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arXiv:1601.07786 · Physical Review A

Coherent population oscillation produced by saturating probe and pump fields on the intercombination line

Azar Vafafard, Mohammad Mahmoudi, G. S. Agarwal

Published Mar 28, 2016• 5 citations
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Abstract

We present a theoretical study of the experiments on coherent population oscillations and coherent population trapping on the intercombination line of $^{174}\mathrm{Yb}$. The transition involves a change of the spin and thus can not be interpreted in terms of an effective lambda system. The reported experiments are done in the regime where both pump and probe fields can saturate the transition. We demonstrate, by both numerical and analytical calculations, the appearance of the interference minimum as both pump and probe start saturating the transition. We present an analytical result for the threshold probe power required for the interference minimum to appear. We also present a detailed study of the appearance of the interference minimum when magnetic fields are applied. The magnetic fields not only create Zeeman splittings, but in addition make the system open because of the couplings to other levels. We show the possibility of interference minimums at the position of subharmonic resonances.

DOI
10.1103/physreva.93.033848

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We present a theoretical study of the experiments on coherent population oscillations and coherent population trapping on the intercombination line of 174Yb^{174}\mathrm{Yb}174Yb. The transition involves a change of the spin and thus can not be interpreted in terms of an effective lambda system. The reported experiments are done in the regime where both pump and probe fields can saturate the transition. We demonstrate, by both numerical and analytical calculations, the appearance of the interference minimum as both pump and probe start saturating the transition. We present an analytical result for the threshold probe power required for the interference minimum to appear. We also present a detailed study of the appearance of the interference minimum when magnetic fields are applied. The magnetic fields not only create Zeeman splittings, but in addition make the system open because of the couplings to other levels. We show the possibility of interference minimums at the position of subharmonic resonances.
Abstract We study coherent population oscillations in an odd isotope of the two-electron atom Yb. The experiments are done using magnetic sublevels of the F g = 5 / 2 → F e = 3 / 2 hyperfine transition in 173 Yb of the 1 S 0 → 3 P 1 intercombination line. The experiments are done both with and without an applied magnetic field. In the absence of an applied field, the complicated sublevel structure along with the saturated fluorescence effect causes the linewidth to be larger than the 190 kHz natural linewidth of the transition. In the presence of a field (of magnitude 330 mG), a well-defined quantization axis is present which results in the formation of two M-type systems. The total fluorescence is then limited by spin coherence among the ground sublevels. In addition, the pump beam gets detuned from resonance which results in a reduced scattering rate from the 3 P 1 state. Both of these effects result in a reduction of the linewidth to a subnatural value of about 100 kHz.
Quantum interference has been predicted to occur in a three-level Λ system with near-degenerate dipole allowed transitions, which are coupled to the same linearly polarized incoherent field. For the Λ system with two degenerate lower levels, we show that (a) quantum interference of incoherent pump processes leads to coherent population trapping (CPT), and (b) when two coherent fields are applied to two transitions on two-photon resonance, CPT appears when the amplitudes and phases of the applied coherent fields and the polarization angle of the incoherent field satisfy certain conditions. Further, the physical mechanism and the above conditions for CPT are presented.
We present a general formalism for studying the interaction between laser fields and degenerate-Zeeman-sublevel atoms correct up to the first order in the weak probe field. We derive from this theory the equations of motion for a \ensuremath{\Lambda}-type system involving S1/2{\mathit{S}}_{1/2}S1/2​, F=2\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1\ensuremath{\leftrightarrows}S1/2{\mathit{S}}_{1/2}S1/2​, F=1 transitions in 87Rb^{87}\mathrm{Rb}87Rb atoms. These equations are used to numerically investigate the coherent population trapping (CPT) schemes in the S1/2{\mathit{S}}_{1/2}S1/2​, F=2\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1 transition induced by a linearly polarized pumping field and the electromagnetically induced transparency exhibited in the weak probe spectrum in the S1/2{\mathit{S}}_{1/2}S1/2​, F=1\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1 transition. We discuss the effects of the CPT on the probe spectrum with and without the Doppler broadenings by comparing the probe spectrum derived from the real system with that derived from an ideal \ensuremath{\Lambda}-type system. We show that the atoms in the CPT states are shielded from interacting with the probe field while those in the absorbent states make contributions to the weak probe by the Raman anti-Stokes process, and the effect of the real system on the probe field becomes equivalent to the ideal \ensuremath{\Lambda} system only in the strong CPT parameter regime. \textcopyright{} 1996 The American Physical Society.
Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We investigate coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.