Quantum control in two-dimensional Fourier-transform spectroscopy

Jongseok Lim, Han-gyeol Lee, Sangkyung Lee, and Jaewook Ahn

Phys. Rev. A 84, 013425 – Published 28 July 2011

Abstract

We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a $V$ -type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5 $P$ $_{1 / 2} \to$ 5 $P$ $_{3 / 2}$ transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.

Received 2 September 2010

DOI:https://doi.org/10.1103/PhysRevA.84.013425

Authors & Affiliations

Jongseok Lim, Han-gyeol Lee, Sangkyung Lee, and Jaewook Ahn

Department of Physics, KAIST, Daejeon 305-701, Korea

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Vol. 84, Iss. 1 — July 2011

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Images

Figure 1
(a) Schematic diagram of the pulse-shaping scenario. The first pulse has a spectral hole around the $D_{2}$ ( $| g 〉 \to | b 〉$ ) transition, and the second pulse is shaped to control the $| a 〉 \to | b 〉$ transition. The third pulse is unshaped. (b) Energy level diagram of atomic rubidium.Reuse & Permissions
Figure 2
Chirped pulse control of $| a 〉 \to | b 〉$ transition: (a) positive chirp case; (b) negative chirp case. Depending on the chirp sign, the sequence of $D_{1}$ and $D_{2}$ transitions is time reversed. The circled numbers indicate the transition sequence. (c),(d) Numerical calculation of the time evolution of $5 S_{1 / 2}$ (blue line), $5 P_{1 / 2}$ (dashed line), and $5 S_{3 / 2}$ (red line) populations as well as the field envelope (solid black line), corresponding to (a) and (b), respectively.Reuse & Permissions
Figure 3
(a)–(e) Experimental results of the 2D measurement of $P_{b}$ as a function of $τ_{1}$ and $τ_{2}$ (column I) and their 2D FT spectra $S$ ( $ω_{1}$ , $ω_{2}$ ) (column II) for shaped pulses with five different chirp coefficients: (a) $-$ 1000 fs $^{2}$ , (b) $-$ 500 fs $^{2}$ , (c) 0 fs $^{2}$ , (d) 500 fs $^{2}$ , and (e) 1000 fs $^{2}$ . The peaks at ( $ω_{a g} - ω_{0}$ , $ω_{b g} - ω_{0}$ ) are marked by white arrows which represent the target two-photon process 5 $P$ $_{1 / 2} \to$ 5 $P$ $_{3 / 2}$ . (f) Extracted peak amplitudes at ( $ω_{a g} - ω_{0}$ , $ω_{b g} - ω_{0}$ ) plotted as a function of chirp of the second pulses (circles) are compared with the numerical calculation of $β_{b a}^{(2)}$ (line).Reuse & Permissions
Figure 4
(a) Experimental and theoretical results for the quantum interference engineering. Dots, measured transition-amplitude absolutes; dashed line, numerical calculation based on Eq. (9); solid line, numerical calculation considering the spectrally smeared phase (see the text). Inset, upper left: The phase diagram for the three transition components in Eq. (10). Inset, lower right: The laser spectrum in the block spectral phase in which the block spectral phase $φ_{b}$ represents the relative phase of the spectral region in $[ω_{a g}, ω_{b g}]$ with respect to the other. (b)–(d) The phase diagrams for the maximal (b),(d) and minimal (c) quantum interference conditions.Reuse & Permissions
Figure 5
Coherent enhancement experiment of the 5 $P$ $_{1 / 2} \to$ 5 $P$ $_{3 / 2}$ transition of Rb by spectral amplitude shaping. The measured transition-probability amplitudes, normalized to the full spectrum limit (dots), are plotted along with the calculated data (dark line) as a function of the cutoff wavelength. The laser spectrum is shown by the gray line. The inset illustrates the spectral shape used in the experiment. The dashed lines are the $D_{1}$ and $D_{2}$ resonant wavelengths.Reuse & Permissions

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