time, ilp Q5 so all of the population in flo(0) projects onto the target state 6). Note that flo(0) has no projeetion on the intermediate field-free state 5 ). The Rabi frequencies of the Stokes and pump pulses that are required for efficient STIRAP-generated population transfer satisfy the condition [66]... 

From Eq. (3.73), we see that the intensity of the CDF is proportional to 0. For given (5), the peak intensity of the CDF is proportional to Tp - r5)/FWHM because the final factor in Eq. (3.75) does not affect the peak value of 0. In the numerical calculations reported below, we take the pump and Stokes pulse centers to be separated by Tp-Tg = FWHM/(2Vln 2), with intensity and width as shown in Table 3.1. All transitions between all of the states shown were included in the calculations. The transitions and transition dipole moments most relevant for these calculations are = 0.2062, figa = 0.2090, hk, = 0.0345, and pigag = 0.4138. 

The generated vibrational wave function after the irradiation of those two pairs of the pump and Stokes pulses is given as... 

Fig. 6.2. Illustration of the frequency-time dependences of pump and Stokes pulses in three different CRS excitation pulse schemes and their corresponding spectral resolution of Raman shifts. A Using a pair of transform-limited femtosecond pulses of broad spectral and narrow temporal widths results in a broad bandwidth of Raman shifts that exceeds the line width of a single Raman resonance. B Using transform-limited picosecond pulses of broad temporal and narrow spectral width readily provides high spectral resolution matching the Raman resonance line width to be probed. Selection of a Raman resonance shifted by AQr is achieved by tuning the frequency of one of the laser beams by the same amount. C Spectral focusing of a pair of identically linear chirped pump and Stokes femtosecond pulses results in a narrow instantaneous frequency difference in the CRS process, thus also providing narrow-bandwidth CRS excitation. Selection of a Raman resonance shifted by AQr is achieved by adjusting the time delay At between the pulses. Shifted pulses in (B) and (C) are depicted hatched...

As shown in Fig. 6.2B, this can be directly achieved by using transform-limited pump and Stokes pulses, of which the spectral bandwidth matches the Raman resonance line width to be probed [37]. The temporal width of the pulses is typically 5ps, corresponding to a spectral width of 2.9cm. A frequency-resolved CRS spectrum is obtained by tuning the wavelength of... 

Fig. 6.8. A Principle of frequency-multiplexed CARS microspectroscopy A narrow-bandwidth pump pulse determines the inherent spectral resolution, while a broad-bandwidth Stokes pulse allows simultaneous detection over a wide range of Raman shifts. The multiplex CARS spectra shown originate from a 70 mM solution of cholesterol in CCI4 (solid line) and the nonresonant background of coverglass (dashed line) at a Raman shift centered at 2900 cm-1. B Energy level diagram for a multiplex CARS process. C Schematic of the multiplex CARS microscope (P polarizer HWP/QWP half/quarter-wave plate BC dichroic beam combiner Obj objective lens F filter A analyzer FM flip mirror L lens D detector S sample). D Measured normalized CARS spectrum of the cholesterol solution. E Maximum entropy method (MEM) phase spectrum (solid line) retrieved from (D) and the error background phase (dashed line) determined by a polynomial fit to those spectral regions without vibrational resonances. F Retrieved Raman response (solid line) calculated from the spectra shown in (E), directly reproducing the independently measured spontaneous Raman response (dashed line) of the same cholesterol sample...

When a pump and a Stokes laser beam coincide on the sample and their difference frequency matches a particular molecular vibrational frequency, then SRS appears in the form of a gain of the Stokes pulse intensity and a loss of the pump pulse intensity, as first observed by Woodbury and Ng in 1962 [170] and by Jones and Stoicheff in 1964 [171], respectively (see Fig. 6.1). SRS has long been recognized as a highly sensitive spectroscopic tool for chemical analyses in the condensed and gas phases [172, 173, 29, 174]. For example, a shot-noise limited SRS spectrum of a single molecular monolayer was demonstrated by Heritage and Allara in 1980 [175]. In this section, we discuss the fundamental properties and applications of SRS microscopy, as was first successfully demonstrated by Nandakumar et al. [20] and subsequently reported by several research teams [21, 12, 13, 22]. 

An example of a STIRAP simulation and experiment is illustrated in Figs. 24 and 25 for SO2. Figure 24 shows the energies of the laser pulses used to transfer population from the vibrationless level to the (9, 1, 0) level of the ground electronic state. Figure 25 shows the experimentally measured and numerically simulated fraction of the population transferred to the excited state as a function of the time delay between the pump and Stokes pulses. The greater efficiency of a counterintuitive pulse sequence is evident. 

