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Study of wavepacket dynamics in rubidium vapor by means of time-frequency analysis

Andrey A. Senin

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

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.

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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.

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Wavepackets formed from the ns and (n-2)d states of Rb and K (n equals 8 for K, 11 and 12 for Rb) have been observed by four wave mixing in pump-probe experiments. The temporal behavior of the wavepacket is observed by monitoring the coherent ultraviolet radiation generated near the alkali mp 2P yields 2S1/2 resonance transitions (7 <EQ m <EQ 12 for Rb) when a approximately 100 fs, red probe pulse ((lambda) approximately 620 nm) is scattered by the wavepacket established by an earlier (identical) pump pulse. The spatial and spectral characteristics of the ultraviolet emission are well-described by axially phase-matched, four wave mixing and all of the prominent frequency components of the wavepackets are associated with energy differences between pairs of excited states for which (Delta) l equals 0 or 2. These results demonstrate that the wavepacket modulates (chi) (3) of the medium, thus rendering the wavepacket detectable.

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Experiments have been carried out in which atomic wavepackets produced on the /spl sim/100 fs time scale interact with a 4-wave mixing process in Rb or K vapor to produce spatially and temporally coherent pulses of UV radiation. Wavepackets are produced by coherently exciting the 9 d, 10 d, 11 s, and 12 s states ensemble of Rb with red (/spl sim/625 nm) pulses from an amplified CPM system. Two pulses of approximately equal energy (/spl sim/75 /spl mu/J) are produced in a beamsplitter and one delayed in time with respect to the other by a delay stage in one leg of a Michelson interferometer.

IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)•Dec 24, 2002•2 citations
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 ( Rb2 ) wavepackets are generated, and that the temporal history of the amplitude of the quantum beats reflects the production of the excited atomic fragments of Rb2 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.
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.
The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7</=m</=12 for Rb; 5</=m</=7 for K) resonance transitions when a probe pulse is scattered by the wave packet established by the earlier (identical) pump pulse. The spatial and spectral characteristics of the UV emission are well described by axially phase-matched four-wave mixing, and all the prominent frequency components of the wave packets are associated with energy differences between pairs of excited states for which Diota=0 or Diota=2 . These results demonstrate that the wave packet modulates chi((3))of the medium, thus rendering the wave packet detectable.
Ultrafast laser pump-probe techniques have been used to study the rovibrational dynamics of the B, C, and D states of the Cesium dimer and to study atomic wavepackets and nonlinear effects in Rubidium and Potassium. Two color, pump-probe techniques have been used to probe the time evolution of wavepackets in the B, C, and D rovibrational levels of Cs$\sb2$. The temporal history of the wavepacket is inferred from the time and energy-integrated photoelectron signal produced when the excited state is photoionized by a time-delayed probe pulse. Oscillatory motion is observed in the photoionization signals, corresponding to the vibrational energy differences of the state begin studied. The period of oscillation ranges between 2.2 and 1.1 ps depending on the state. Quantum mechanical simulations of the wavepacket motion show excellent agreement with the experimental data. Experiments have been carried out in which atomic wavepackets interact with a four-wave mixing process in Rb and K to produce spatially and temporally coherent pulses of UV radiation. Wave packets are produced by coherently exciting an ensemble of states using the broad bandwidth of a femtosecond pulse. Oscillations corresponding to the energy differences between the levels in the wavepacket are superimposed on the UV signal when two identical pump and delayed probe pulses are introduced into the alkali vapor. Analyses of the UV emission line profiles show excellent agreement with the four-wave mixing process.
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.
Wavepackets formed from the ns and (n-2)d states of Rb and K (n equals 8 for K, 11 and 12 for Rb) have been observed by four wave mixing in pump-probe experiments. The temporal behavior of the wavepacket is observed by monitoring the coherent ultraviolet radiation generated near the alkali mp 2P yields 2S1/2 resonance transitions (7 <EQ m <EQ 12 for Rb) when a approximately 100 fs, red probe pulse ((lambda) approximately 620 nm) is scattered by the wavepacket established by an earlier (identical) pump pulse. The spatial and spectral characteristics of the ultraviolet emission are well-described by axially phase-matched, four wave mixing and all of the prominent frequency components of the wavepackets are associated with energy differences between pairs of excited states for which (Delta) l equals 0 or 2. These results demonstrate that the wavepacket modulates (chi) (3) of the medium, thus rendering the wavepacket detectable.
Experiments have been carried out in which atomic wavepackets produced on the /spl sim/100 fs time scale interact with a 4-wave mixing process in Rb or K vapor to produce spatially and temporally coherent pulses of UV radiation. Wavepackets are produced by coherently exciting the 9 d, 10 d, 11 s, and 12 s states ensemble of Rb with red (/spl sim/625 nm) pulses from an amplified CPM system. Two pulses of approximately equal energy (/spl sim/75 /spl mu/J) are produced in a beamsplitter and one delayed in time with respect to the other by a delay stage in one leg of a Michelson interferometer.