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Journal of Physics B Atomic Molecular and Optical Physics

Molecular dissociation and nascent product state distributions detected with atomic wavepacket interferometry and parametric four-wave mixing: Rb2predissociation observed by quantum beating in Rb at 18.2 THz

Y Xiao, Andrey A. Senin, Brian J. Ricconi, R. Kogler, Chang Jun Zhu, James Gary Eden

Published Sep 2, 2008• 2 citations
Publisher

Abstract

Dissociation of a diatomic molecule and the excited-state distribution of the nascent atomic fragments can be detected and characterized by atomic wavepacket interferometry and a coherent nonlinear optical process, such as parametric four-wave mixing (PFWM), in ultrafast pump–probe experiments. Underlying these experiments is a reliance on atom–atom interaction to alter the properties of an atomic wavepacket which, in turn, impacts the phase and amplitude of a coherent optical signal. Specifically, quantum beating in the atomic species provides a sensitive, in situ probe of molecular dissociation by detecting approaching dissociation fragments through long-range dipole–dipole interaction. The resulting influence of this interaction on the amplitude and phase of the quantum beating is observed in temporal or Fourier domains by probing the wavepacket by interferometry and PFWM with 100–150 fs laser pulses. The wavepacket thus serves as a detector of molecular dissociation fragments and the dynamics of atom–atom interactions are converted into the macroscopic domain by the PFWM signal and idler waves. Femtosecond pump–probe experiments are described in which the predissociation of electronically excited Rb2 states in the ~24 000–28 000 cm−1 interval, and the distribution of nascent atomic fragments into Rb excited states (7s, 5d, 6s, 4d and 5p) spanning an energy range >1.25 eV, have been observed in Rb vapour with atomic number densities of ~6 × 1013–3 × 1017 cm−3. Quantum beating at 18.2 THz (corresponding to the Rb 7s–5dJ (J = 5/2) energy defect of ~608 cm−1) is superimposed onto the axially phase matched PFWM signal wave generated at λS ~ 420 nm (Rb 62PJ → 52S1/2 transitions) and recovered by Fourier analysis of the signal wave intensity as the pump–probe time delay (Δt) is scanned. The dominant exit channels for Rb2 predissociation are found to be sensitive to the interval of internuclear separation R in which the molecular wavepacket, produced by the pump pulse through two-photon association of Rb–Rb collision pairs, is localized. Generating Rb2 wavepackets on 3Λu (Λ = Σ, Δ) potential surfaces at large R (~7–9 A) favours the Rb 7s and 5d dissociation channels. In contrast, producing dimer wavepackets localized in the R ~ 3–4 A region suppresses Rb (7s, 5d) generation and favours the production of Rb atomic fragments (primarily 5p) with less internal energy, but maximum velocities of ~15–20 A ps−1. Laser excitation spectroscopy on the nanosecond time scale suggests that the (3)3Δu and (7)3Σ+u states of Rb2 (correlated with Rd (5d) + Rb (6s) in the separated atom limit), and possibly a 3Σ+u state derived from the Rb (7p) + Rb (5s) asymptote, are populated by two-photon absorption of Rb–Rb ground-state collision pairs and predissociation of these levels provides the excited atomic fragments subsequently detected by atomic wavepackets. The data presented here demonstrate the observation of the molecular dissociation transient and the determination of the nascent statistical distribution of atomic product states in a manner that is unencumbered by radiative lifetime or collisional effects. A wavepacket, in tandem with the dipole–dipole interaction and a coherent nonlinear optical process, provides a new avenue for pursuing atom–atom and atom–molecular interactions over a broad range in inter-particle separations.

DOI
10.1088/0953-4075/41/18/185101

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\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.32]{Fig1.eps} \end{wrapfigure} Coherences at 386.2 THz and 384.1 THz, corresponding to the 5d$_{5/2}$ – 5p$_{3/2}$ and 5p$_{3/2}$ – 5s$_{1/2}$ difference frequencies, respectively, have been established in the Rb atom during pump-probe experiments involving pairs of identical ~150 fs pulses produced by a Ti:\chem{Al_2O_3} laser and a Michelson interferometer. The interference between the two coherences within the atom is observed through a parametric four-wave mixing process in Rb and detection of the signal wave intensity at 420 nm. Scanning the time delay between the pump and probe pulses over a 600 ps interval produces a sampling rate over 300 THz and allows for a spectral domain resolution of 0.05 cm$^{-1}$ to be achieved. The figure at right shows several spectra recorded near 2.1 THz, the (5d$_{5/2}$ – 5p$_{3/2}$) - (5p$_{3/2}$ – 5s$_{1/2}$) difference frequency, with varying angle between the pump and probe pulses (i.e., the phase matching angle) and varying Rb background density. A Fano interference window is clearly observed, and analysis of these and similar spectra demonstrates that the amplitude and phase of the coherently-coupled, three Rb state system can be controlled precisely.

