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Numerical simulation of the dynamics of a trapped molecular ion
Umeå University, Faculty of Science and Technology, Department of Physics.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis explores the dynamics of a heteronuclear diatomic molecular ion, possessing a permanent electric dipole moment, µ, which is trapped in a linear Paul trap and can interact with an off-resonance laser field. To build our model we use the rigid-rotor approximation, where the dynamics of the molecular ion are limited to its translational and rotational motions of the center-of-mass. These dynamics are investigated by carrying out suitable numerical calculations.

To introduce our numerical methods, we divide our research topic into two different subjects. First, we ignore the rotational dynamics of the ion by assuming µ = 0. By this assumption, the system resembles an atomic ion, which mainly exhibits translational motion for its center of the mass when exposed to an external trapping field. To study this translational behavior, we implement full-quantum numerical simulations, in which a wave function is attributed to the ion. Finally, we study the quantum dynamics of the mentioned wave packet and we compare our results with those obtained classically.

In the latter case, we keep the permanent dipole moment of the ion and we study the probable effects of the interaction between the dipole moment and the trapping electric field, on both the translational and the rotational dynamics of the trapped molecular ion. In order to study these dynamics, we implement both classical and semi-classical numerical simulations. In the classical method, the rotational and the translational motions of the center of mass of the ion are obtained via classical equations of motion. On the other hand, in the semi-classical method, while the translational motion of the center-of-mass is still obtained classically, the rotation is treated full-quantum mechanically by considering the rotational wave function of the ion. In the semi-classical approach, we mainly study the probable couplings between the rotational states of the molecular ion, due to the interaction of the permanent dipole moment with the trapping electric field. In the end, we also present a semi-classical model, where the trapped molecular ion interacts with an off-resonance laser field.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2016. , 72 p.
Keyword [en]
diatomic molecular ion, linear Paul trap, rigid rotor, quantum rotational dynamics, wave-packet dynamics, time-dependent Schrödinger equation, stability
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:umu:diva-118899ISBN: 978-91-7601-448-6 (print)OAI: oai:DiVA.org:umu-118899DiVA: diva2:917343
Public defence
2016-04-28, N420, Naturvetarhuset, Umeå University, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2016-04-07 Created: 2016-04-06 Last updated: 2016-04-20Bibliographically approved
List of papers
1. Program for quantum wave-packet dynamics with time-dependent potentials
Open this publication in new window or tab >>Program for quantum wave-packet dynamics with time-dependent potentials
2014 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 185, no 1, 407-414 p.Article in journal (Refereed) Published
Abstract [en]

We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schrödinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator method. The program can be compiled for execution either on a single processor or on a distributed-memory parallel computer.

Place, publisher, year, edition, pages
Elsevier, 2014
Keyword
Wave-packet dynamics, Time-dependent Schrödinger equation, Ion traps, Laser control
National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-83167 (URN)10.1016/j.cpc.2013.09.012 (DOI)000328666100041 ()
Funder
Swedish National Infrastructure for Computing (SNIC), 001/12-202
Available from: 2013-11-20 Created: 2013-11-20 Last updated: 2017-12-06Bibliographically approved
2. Wave packet dynamics of an atomic ion in a Paul trap: Approximations and stability
Open this publication in new window or tab >>Wave packet dynamics of an atomic ion in a Paul trap: Approximations and stability
2016 (English)In: International Journal of Modern Physics C, ISSN 0129-1831, Vol. 27, no 2, 1650014Article in journal (Refereed) Published
Abstract [en]

Using numerical simulations of the time-dependent Schrödinger equation, we study the fullquantum dynamics of the motion of an atomic ion in a linear Paul trap. Such a trap is based on atime-varying, periodic electric ̄eld and hence corresponds to a time-dependent potential for theion, which we model exactly. We compare the center-of-mass motion with that obtained fromclassical equations of motion, as well as to results based on a time-independent e®ective po-tential. We also study the oscillations of the width of the ion's wave packet, including close tothe border between stable (bounded) and unstable (unbounded) trajectories. Our results con- ̄rm that the center-of-mass motion always follows the classical trajectory, that the width of thewave packet is bounded for trapping within the stability region, and therefore that the classicaltrapping criterion is fully applicable to quantum motion.

Keyword
Paul trap, atomic ion, wave packet, time-dependent Schrödinger equation, stability
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-106729 (URN)10.1142/S0129183116500145 (DOI)000367402200003 ()
Funder
Swedish National Infrastructure for Computing (SNIC), 2014/1-118
Available from: 2015-08-05 Created: 2015-08-05 Last updated: 2017-12-04Bibliographically approved
3. Rotational dynamics of a diatomic molecular ion in a Paul trap
Open this publication in new window or tab >>Rotational dynamics of a diatomic molecular ion in a Paul trap
2015 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 143, 204308Article in journal (Refereed) Published
Abstract [en]

We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical and the other where the center-of-mass motion is treated classically, while rotational motion is quantized. We study the rotational dynamics and their influenceon the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion and that it departs from the Mathieu equation solution found for atomic ions. For the case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.

National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:umu:diva-111920 (URN)10.1063/1.4936425 (DOI)000366319700019 ()26627960 (PubMedID)
Funder
Swedish National Infrastructure for Computing (SNIC), 2014/1-305
Available from: 2015-11-25 Created: 2015-11-25 Last updated: 2017-12-01Bibliographically approved
4. Quantum stability of an atomic ion in a Paul trap revisited
Open this publication in new window or tab >>Quantum stability of an atomic ion in a Paul trap revisited
2017 (English)In: Molecular Physics, ISSN 0026-8976, E-ISSN 1362-3028, Vol. 115, no 15-16, 1927-1933 p.Article in journal (Refereed) Published
Abstract [en]

We study the quantum stability of the dynamics of atomic ions in a Paul trap. We revisit the results of Wang et al [Phys. Rev. A 52, 1419 (1995)], which showed that quantum trajectories did not have the same region of stability as their classical counterpart, contrary to what is obtained from a Floquet analysis of the motion in the periodic trapping field. Using numerical simulations of the full wave-packet dynamics, we confirm that the classical trapping criterion are fully applicable to quantum motion, when considering both the expectation value of the position of the wave packet and its width.

Place, publisher, year, edition, pages
Abingdon: Taylor & Francis, 2017
Keyword
Ion trapping, Paul trap, stability
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:umu:diva-118898 (URN)10.1080/00268976.2017.1313464 (DOI)000406645600021 ()
Note

Originally published in manuscript form with title [Quantum stability of an atomic ion in a Paul trap revisited]

Special Issue

Available from: 2016-04-06 Created: 2016-04-06 Last updated: 2017-10-20Bibliographically approved

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