By using Stark-induced adiabatic Raman passage (SARP) with partially overlapping nanosecond pump (532 nm) and Stokes (683 nm) laser pulses, 73% ± 6% of the initial ground vibrational state population of H(2) (v = 0, J = 0) is transferred to the single vibrationally excited eigenstate (v = 1, J = 0). In contrast to other Stark chirped Raman adiabatic passage techniques, SARP transfers population from the initial ground state to a vibrationally excited target state of the ground electronic surface without using an intermediate vibronic resonance within an upper electronic state. Parallel linearly polarized, co-propagating pump and Stokes laser pulses of respective durations 6 ns and 4.5 ns, are combined with a relative delay of ~4 ns before orthogonally intersecting the molecular beam of H(2). The pump and Stokes laser pulses have fluences of ~10 J/mm(2) and ~1 J/mm(2), respectively. The intense pump pulse generates the necessary sweeping of the Raman resonance frequency by ac (second-order) Stark shifting the rovibrational levels. As the frequency of the v = 0 → v = 1 Raman transition is swept through resonance in the presence of the strong pump and the weaker delayed Stokes pulses, the population of (v = 0, J = 0) is coherently transferred via an adiabatic passage to (v = 1, J = 0). A quantitative measure of the population transferred to the target state is obtained from the depletion of the ground-state population using 2 + 1 resonance enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer. The depletion is measured by comparing the REMPI signal of (v = 0, J = 0) at Raman resonance with that obtained when the Stokes pulse is detuned from the Stark-shifted Raman resonance. No depletion is observed with either the pump or the Stokes pulses alone, confirming that the measured depletion is indeed caused by the SARP-induced population transfer from the ground to the target state and not by the loss of molecules from photoionization or photodissociation. The two-photon resonant UV pulse used for REMPI detection is delayed by 20 ns with respect to the pump pulse to avoid the ac Stark shift originating from the pump and Stokes laser pulses. This experiment demonstrates the feasibility of preparing a large ensemble of isolated molecules in a preselected single quantum state without requiring an intermediate vibronic resonance.
By using Stark-induced adiabatic Raman passage (SARP) with partially overlapping nanosecond pump (532 nm) and Stokes (683 nm) laser pulses, 73% ± 6% of the initial ground vibrational state population of H(2) (v = 0, J = 0) is transferred to the single vibrationally excited eigenstate (v = 1, J = 0). In contrast to other Stark chirped Raman adiabatic passage techniques, SARP transfers population from the initial ground state to a vibrationally excited target state of the ground electronic surface without using an intermediate vibronic resonance within an upper electronic state. Parallel linearly polarized, co-propagating pump and Stokes laser pulses of respective durations 6 ns and 4.5 ns, are combined with a relative delay of ~4 ns before orthogonally intersecting the molecular beam of H(2). The pump and Stokes laser pulses have fluences of ~10 J/mm(2) and ~1 J/mm(2), respectively. The intense pump pulse generates the necessary sweeping of the Raman resonance frequency by ac (second-order) Stark shifting the rovibrational levels. As the frequency of the v = 0 → v = 1 Raman transition is swept through resonance in the presence of the strong pump and the weaker delayed Stokes pulses, the population of (v = 0, J = 0) is coherently transferred via an adiabatic passage to (v = 1, J = 0). A quantitative measure of the population transferred to the target state is obtained from the depletion of the ground-state population using 2 + 1 resonance enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer. The depletion is measured by comparing the REMPI signal of (v = 0, J = 0) at Raman resonance with that obtained when the Stokes pulse is detuned from the Stark-shifted Raman resonance. No depletion is observed with either the pump or the Stokes pulses alone, confirming that the measured depletion is indeed caused by the SARP-induced population transfer from the ground to the target state and not by the loss of molecules from photoionization or photodissociation. The two-photon resonant UV pulse used for REMPI detection is delayed by 20 ns with respect to the pump pulse to avoid the ac Stark shift originating from the pump and Stokes laser pulses. This experiment demonstrates the feasibility of preparing a large ensemble of isolated molecules in a preselected single quantum state without requiring an intermediate vibronic resonance.
We prepare an ensemble of isolated rovibrationally excited (v = 1, J = 2) H2 molecules in a phase-locked superposition of magnetic sublevels M using Stark-induced adiabatic Raman passage with linearly polarized single-mode pump (at 532 nm, ∼6 ns pulse duration, 200 mJ/pulse) and Stokes (699 nm, ∼4 ns pulse duration, 20 mJ/pulse) laser excitation. A biaxial superposition state, given by [line]ψ(t)⟩ = 1/√(2)[[line]ν = 1, J = 2, M = -2⟩ - [line]ν = 1, J = 2, M = +2⟩], is prepared with linearly but cross-polarized pump and Stokes laser pulses copropagating along the quantization z-axis. The degree of phase coherence is measured by using the O(2) line of the H2 E,F-X (0,1) band via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 210.8 nm by recording interference fringes in the REMPI signal in a time-of-flight mass spectrometer as the direction of the UV laser polarization is rotated using a half-wave plate. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of the Q(0) line of the E,F-X (0,0) band as the Stokes frequency is tuned across the (v = 0, J = 0) → (v = 1, J = 2) Raman resonance.
