Numerical Study on Quantum Walks Implemented on Cascade Rotational Transitions in a Diatomic Molecule

Matsuoka, Leo; Kasajima, Tatsuya; Hashimoto, Masashi; Yokoyama, Keiichi

doi:10.3938/jkps.59.2897

Cited by 19 publications

(10 citation statements)

References 13 publications

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“…First, we apply the rotating-wave approximation, in which only the slowest oscillating terms are used and other quickly oscillating terms are ignored. We previously used this approximation to find the analogy between consecutive rotational excitation in a pulse train and continuous-time quantum walk (CTQW) [36]. Under a fully resonant condition…”

Section: Mathematical Modeling a Physical Systemmentioning

confidence: 99%

Unified parameter for localization in isotope-selective rotational excitation of diatomic molecules using a train of optical pulses

Matsuoka

2015

Phys. Rev. A

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We obtained a simple theoretical unified parameter for the characterization of rotational population propagation of diatomic molecules in a periodic train of resonant optical pulses.The parameter comprises the peak intensity and interval between the pulses, and the level energies of the initial and final rotational states of the molecule. Using the unified parameter, we can predict the upper and lower boundaries of probability localization on the rotational level network, including the effect of centrifugal distortion. The unified parameter was tentatively derived from an analytical expression obtained by performing rotating-wave approximation and spectral decomposition of the time-dependent Schrödinger equation under an assumption of time-order invariance. The validity of the parameter was confirmed by comparison with numerical simulations for isotope-selective rotational excitation of KCl molecules.

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Section: Mathematical Modeling a Physical Systemmentioning

confidence: 99%

Unified parameter for localization in isotope-selective rotational excitation of diatomic molecules using a train of optical pulses

Matsuoka

2015

Phys. Rev. A

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“…The quantum walks (QWs) were introduced by Aharonov et al [1] as the quantum version of the usual random walks. QWs have been intensively studied from various fields, such as quantum algorithm [9], the topological insulator [3], and radioactive waste reduction [8].…”

Section: Introductionmentioning

confidence: 99%

Localization does not occur for the Fourier walk on the multi-dimensional lattice

Narimatsu¹

2020

Preprint

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“…QWs have been intensively studied from various fields. For example, quantum algorithm [9], the topological insulator [5], and radioactive waste reduction [8].…”

Section: Introductionmentioning

confidence: 99%

The Fourier and Grover walks on the two-dimensional lattice and torus

Asano,

Komatsu,

Konno

et al. 2018

Preprint

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In this paper, we consider discrete-time quantum walks with moving shift (MS) and flip-flop shift (FF) on two-dimensional lattice Z 2 and torus π 2 N = (Z/N ) 2 . Weak limit theorems for the Grover walks on Z 2 with MS and FF were given by Watabe et al. and Higuchi et al., respectively. The existence of localization of the Grover walks on Z 2 with MS and FF was shown by Inui et al. and Higuchi et al., respectively. Non-existence of localization of the Fourier walk with MS on Z 2 was proved by Komatsu and Tate. Here our simple argument gave non-existence of localization of the Fourier walk with both MS and FF. Moreover we calculate eigenvalues and the corresponding eigenvectors of the (k1, k2)-space of the Fourier walks on π 2 N with MS and FF for some special initial conditions. The probability distributions are also obtained. Finally, we compute amplitudes of the Grover and Fourier walks on π 2 2 .

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Numerical Study on Quantum Walks Implemented on Cascade Rotational Transitions in a Diatomic Molecule

Cited by 19 publications

References 13 publications

Unified parameter for localization in isotope-selective rotational excitation of diatomic molecules using a train of optical pulses

Unified parameter for localization in isotope-selective rotational excitation of diatomic molecules using a train of optical pulses

Localization does not occur for the Fourier walk on the multi-dimensional lattice

The Fourier and Grover walks on the two-dimensional lattice and torus

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