Stokes pulse (labeled S), is in near resonance with the transition from [Eq) to E2). In most applications one chooses the two frequencies to fulfill the two-photon resonance condition,... 

Fig. 9.4 Experimental results on population transfer between two states of Ne as a of laser pulse ordering. The ordering of the two laser pulses is shown at the top-controlled by the displacement between the two cw laser beams transversing the path of beam, thereby introducing an effective time delay between pulses. S of the figure del Stokes pulse (the dump pulse of the text), and P of the figure denotes the pump pulse. text. (From Fig. 9, Ref. [245].)...

The light-matter interactions of the Raman FID experiment are illustrated in Fig. 3a. Light pulses are needed at two frequencies Laser (L) and Stokes (S), with their frequency difference adjusted to the vibrational transition energy. An initial pair of Laser and Stokes pulses (pair I) excites the vibration through a Raman interaction. The density matrix of the vibration is transferred from the pure ground state (pm) to a coherent superposition of the v = 0 and v = 1 states (poi)-... 

The adiabatic passage induced by two delayed laser pulses, the well-known process of STIRAP [69], produces a population transfer in A systems (see Fig. 7a). The pump field couples the transition 1-2, and the Stokes field couples the transition 2-3. It is known that, with the initial population in state 11), a complete population transfer is achieved with delayed pulses, either (i) with a so-called counterintuitive temporal sequence (Stokes pulse before pump) for various detunings as identified in Refs. 73 and 74 or (ii) with two-photon resonant (or quasi-resonant) pulses but far from the one-photon resonance with the intermediate state 2), for any pulse sequence (demonstrated in the approximation of adiabatic elimination of the intermediate state [75]). Here we analyze the STIRAP process through the topology of the associated surfaces of eigenenergies as functions of the two field amplitudes. Our results are also valid for ladder and V systems. 

In the following, we describe in detail the case of Fig. 8. For the process in A or ladder systems, where the initial population resides in state 1), two different adiabatic paths lead to the complete population transfer, depending on the pulse sequence. The path denoted (a) corresponds to an intuitive sequence for the rise of the pulses. The pump pulse is switched on first, making the levels connected to the states 1) and 2) repel each other (dynamical Stark shift) until the level connected to 11) crosses the level connected to 3). The Stokes pulse is switched on after the crossing. Next the two pulses can decrease in any order. Path (b) is associated to a counterintuitive sequence for the decrease of the pulses. The two... 

Figure 10 shows that, for the process in A (or ladder) systems, two different adiabatic paths lead to different complete population transfers, depending on the pulse sequence. Path (a) corresponds to an intuitive pulse sequence (for the decrease of the pulses) and allows pulses to populate at the end the state 2). The Stokes and pump pulses can be switched on in any sequence and the pump pulse is switched off before the Stokes one. The path (b) corresponds to a counterintuitive pulse sequence (for the rise of the pulses) and allows pulses to populate at the end the state 3). The Stokes pulse is switched on before the pump, and the stokes pulse has to be switched off before the pump. We can thus selectively populate the states 2) or 3), provided that the peak amplitudes are sufficiently strong to induce the adiabatic path to cross the intersection involved. 

To ensure that the interactions have a finite duration, we consider truncated sin2 envelopes. Time and frequency are scaled with respect to 8. The scaled pulse length is set to T = 100/fio and the delay x = 0.33 T. The pulses have to be applied in the so-called counterintuitive order The fo2 Stokes pulse precedes the 0)j pump pulse with the delay x. To fulfill the standard adiabatic condition, the relevant Rabi frequencies ft have to be sufficiently large 7 1. 

Figure 21. From the dressed Schrodinger equation, with the same parameters as in Fig. 20. (a) Population histories P (t) for n = 1,2,3 (top frame), (c) photon histories (bottom frame), associated with the dressed spectrum in middle frame (b). The arrow characterizes the transfer eigenvector. Vertical lines indicate where the pump pulse starts and the Stokes pulse ends.

The direction, delay time Td, and rate of retrieval are determined by the direction, timing, and intensity of the retrieve laser, allowing control over the spatio-temporal properties of the retrieved pulse (referred to as the anti-Stokes pulse). Since the storage and retrieval processes ideally result in identical photon numbers in the Stokes and anti-Stokes pulses [Lukin 1999], this technique should allow preparation of an n-photon Fock state in the anti-Stokes pulse conditioned on detection of n Stokes photons. 

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