We have theoretically investigated the population transfer from the initial ground rovibrational level v(g)=0, J(g)=0 to the final rovibrational levels v(f)=1,2, J(f)=0 of the ground electronic state X (1)Sigma(g) (+) via the resonant intermediate level v(i)=6, J(i)=0 of the excited electronic state EF (1)Sigma(g) (+) of H(2) molecule by (2+2)-photon stimulated hyper-Raman passage (STIHRP). The density matrix technique has been employed to evaluate the population transfer to the final target levels using linearly chirped pump and Stokes laser pulses with different chirp rates. Both the pulses are considered to have the same temporal shape, pulse width, and linear parallel polarizations. We have studied in detail the dependence of the population transfer on the set of laser parameters for pulse (peak) intensities in the ranges of 1.5 x 10(11)-1.0 x 10(12) and 1.0 x 10(12)-7.0 x 10(12) W/cm(2). The corresponding pulse widths (full width at half maximum) are of the order of 115-200 and 15-30 ps. We have found that the chirp rate parameters can be optimized to achieve almost complete population transfer from the ground (g) to the final (f) target levels. This, to our knowledge, is the first application of a (2+2)-photon STIHRP process with chirpings to a model molecular system (H(2)). The study demonstrates the suitability of the chirped (2+2)-photon STIHRP technique for selective and almost total inversion of vibrational population in a diatomic molecule.
We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r0v) and the difference of the optical polarizabilities (Δα00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) in a beam of D2 (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r02 ≈ 0.3 × 10−41 Cm/(V/m) and the difference polarizabilities Δα00→20 ≈ 1.4 × 10−41 Cm/(V/m) and Δα00→22 ≈ 3.4 × 10−41 Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.
We demonstrate and analyze a novel scheme for complete transfer of atomic or molecular population between two bound states, by means of Stark-chirped rapid adiabatic passage (SCRAP). In this two-laser technique a delayed-pulse laser-induced Stark shift sweeps the transition frequency between two coupled states twice through resonance with the frequency of the population-transferring coupling laser. The delay of the Stark-shifting pulse with respect to the pulse of the coupling-laser Rabi frequency guarantees adiabatic passage of population at one of the two resonances while the evolution is diabatic at the other. The SCRAP method can give a population-transfer efficiency approaching unity. We discuss the general requirements on the intensity and timing of the pulses that produce the Rabi frequency and, independently, the Stark shift. We particularly stress extension to a double-SCRAP technique, a coherent variant of stimulated emission pumping in the limit of strong saturation. We demonstrate the success of the SCRAP method with experiments in metastable helium, where a two-photon transition provides the Rabi frequency.
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), hitherto used for complete population transfer between two quantum states, offers a simple and robust method for complete population transfer amongst three states in atoms and molecules. In this case SCRAP uses three laser pulses: a strong far-off-resonant pulse modifies the transition frequencies by inducing dynamic Stark shifts and thereby creating time-dependent level crossings amongst the three diabatic states, while near-resonant and moderately strong pump and Stokes pulses, appropriately offset in time, drive the population between the initial and final states via adiabatic passage. The population transfer efficiency is robust to variations in the intensities of the lasers, as long as these intensities are sufficiently large to enforce adiabatic evolution. With suitable pulse timings the population in the (possibly decaying) intermediate state can be minimized, as with stimulated Raman adiabatic passage (STIRAP). This technique applies to one-photon as well as multiphoton transitions and it is also applicable to media exhibiting inhomogeneous broadening; these features represent clear advantages over STIRAP by overcoming the inevitable dynamical Stark shifts that accompany multiphoton transitions as well as unwanted detunings, e.g., induced by Doppler shifts.
We have theoretically investigated the population transfer in a four-level H2 system by stimulated Raman transition from the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}({\ensuremath{\nu}}_{g}{=0,J}_{g}=0)$ level to higher rovibrational levels $({\ensuremath{\nu}}_{f}{,J}_{f})$ of the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state via the excited intermediate $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}({\ensuremath{\nu}}_{i}{=14,J}_{i}=1)$ and $C{}^{1}{\ensuremath{\Pi}}_{u}^{+}({\ensuremath{\nu}}_{i}{=3,J}_{i}=1)$ levels coupled with each other by nonadiabatic interaction, using time-dependent overlapping pump and Stokes laser fields. The density-matrix treatment, which permits the convenient inclusion of the spontaneous emissions from the intermediate levels, has been employed to describe the dynamics of the two-photon Raman resonance process. The present study performs the calculations of final populations (after both the pulses are over) of the ground and terminal levels for Q-branch (Jf=0) fundamental $({\ensuremath{\nu}}_{f}=1)$ and first overtone $({\ensuremath{\nu}}_{f}=2)$ transitions and the S-branch (Jf=2) fundamental $({\ensuremath{\nu}}_{f}=1)$ transition as a function of time delay between the two pulses for the cases of on-resonance as well as off-resonance excitations in a wide range $(2\ifmmode\times\else\texttimes\fi{}{10}^{5}--2\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ of peak intensities IP0(IS0) of the pump (Stokes) fields. Both fields are assumed to have the same temporal shape, duration, peak intensities, and linear parallel polarizations. The accurate values of spontaneous radiative relaxation rates of the intermediate levels to the initial and final levels, taking into account their J and M dependence, are explicitly included in our calculations. The pulse width (full width at half maximum) ${\ensuremath{\tau}}_{p}$ is taken as 170 ns so that total spontaneous decay can occur during the pulse duration. The transfer efficiency is found to be very sensitive to the peak intensities of the laser pulses in each case of transition considered. Special attention is paid to the effects of the nonadiabatic (NA) interaction between B(14,1) and C(3,1) levels on population transfer efficiency. Calculations are also done in some particular cases using the adiabatic Born-Oppenheimer (ABO) approximation. The results with ABO approximation are found to differ remarkably from those obtained including NA interaction. Our calculations for the four-level H2 system reveal that almost complete population is transferred in counterintuitive pulse order for both on-resonance and off-resonance excitations with intermediate and high values of IP0(IS0). For intuitive pulse sequence also a large population transfer is achieved for on-resonance excitation at intermediate values of IP0(IS0) and for off-resonance excitation at intermediate and high values of IP0(IS0).