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Chinese Journal of Chemical Physics

Coherent Control of Multiple 2nd-Order Quantum Pathways

Fang Gao, Yao-xiong Wang, Dewen Cao, Feng Shuang

Published Aug 1, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1674-0068/28/cjcp1506124

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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.
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 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.
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.
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.
A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).