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Dissociation of a diatomic molecule and the excited-state distribution of the nascent atomic fragments can be detected and characterized by atomic wavepacket interferometry and a coherent nonlinear optical process, such as parametric four-wave mixing (PFWM), in ultrafast pump–probe experiments. Underlying these experiments is a reliance on atom–atom interaction to alter the properties of an atomic wavepacket which, in turn, impacts the phase and amplitude of a coherent optical signal. Specifically, quantum beating in the atomic species provides a sensitive, in situ probe of molecular dissociation by detecting approaching dissociation fragments through long-range dipole–dipole interaction. The resulting influence of this interaction on the amplitude and phase of the quantum beating is observed in temporal or Fourier domains by probing the wavepacket by interferometry and PFWM with 100–150 fs laser pulses. The wavepacket thus serves as a detector of molecular dissociation fragments and the dynamics of atom–atom interactions are converted into the macroscopic domain by the PFWM signal and idler waves. Femtosecond pump–probe experiments are described in which the predissociation of electronically excited Rb2 states in the ~24 000–28 000 cm−1 interval, and the distribution of nascent atomic fragments into Rb excited states (7s, 5d, 6s, 4d and 5p) spanning an energy range >1.25 eV, have been observed in Rb vapour with atomic number densities of ~6 × 1013–3 × 1017 cm−3. Quantum beating at 18.2 THz (corresponding to the Rb 7s–5dJ (J = 5/2) energy defect of ~608 cm−1) is superimposed onto the axially phase matched PFWM signal wave generated at λS ~ 420 nm (Rb 62PJ → 52S1/2 transitions) and recovered by Fourier analysis of the signal wave intensity as the pump–probe time delay (Δt) is scanned. The dominant exit channels for Rb2 predissociation are found to be sensitive to the interval of internuclear separation R in which the molecular wavepacket, produced by the pump pulse through two-photon association of Rb–Rb collision pairs, is localized. Generating Rb2 wavepackets on 3Λu (Λ = Σ, Δ) potential surfaces at large R (~7–9 A) favours the Rb 7s and 5d dissociation channels. In contrast, producing dimer wavepackets localized in the R ~ 3–4 A region suppresses Rb (7s, 5d) generation and favours the production of Rb atomic fragments (primarily 5p) with less internal energy, but maximum velocities of ~15–20 A ps−1. Laser excitation spectroscopy on the nanosecond time scale suggests that the (3)3Δu and (7)3Σ+u states of Rb2 (correlated with Rd (5d) + Rb (6s) in the separated atom limit), and possibly a 3Σ+u state derived from the Rb (7p) + Rb (5s) asymptote, are populated by two-photon absorption of Rb–Rb ground-state collision pairs and predissociation of these levels provides the excited atomic fragments subsequently detected by atomic wavepackets. The data presented here demonstrate the observation of the molecular dissociation transient and the determination of the nascent statistical distribution of atomic product states in a manner that is unencumbered by radiative lifetime or collisional effects. A wavepacket, in tandem with the dipole–dipole interaction and a coherent nonlinear optical process, provides a new avenue for pursuing atom–atom and atom–molecular interactions over a broad range in inter-particle separations.
Wavepackets are excited in rubidium vapor by intense ultrashort (∼100 fs) pulses centered at a wavelength of 620 nm or 770 nm. The generated atomic wavepackets are optically detected via a pump-probe experiment based on axially phase-matched parametric four-wave mixing (FWM). This nonlinear process results in coherent ultraviolet (UV) or violet emission that carries information about the relative number densities of the excited states. The frequency spectrum of the UV/violet signal intensity, recorded while varying the pump-probe time delay, shows the presence of quantum beats between energy levels involved in the FWM process. The time-frequency analysis of that temporal UV/violet data is done by means of the short-time Fourier transform that leads to retrieval of the temporal evolution of amplitude and phase of the quantum beats. The observed dynamics suggest that not only atomic but also molecular ( Rb*2 ) wavepackets are generated, and that the temporal history of the amplitude of the quantum beats reflects the production of the excited atomic fragments of Rb*2 dissociation. More precisely, changes in the Rb excited state number densities alter the third-order nonlinear susceptibility chi(3) of the Rb vapor, which affects generation of the output signal wave by FWM. Dissociation into several product states is detected, and their branching ratios are estimated. Thus, atomic wavepackets, combined with FWM, appear to be a sensitive new multichannel spectroscopic means to study the fundamental process of molecular dissociation.
