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Frontiers in Optics

Interference Between Coherences at 384 THz and 386.1 THz in Rb Observed at 2.1 THz

Thomas Reboli, James Gary Eden

Published Jan 1, 2023• 0 citations
Publisher

Abstract

Interference between coherences established at 384 and 386 THz in atomic Rb (5d5/2- 5p3/2 and 5p3/2-5s1/2, respectively) is observed at the 2.1 THz difference frequency. Interaction between the two coherences is observed in the spectral domain in the form of a Fano resonance, and the characteristics of the coupled oscillator are described.

DOI
10.1364/fio.2023.jtu4a.17

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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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Physical Review Letters•Oct 5, 2007•41 citations
Interference between coherences established at 384 and 386 THz in atomic Rb (5d5/2- 5p3/2 and 5p3/2-5s1/2, respectively) is observed at the 2.1 THz difference frequency. Interaction between the two coherences is observed in the spectral domain in the form of a Fano resonance, and the characteristics of the coupled oscillator are described.
\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.
We seek to illustrate Fano interference in a classical coupled oscillator by using classical analogues of the atom–laser interaction. We present an analogy between the dressed state picture of coherent atom–laser interaction and a classical coupled oscillator. The Autler–Townes splitting due to the atom–laser interaction is analogous to the splitting of normal-mode frequencies of a coupled oscillator. Using this analogy, we simulate and experimentally demonstrate Fano interference and the associated phenomena in three-level atoms in a coupled electrical resonator circuit. This work aims to highlight analogies between classical and quantum systems for students at the postgraduate and graduate levels. Also, the reported technique can be easily realized in undergraduate laboratories.
We present the experimental observation of the Fano-type interference in a coupled cavity-atom system by confining the laser-cooled 85 Rb atoms in an optical cavity. The asymmetric Fano profile is obtained through quantum interference in a three-level atomic system coherently coupled to a single mode cavity field. The observed Fano profile can be explained by the interference between the intra-cavity dark state and the polariton state of the coupled cavity-atom system. The possible applications of our observations include all-optical switching, optical sensing and narrow band optical filters.
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.