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arXiv:1710.03387 · Optics Express

Ultrafast spatial coherent control methods for transition pathway resolving spectroscopy of atomic rubidium

Minhyuk Kim, Kyungtae Kim, Dewen Cao, Fang Gao, Feng Shuang, Jaewook Ahn

Published Jan 12, 2018• 2 citations
arXivHTMLPDF

Abstract

-5D pathways, both simultaneously and at distinct spatial locations. Three different pulse-shaping solutions are introduced that combine amplitude shaping, which avoids direct intermediate resonances, and phase programming, which enables the remaining spectral components to be coherently interfered through the targeted transition pathways. Experiments were performed with a room-temperature vapor cell, and the results agree well with theoretical analysis.

DOI
10.1364/oe.26.001324

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-5D pathways, both simultaneously and at distinct spatial locations. Three different pulse-shaping solutions are introduced that combine amplitude shaping, which avoids direct intermediate resonances, and phase programming, which enables the remaining spectral components to be coherently interfered through the targeted transition pathways. Experiments were performed with a room-temperature vapor cell, and the results agree well with theoretical analysis.
The spatial coherent control of resonant two-photon transitions in atomic rubidium using counter-propagating ultra-short laser pulses is investigated in this work. There are two transition pathways involved in the spatial excitation pattern. A special pulse shaping scheme is designed to distinguish their individual contribution. The scheme consists of a n-step function flipping at the poles and zeros of the transition amplitude function and two segmented linear function with different slopes, and it can make the desired transition pathway dominate at the assigned spatial position. The simulations show that our scheme is quite effective compared to the previous single linear shaping scheme.
We have investigated multiphoton-ionization passages of rubidium atoms initiated from the excited 5P3/25{P}_{3/2}5P3/2​ energy state. For this we used coherent control schemes based on femtosecond laser pulse shaping applied to cold atoms spatially isolated in a magneto-optical trap. With programed laser pulses of spectral $\ensuremath{\pi}$-phase step, of which location was varied within the laser spectrum, the sequential two-photon-ionization passage along the 5P3/25{P}_{3/2}5P3/2​-5D5D5D continuum was probed in terms of trap-loss spectroscopy. The coherent control two-photon-ionization method unveiled not only the resonantly enhanced two-photon ionization but also the asymmetric nature of the ionization profile structure given as a function of the spectral phase step location. Experimental results show good agreement with the second-order perturbation calculation of the constituent possible ionization passages.
There is an increasing interest in the extraction and control of the interfering quantum pathway amplitudes induced by control fields during laser-matter interactions. The Hamiltonian-encoding and observable-decoding (HE-OD) technique has been introduced for extracting the amplitudes of the pathways present in the dynamics and has recently been experimentally applied to the pathway manipulation of atomic rubidium. This paper theoretically explores various strategies for manipulating pathway amplitudes in the context of a laser field interacting with a multilevel system similar to atomic rubidium for both narrow-band and broadband ultrafast fields. In the perturbation regime, two second-order quantum pathways connecting the Rb states 5S1/25{S}_{1/2}5S1/2​ and 5D3/25{D}_{3/2}5D3/2​ dominate the dynamics, namely, $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 1) and $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{1/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 2). For narrow-band field control, the analysis is carried out in the time domain with the laser field including only four narrow-band envelope subpulses centered at the resonant frequencies. When the two pathways cooperate constructively, temporal oscillations appear in the ratio of the two pathway amplitudes, and we conclude in this case that the period corresponds to the detuning between transitions $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}$ and $5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$. For broadband field control, the dynamics are treated in the frequency domain with the laser field including both resonant and continuous nonresonant frequency components. Various control strategies based on manipulating the phase of selected spectral components are tested. Compared to the outcome from a transform limited pulse, a $\frac{\ensuremath{\pi}}{2}$ step scheme can increase the dynamic range of the ratio between the two pathway amplitudes by a factor of $\ensuremath{\sim}3$. A scheme that manipulates eight spectral blocks, in which the spectral boundaries depend on the resonant frequencies, can increase the ratio by several orders of magnitude. Numerical simulations show that further dividing the spectrum into hundreds of evenly spaced blocks does not significantly enhance the pathway ratio over the eight-block scheme. The quantum control of pathways investigated in this work provides valuable insights on how to incorporate known information about the structure of quantum systems for the effective reduction of quantum control complexity.
We describe optimized coherent control methods for two-photon transitions in atoms of a ladder-type three-state energy configuration. Our approach is based on the spatial coherent control scheme, which uses counterpropagating ultrashort laser pulses to produce complex excitation patterns in an extended space. Because coherent control requires constructive interference of constituent transition pathways, applying it to an atomic transition with a specific energy configuration requires specially designed laser pulses. We show in an experimental demonstration that two-photon transition with an intermediate resonant energy state can be coherently controlled and retrieved from the resonance-induced background, when phase flipping of the laser spectrum near the resonant intermediate transition is used. A simple reason for this behavior is the fact that the transition amplitude function (added to give an overall two-photon transition) changes its sign at the intermediate resonant frequency and, thus, by proper spectral-phase programing, the excitation patterns (or the position-dependent interference of the transition given as a consequence of the spatial coherent control) can be well isolated in space along the focal region of the counterpropagating pulses.
The manipulation of two 2nd-order quantum pathways has been successfully demonstrated experimentally in atomic Rubidium. This work would explore the coherent control of pathways in the quantum system with N intermediate states connecting the initial and target states. A 4N-block scheme is proposed to control the N 2nd-order pathways which are driven by a weak broadband pulse. The model with N=3 is given as an example to demonstrate our strategy. In this scheme, boundaries of the spectral blocks are functions of the resonant frequencies, and the resonant and non-resonant contributions interfere mutually to achieve the quantum pathway control effectively. The simple strategy may provide a practical choice for pathway manipulation experiments since there are only 2N phase variables to adjust.