We demonstrate that atomic wavepackets can serve as sensitive detectors for investigating atomic and molecular dynamics. In concert with parametric four-wave mixing, the interference between coherent superpositions of atomic excited states produced by ultrafast (/spl sim/150 fs) pump and probe pulses provides a new and powerful tool with which fundamental processes, such as molecular dissociation and Rydberg-Rydberg atomic collisions, can be observed with the extraordinary sensitivity afforded by a coherent nonlinear optical process. Experiments are described in which the dissociation of an electronically excited molecule (Rb/sub 2/) and the distribution of atomic fragments into excited states spanning >10 000 cm/sup -1/ are observed. Also, resonant collisions between Rb atoms in the 7s and 5d states are detected by monitoring the shift in the frequency of an atomic wavepacket induced by the dipole-dipole interaction.
Dipole-dipole interactions between excited Rb atoms at long range (approximately 300a0-2150a0) have been observed with molecular wave packets and a coherent nonlinear optical process. Fourier analysis of the parametric four-wave mixing (PFWM) signal wave intensity produced in femtosecond pump-probe experiments demonstrates the appearance of sidebands associated with the Rb 7s-5d(5/2) quantum beating frequency of approximately 18.3 THz. Calculations show that the observed sideband splittings and Fourier domain profiles result from multiple atom, dipole-dipole interactions, and ensembles comprising five or fewer Rb (7s, 6p) atoms account for virtually all of the data.
\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.32]{Fig1.eps} \end{wrapfigure} Coherences at 386.2 THz and 384.1 THz, corresponding to the 5d5/2_{5/2}5/2​ – 5p3/2_{3/2}3/2​ and 5p3/2_{3/2}3/2​ – 5s1/2_{1/2}1/2​ difference frequencies, respectively, have been established in the Rb atom during pump-probe experiments involving pairs of identical ~150 fs pulses produced by a Ti:\chem{Al_2O_3} laser and a Michelson interferometer. The interference between the two coherences within the atom is observed through a parametric four-wave mixing process in Rb and detection of the signal wave intensity at 420 nm. Scanning the time delay between the pump and probe pulses over a 600 ps interval produces a sampling rate over 300 THz and allows for a spectral domain resolution of 0.05 cm−1^{-1}−1 to be achieved. The figure at right shows several spectra recorded near 2.1 THz, the (5d5/2_{5/2}5/2​ – 5p3/2_{3/2}3/2​) - (5p3/2_{3/2}3/2​ – 5s1/2_{1/2}1/2​) difference frequency, with varying angle between the pump and probe pulses (i.e., the phase matching angle) and varying Rb background density. A Fano interference window is clearly observed, and analysis of these and similar spectra demonstrates that the amplitude and phase of the coherently-coupled, three Rb state system can be controlled precisely.
Abstract Coupled oscillators are prevalent in nature and fundamental to fields as disparate as astrophysics, photonics, the mechanical sciences, and geophysics. Theory has identified singularities in the response of coupled oscillators, known as exceptional points (EPs), that are associated with non-Hermitian operators and lie at the transition between weak and strong coupling of the oscillator. Although several EPs have been reported or predicted to exist in nanophotonic resonators and Feshbach resonances, for example, tuning the phase of two interfering atomic or molecular coherences near an EP has not been demonstrated previously. We report the observation of an EP associated with a pair of interfering atomic coherences in Rb, oscillating at 386.3 and 384.2 THz, and confirm the theoretical prediction of an abrupt phase shift of ∼π/4 as the EP is traversed by independently varying two experimental parameters. Pairs (and trios) of coupled coherences in thermal Rb atoms are established among the 7s 1/2, 5d 5/2, 5p 3/2, and 5s 1/2 states in pump–probe experiments with <200 fs laser pulses, and observed directly in the temporal and spectral domains through the ensuing quantum beating in the ∼2–36 THz interval. Interference between the (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences is mediated by the 5p 3/2 state and detected through quantum beating in the vicinity of the (5d 5/2–5p 3/2)–(5p 3/2–5s 1/2) difference frequency of 2.11 THz which is monitored by a parametric four-wave mixing process. Phase of this composite atomic oscillator is first controlled by varying the mean Rb–Rb nearest neighbor distance (⟨R⟩) in a thermalized vapor. A discontinuous transition of (0.8 ± 0.2) ∼ π/4 radians in the phase of the coupled oscillator occurs when ⟨R⟩ is varied over the ∼80–90 nm interval, a phase shift associated with the transformation of a broadband, dissipative oscillator (characterized by a Fano interference window) into a strongly-coupled system resonant at 2.1 THz.