Quantum control and pathway manipulation in rubidium

Abstract

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 narrowband and broadband ultrafast fields. In the perturbation regime, two 2nd-order quantum pathways connecting the Rb states 5S 1/2 and 5D 3/2 dominate the dynamics, namely 5S 1/2 →5P 3/2 →5D 3/2 (pathway 1) and 5S 1/2 →5P 1/2 →5D 3/2 (pathway 2). For narrowband field control, the analysis is carried out in the time domain with the laser field including only four narrowband-envelope sub-pulses 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 5S 1/2 → 5P 3/2 and 5P 3/2 → 5D 3/2. For broadband field control, the dynamics are treated in the frequency domain with the laser field including both resonant and continuous non-resonant 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 π 2 step scheme can increase the dynamic range of the ratio between the two pathway amplitudes by a factor of ∼ 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.

Selective Excitation on Tip-Enhanced Raman Spectroscopy by Pulse Shaping Femtosecond Laser

“…Coherent control was intensely studied in the application of selective excitation of Raman scattering by shaping the ultrafast pump and Stokes laser pulses [19][20][21][22][23][24][25][26][27]. In the following, we theoretically study how to achieve a high degree selective excitation of two Raman peaks among three excited states.…”

“…An effective method for the coherent control of Raman scattering is femtosecond pulse shaping technique, where the laser spectral phase and/or amplitude were modulated to achieve the constructive/destructive interference between different path integral leading to expected/depressed outcomes [19][20][21][22][23][24][25][26][27]. This method was widely used in controlling molecular vibration state, rotation state, ionization state, isomerization, and other molecule dynamics.…”

Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions

“…We provide a method for obtaining a good approximation for a large number of identical copies of |ψ in the following proposition, which is an application of noncommutative union bound [37]. The proof of the proposition is presented in Appendix C.…”

“…Proposition 10 is proven by using the noncommutative union bound for sequential projections presented in Ref. [37] stated as the following Lemma.…”

Identifying a cooperative control mechanism between an applied field and the environment of open quantum systems

“…The Hamiltonian-encoding and observabledecoding (HE-OD) methodology has provided a feasible means for systematic mechanism extraction in closed quantum systems [18][19][20][21][22][23][24][25][26]. Within HE-OD, a quantum pathway is defined as a set of physically relevant transitions connecting an initial to a final state(s), and the associated pathway amplitudes each have a modulus and phase extracted from the Dyson expansion that quantifies the pathway's importance in the underlying dynamics [18,27]. The mechanism extracted through the HE-OD procedure is given as the set of pathway amplitudes of significant magnitude.…”