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Optics Letters

Interaction of atomic wave packets with four-wave mixing:?detection of rubidium and potassium wave packets by coherent ultraviolet emission

Henry Tran, P. C. John, Ju Gao, J. Gary Eden

Published Jan 1, 1998• 26 citations
Publisher

Abstract

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.

DOI
10.1364/ol.23.000070

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Coherent ultraviolet generated by wave packets interacting with χ(3)in Rb and K atoms

Ju Gao, Henry Tran, P. C. John +1 more

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 29, 1998•0 citations

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

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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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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.

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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.

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Summary form only given. Recently, the detection of atomic wavepackets in alkali vapor by monitoring the coherent UV light produced by four-wave mixing was reported. In the pump-probe experiments reported here, the dynamical behavior of wavepackets in Rb has been observed by monitoring the evolving frequency composition of the wavepacket.

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We show that quantum beating appears in the intensity of Stokes and uv radiation generated via hyper-Raman scattering (HRS) and four-wave mixing (FWM), respectively, when a large number of close-lying upper states of atoms or molecules is excited by two-photon interaction with consecutive ultrashort laser pulses. The quantum beating at frequencies correlated with the energy difference between atomic states results from a Ramsey-like interference of atomic wave packets created by the pump and probe laser fields. We reveal that the destructive interference between HRS and FWM is superimposed on the wave packet interference, leading to substantial enhancement of the beating fringe visibility. We examine the effect of laser phase fluctuations and show that they strongly limit the number of beating modes. An analytical solution of transient Maxwell-Bloch equations is obtained, and the oscillatory dependence of uv emission on the delay between two laser pulses is revealed, allowing atomic wave packets to be detected optically. A comparison to available pump-probe experiments is made.

Physical Review A•Nov 3, 2008•4 citations
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.
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.
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.
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.
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 show that quantum beating appears in the intensity of Stokes and uv radiation generated via hyper-Raman scattering (HRS) and four-wave mixing (FWM), respectively, when a large number of close-lying upper states of atoms or molecules is excited by two-photon interaction with consecutive ultrashort laser pulses. The quantum beating at frequencies correlated with the energy difference between atomic states results from a Ramsey-like interference of atomic wave packets created by the pump and probe laser fields. We reveal that the destructive interference between HRS and FWM is superimposed on the wave packet interference, leading to substantial enhancement of the beating fringe visibility. We examine the effect of laser phase fluctuations and show that they strongly limit the number of beating modes. An analytical solution of transient Maxwell-Bloch equations is obtained, and the oscillatory dependence of uv emission on the delay between two laser pulses is revealed, allowing atomic wave packets to be detected optically. A comparison to available pump-probe experiments is made.