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arXiv:2310.13293 · Physical Review Letters

Probing Rotational Decoherence with a Trapped-Ion Planar Rotor

Neil Glikin, Benjamin A. Stickler, Ryan Tollefsen, Sara Mouradian, Neha Yadav, Erik Urban, Klaus Hornberger, Hartmut Häffner

Published Jan 23, 2025• 3 citations
arXivHTMLPDF

Abstract

The quantum rotor is one of the simplest model systems in quantum mechanics, but only in recent years has theoretical work revealed general fundamental scaling laws for its decoherence. For example, a superposition of orientations decoheres at a rate proportional to the sine squared of the angle between them. Here, we observe scaling laws for rotational decoherence dynamics for the first time, using a 4 μm diameter planar rotor composed of two Paul-trapped ions. We prepare the rotational motion of the ion crystal into superpositions of angular momentum with well-defined differences ranging from 1-3ℏ, and measure the rate of decoherence. We also tune the system-environment interaction strength by introducing resonant electric field noise. The observed scaling relationships for decoherence are in excellent agreement with recent theoretical work, and are directly relevant to the growing development of rotor-based quantum applications.

DOI
10.1103/physrevlett.134.033601

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The quantum rotor is one of the simplest model systems in quantum mechanics, but only in recent years has theoretical work revealed general fundamental scaling laws for its decoherence. For example, a superposition of orientations decoheres at a rate proportional to the sine squared of the angle between them. Here, we observe scaling laws for rotational decoherence dynamics for the first time, using a 4 μm diameter planar rotor composed of two Paul-trapped ions. We prepare the rotational motion of the ion crystal into superpositions of angular momentum with well-defined differences ranging from 1-3ℏ, and measure the rate of decoherence. We also tune the system-environment interaction strength by introducing resonant electric field noise. The observed scaling relationships for decoherence are in excellent agreement with recent theoretical work, and are directly relevant to the growing development of rotor-based quantum applications.
A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations. We theoretically study the quantum dynamics of a QTR, particularly when the spin state of one of the ions is flipped. We show that the quantum dynamics of an N\mathit{N}N-ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.
We demonstrate the preparation and coherent control of the angular momentum state of a two-ion crystal. The ions are prepared with an average angular momentum of 7850ℏ freely rotating at 100 kHz in a circularly symmetric potential, allowing us to address rotational sidebands. By coherently exciting these motional sidebands, we create superpositions of states separated by up to four angular momentum quanta. Ramsey experiments show the expected dephasing of the superposition which is dependent on the number of quanta separating the states. These results demonstrate coherent control of a collective motional state described as a quantum rotor in trapped ions. Moreover, our Letter offers an expansion of the utility of trapped ions for quantum simulation, interferometry, and sensing.
When molecular ions are trapped together with atomic ions in a Paul trap, their dipole moment couples the molecular rotation to the joint vibrational motion of the particles in the trap. To leverage this coupling for quantum control, a rotational transition in the molecule should be resonant with one of the ion crystal vibrational modes. Focusing on the example of singly charged thorium fluoride molecular ions, cotrapped with two ytterbium ions, we determine the conditions for resonant dipole-phonon coupling, fully accounting for the molecular hyperfine structure. We identify several choices for resonant coupling and discuss its detection using sideband-resolved laser spectroscopy and measurements of decoherence.
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.
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 influence on 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.