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Physical Review A

Quantum interference control of a four-level diamond-configuration quantum system

Han-gyeol Lee, Hyosub Kim, Jongseok Lim, Jaewook Ahn

Published Nov 27, 2013• 18 citations
Publisher

Abstract

We investigate coherent control of the two-photon transition pathways of a four-level atomic system in a diamond configuration. When an ultrashort laser pulse interacts with this system in the ground state $5{S}_{1/2}$ of rubidium, the two-photon transition probability amplitude of $5{D}_{3/2}$ is obtained by a summation of all possible resonant and nonresonant two-photon transition probability amplitudes via $5{P}_{1/2}$ and $5{P}_{3/2}$. Second-order perturbation theory predicts that the maximal constructive interference of the transition probability amplitudes occurs when the phases of eight different spectrum blocks satisfy four different phase relations. Experiments carried out with spectrally phase-coded laser pulses show good agreement with the theoretical prediction.

DOI
10.1103/physreva.88.053427

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We investigate coherent control of the two-photon transition pathways of a four-level atomic system in a diamond configuration. When an ultrashort laser pulse interacts with this system in the ground state 5S1/25{S}_{1/2}5S1/2​ of rubidium, the two-photon transition probability amplitude of 5D3/25{D}_{3/2}5D3/2​ is obtained by a summation of all possible resonant and nonresonant two-photon transition probability amplitudes via 5P1/25{P}_{1/2}5P1/2​ and 5P3/25{P}_{3/2}5P3/2​. Second-order perturbation theory predicts that the maximal constructive interference of the transition probability amplitudes occurs when the phases of eight different spectrum blocks satisfy four different phase relations. Experiments carried out with spectrally phase-coded laser pulses show good agreement with the theoretical prediction.
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.
Two-photon absorption (TPA) is an important quantum process in the light-matter interaction. When more than one TPA pathway exists in a quantum system, it is necessary to utilize the interference of these pathways to increase the sum TPA amplitude. A simple block scheme (Phys. Rev. A 2013, 88, 053427) is proposed to maximize the constructive interference of two TPA pathways in a four-level diamond-configuration quantum system. It can also be expanded to control multiple TPA pathways (Chin. J. Chem. Phys. 2015, 28, 426). The spectral boundaries in the scheme is related to the energy structure of the system. This work tries to give an analysis of the boundaries for general four-level and five-level quantum systems, which have two and three TPA pathways, respectively. How the boundaries and thus the number of blocks change with the energy structure will be explored.
This study investigates the phase-dependent behaviour of the four-level closed-loop atomic diamond configuration. A ground state is quasi-resonantly coupled to two intermediate states which are themselves coupled to an excited state. Transitions between any two states occur via two alternative paths. The interference between these transition amplitudes can be constructive or destructive, depending on the relative phase between the excitation amplitudes. As a consequence also the population as well as the one- and two-photon coherences are periodic functions of the relative phase. This phase in general comprises the wavevector mismatch, the two-photon detuning, the initial laser phases and the individual atomic-dipole phases. In this paper, the authors concentrate on the steady state solutions for the case of two-photon resonance. The behaviour of the system is determined by the concurrence of the phase-dependent Hamiltonian dynamics and the relaxation processes.
We analyze the behavior of a four-state, two-path atomic interferometer driven by shaped ultrafast laser pulses. The laser pulses interact with atomic rubidium, exciting the atoms to the 5D5D5D state via two intermediate resonances (the 5P1/25{P}_{1/2}5P1/2​ and 5P3/25{P}_{3/2}5P3/2​). The relative phase of the two paths can be modified by applying a varying spectral phase at the wavelength corresponding to one of the resonant transitions for each pathway. We trace out the behavior of the system from the simplest case of weak-field excitation with resonant fields to strong-field excitation with a broadband source. Our measurements and analysis reveal that while interference is observed for all field strengths and spectral widths, the character of the interference changes substantially.
Abstract The dynamics of two two-photon absorption (TPA) pathways in a four-level quantum system driven by a laser pulse is investigated in this work. An analytical solution for pulse shaping is proposed to be globally optimal for constructive interference between the two pathways, and accurate spectral boundaries for phase modulation are obtained. The TPA rate can be enhanced by a factor of 8.33 with the optimal pulse instead of the transform limited pulse (TL pulse). Simple control strategies modulating both amplitudes and phases are also designed to increase the TPA amplitude along one pathway while decreasing that along the other simultaneously. The strategies are intuitive and the two pathway amplitudes can differ by two orders of magnitude.
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.