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Quantum beat observations in rubidium vapor

Brian J. Ricconi

Published Jun 27, 2012• 1 citation
OpenAlex

Abstract

Probing the interactions between a mode-locked laser pulse and saturated rubidium vapor with a pump–probe technique has resulted in observations of coherences within the atom that persist longer than 150 ps. Quantum beats due to the interference between the 7S and 5D_{5/2} energy states were observed by a four-wave mixing process. The difference frequency between the 5D–5P_{3/2} and the 5P_{3/2}–5S transitions was also observed for interpulse delays up to 180 ps. The temporal evolution of the beat amplitude indicates the existence of a superfluorescent process and a scattering process detected simultaneously with the four-wave mixing process. A model was developed to explain the processes and was used to predict the range of pulse parameters for which the scattering process and four-wave mixing could be simultaneously detected.

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Interference between atomic Rb (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences: observation of an exceptional point by quantum beating at ∼2.1 THz

William Goldshlag, R Su, Sehyun Park +2 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 2, 2021•3 citations

Free Precession Beat of Two-Photon Induced Coherence in Atomic Rubidium Vapor

Hiroki Nakatsuka, Jumpei Okada, Masahiro Matsuoka

Free precession beat of two-photon induced coherence was observed by the use of delayed probe pulses in atomic rubidium vapor. The two-photon coherence was created in the superposition state of the 5S 1/2 and 5D 5/2 levels of Rb by two-photon resonant excitation with a mode-locked dye laser pulse. The origin of the beat is attributed to the hyperfine splittings of the 5S 1/2 ground state of both Rb 85 and Rb 87 . The observed results are explained by a theory presented in this paper.

Journal of the Physical Society of Japan•May 1, 1981•0 citations

INTERFERENCE BETWEEN THE 5d5/2 – 5p3/2 AND 5p3/2 – 5s1/2 COHERENCES (386.4 AND 384.1 THz) IN Rb OBSERVED BY ULTRAFAST FOUR-WAVE MIXING SPECTROSCOPY

Thomas Reboli, J. Eden

\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.

International Symposium on Molecular Spectroscopy (ISMS)•Jun 23, 2022•0 citations

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

Andrey A. Senin

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.

•Jan 1, 2003•0 citations

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 +1 more

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.

Optics Letters•Jan 1, 1998•26 citations

Switching from a sequential transition to quantum beating in atomic rubidium pumped by a femtosecond laser

Gombojav O. Ariunbold, Vladimir A. Sautenkov, Marlan O. Scully

We demonstrate temporal coherent control in two-photon transitions. A pair of broadband (Δλ∼20nm), ultrashort (Δt∼100fs), collinear pulses with a variable time delay excites the rubidium atoms into the 5D state from the 5S ground state where the two-photon transitions are enhanced by the intermediate level 5P. The excited atoms radiate 5μm (5D–6P) and 420nm (6P–5S) light. As a result of tuning the wavelength of the input laser, a superfluorescence at 420nm exhibits different temporal behaviors. A switching from a beating at the frequency given by the difference between the sequential atomic transitions that involve the 5P3/2 intermediate level, to a quantum beating due to two different two-photon excitation paths, 5S→5P1/2→5D and 5S→5P3/2→5D is observed. Based on the simple atom-field interaction theory, an analytic solution, which qualitatively elucidates experimental results, is obtained.

Journal of the Optical Society of America B•Feb 18, 2011•11 citations
Probing the interactions between a mode-locked laser pulse and saturated rubidium vapor with a pump–probe technique has resulted in observations of coherences within the atom that persist longer than 150 ps. Quantum beats due to the interference between the 7S and 5D_{5/2} energy states were observed by a four-wave mixing process. The difference frequency between the 5D–5P_{3/2} and the 5P_{3/2}–5S transitions was also observed for interpulse delays up to 180 ps. The temporal evolution of the beat amplitude indicates the existence of a superfluorescent process and a scattering process detected simultaneously with the four-wave mixing process. A model was developed to explain the processes and was used to predict the range of pulse parameters for which the scattering process and four-wave mixing could be simultaneously detected.
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.
\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.
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.
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.
We demonstrate temporal coherent control in two-photon transitions. A pair of broadband (Δλ∼20nm), ultrashort (Δt∼100fs), collinear pulses with a variable time delay excites the rubidium atoms into the 5D state from the 5S ground state where the two-photon transitions are enhanced by the intermediate level 5P. The excited atoms radiate 5μm (5D–6P) and 420nm (6P–5S) light. As a result of tuning the wavelength of the input laser, a superfluorescence at 420nm exhibits different temporal behaviors. A switching from a beating at the frequency given by the difference between the sequential atomic transitions that involve the 5P3/2 intermediate level, to a quantum beating due to two different two-photon excitation paths, 5S→5P1/2→5D and 5S→5P3/2→5D is observed. Based on the simple atom-field interaction theory, an analytic solution, which qualitatively elucidates experimental results, is obtained.