Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

Schatz, Konrad; Friedrich, Břetislav; Becker, Simon F.; Schmidt, Burkhard

doi:10.1103/physreva.97.053417

Cited by 13 publications

(11 citation statements)

References 75 publications

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“…. compatible with the selection rule ∆J = ±1, whereas the peaks in the spectra of alignment, (48), appear at 0, 6, 10, . .…”

Section: Field-free Orientation and Alignment Due To δ-Kicksmentioning

confidence: 81%

“…Although our study is chiefly analytic concentrating on the effects of ultra-short pulses (or δ-pulses), it also offers numerical solutions to the corresponding Schrödinger equation involving finite-width pulses. We note that quasi-analytic solutions of the time-independent Schrödinger equation for the combined fields have been recently investigated via supersymmetric quantum mechanics [44][45][46][47] and its complex-plane variant [48]. This paper is organized as follows: In Section II, we introduce the general Hamiltonian of a 3D linear rotor under combined orienting and aligning interactions, the time-dependent Schrödinger equation (TDSE), and the analytic and numerical approaches to solving the TDSE.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Mirahmadi

Schmidt

Karra

et al. 2018

The Journal of Chemical Physics

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We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, ∆τ , with respect to the rotational period of the rotor, τ r . In the sudden, non-adiabatic limit, ∆τ τ r , we derive analytic expressions for the rotor's wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding timedependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, ∆τ τ r , where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of populations quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit a sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration. * burkhard.schmidt@fu-berlin.de † bretislav.friedrich@fhi-berlin.mpg.de arXiv:1806.11329v3 [quant-ph] 9 Aug 2018 basis set for expanding the time-dependent wavefunction, with the resultwhere E J = J(J + 1). Note that the expansion coefficients, C J J 0 ,M 0 , are time-independent, in consequence of the fact that the time dependence in Eq. (10) only arises from the e −iJ 2 τ term.The final form of the wavefunction in the sudden limit is given by (for a detailed derivationare the Clebsch-Gordan coefficients and only c J is a function of the kick strengths, cf. Eq. (A5).Throughout the remainder of this paper, we restrict ourselves to the case when the free rotor is initially in its ground state, J 0 = M 0 = 0. As a result, the C J J 0 ,M 0 coefficients in Eq. (11) reduce toThe coefficients C J J 0 ,M 0 arising in Eq. (11) can be found by expanding the time-independent term in Eq. (10) in terms of spherical harmonics,with Γ the gamma function; we applied the Legendre duplication formula [49] to achieve the final form of Eq. (A4).By making use of Eq. (A2) and Eq. (A5) we can evaluateC J J 0 ,M 0 in Eq. (A1) as follows,where J 1 M 1 , J 2 M 2 |J 3 M 3 are the Clebsch-Gordan coefficients, which vanish unless |J −J 0 | ≤ J ≤ J + J 0 and J + J + J 0 is an even integer [49]. Finally, we obtainIn all the analytic results presented in this paper, Eqs. (A5) and (A7) were found to converge satisfactorily for κ and J up to 80 and 50, respectively (e.g. for P η = P ζ = 8 the 80th term of the sum over k in Eq. (A5) is close to 10 −30 for C 50 0,0 ≈ 1...

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“…. compatible with the selection rule ∆J = ±1, whereas the peaks in the spectra of alignment, (48), appear at 0, 6, 10, . .…”

Section: Field-free Orientation and Alignment Due To δ-Kicksmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Mirahmadi

Schmidt

Karra

et al. 2018

The Journal of Chemical Physics

Self Cite

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“…Whereas either adiabatic interactions [26][27][28][29][30][31][32][33][34][35][36][37][38] or their impulsive, non-adiabatic counterparts [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] have received much attention, interactions with finiteduration pulses have been scarce [54][55][56]. It is the last that are the focus of the present study.…”

Section: Introductionmentioning

confidence: 94%

Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration

2021

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As demonstrated in our previous work [J. Chem. Phys. 149, 174109 (2018)], the kinetic energy imparted to a quantum rotor by a non-resonant electromagnetic pulse with a Gaussian temporal profile exhibits quasi-periodic drops as a function of the pulse duration. Herein, we show that this behaviour can be reproduced with a simple waveform, namely a rectangular electric pulse of variable duration, and examine, both numerically and analytically, its causes. Our analysis reveals that the drops result from the oscillating populations that make up the wavepacket created by the pulse and that they are necessarily accompanied by drops in the orientation and by a restoration of the pre-pulse alignment of the rotor. Handy analytic formulae are derived that allow to predict the pulse durations leading to diminished kinetic energy transfer and orientation. Experimental scenarios are discussed where the phenomenon could be utilised or be detrimental.

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“…Interestingly, the time-independent Schrödinger equation for a rotor subject to the combined interactions belongs to the class of conditionally quasi-exact solvable (C-QES) problems, unlike the purely aligning or orienting interaction. In our previous work, we established that the condition under which the analytic solutions obtain is intimately connected with the topological index [16,46,48,59,60]. We make use of the analytic solutions to derive aspects of the driven rotor's dynamics analytically.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

Mirahmadi,

Schmidt,

Friedrich

2021

Preprint

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We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work [Frontiers in Physics 2, 37 (2014); Eur. Phys. J. D 71, 149 (2017)]. This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.

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Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

Cited by 13 publications

References 75 publications

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

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