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arXiv:2306.06776 · Physical Review A

Comment on “Matter-wave interferometry with helium atoms in low- l Rydberg states”

D. Chan, J. D. D. Martin

Published Jan 12, 2024• 1 citation
arXivHTMLPDF

Abstract

Tommey and Hogan [Phys. Rev. A 104, 033305 (2021)] have reported a matter-wave interference experiment using Rydberg atoms traveling through inhomogeneous electric fields at approximately $2000\phantom{\rule{0.28em}{0ex}}\mathrm{m}/\mathrm{s}$. Using a simplified model containing the essential physics of their experiment, we show that the phase difference measured by their observed interference fringes does not depend, in any significant way, on the acceleration of the Rydberg atoms, but instead simply on the uniform motion of the atoms through the inhomogeneous electric field.

DOI
10.1103/physreva.109.017301

Related papers

Matter-wave interferometry with helium atoms in low- l Rydberg states

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Electric Rydberg-atom interferometry has been performed with helium atoms in coherent superpositions of the $1s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $1s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ Rydberg levels. The experiments were carried out in a longitudinal geometry with the atoms traveling at 2000 m/s in pulsed supersonic beams. After laser photoexcitation from the $1s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ metastable level, coherent manipulation of the population of the Rydberg states was achieved using sequences of microwave pulses. The difference in the static electric dipole polarizabilities of the $1s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $1s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ levels allowed superpositions of external momentum states to be generated when inhomogeneous electric fields were used to exerted forces on the atoms prepared in superpositions of these internal states. Interference fringes, with contributions arising from the spatial separation of these Rydberg-atom wave packets in the direction of propagation of the atomic beam, were identified through changes in the internal-state populations as the magnitudes and durations of the time-dependent electric-field gradient pulses were adjusted. The maximal displacement of the atomic wave packets for which interference fringes were observed was $\ensuremath{\sim}0.75\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$, limited by the longitudinal velocity spread in the atomic beam and the characteristics of the inhomogeneous electric-field distribution in the apparatus. The experimental data are in good quantitative agreement with the results of numerical calculations of the time evolution of the atomic states under the experimental conditions.

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Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.

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Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.

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Tommey and Hogan [Phys. Rev. A 104, 033305 (2021)] have reported a matter-wave interference experiment using Rydberg atoms traveling through inhomogeneous electric fields at approximately 2000m/s2000\phantom{\rule{0.28em}{0ex}}\mathrm{m}/\mathrm{s}2000m/s. Using a simplified model containing the essential physics of their experiment, we show that the phase difference measured by their observed interference fringes does not depend, in any significant way, on the acceleration of the Rydberg atoms, but instead simply on the uniform motion of the atoms through the inhomogeneous electric field.
Electric Rydberg-atom interferometry has been performed with helium atoms in coherent superpositions of the 1s56s3S11s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s56s3S1​ and 1s57s3S11s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s57s3S1​ Rydberg levels. The experiments were carried out in a longitudinal geometry with the atoms traveling at 2000 m/s in pulsed supersonic beams. After laser photoexcitation from the 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ metastable level, coherent manipulation of the population of the Rydberg states was achieved using sequences of microwave pulses. The difference in the static electric dipole polarizabilities of the 1s56s3S11s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s56s3S1​ and 1s57s3S11s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s57s3S1​ levels allowed superpositions of external momentum states to be generated when inhomogeneous electric fields were used to exerted forces on the atoms prepared in superpositions of these internal states. Interference fringes, with contributions arising from the spatial separation of these Rydberg-atom wave packets in the direction of propagation of the atomic beam, were identified through changes in the internal-state populations as the magnitudes and durations of the time-dependent electric-field gradient pulses were adjusted. The maximal displacement of the atomic wave packets for which interference fringes were observed was $\ensuremath{\sim}0.75\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$, limited by the longitudinal velocity spread in the atomic beam and the characteristics of the inhomogeneous electric-field distribution in the apparatus. The experimental data are in good quantitative agreement with the results of numerical calculations of the time evolution of the atomic states under the experimental conditions.
Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.
Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.
Matter-wave interferometry has many possible uses, ranging from tests of funda- mental physics to applications in sensing. In order to achieve this interferometry, quantum superpositions of spatially-separated components need to be generated. There are several possible methods to accomplish this using Rydberg atoms; this thesis presents the experimental investigation of two of these. Both of these methods use inhomogeneous electric fields to spatially split beams of Rydberg atoms. In the first method, field distributions were generated above two-dimensional electrode structures and used to transversely split beams of helium Rydberg atoms into pairs of components spatially separated by up to 15.6 mm. Effects of amplitude modulation of the electric fields of this beam splitter were shown to cause particle losses through transitions into unconfined Rydberg-Stark states. This led to further studies of the depolarisation of Rydberg-Stark states in radio-frequency electric fields. Through this work it is shown that both ‘resonant’ and ‘non-resonant’ broadband modulation with amplitudes on the order of 10 mV·cm⁻¹ are sufficient to cause significant depolarisation of initially prepared quantum states on a timescale of 5 μs in a static offset electric field of 0.43 V·cm⁻¹. In a second class of experiments, matter-wave interferometry has been per- formed with helium atoms in high Rydberg states. In this work a series of mi- crowave and electric field gradient pulses were used to create a spatial separation between two components of a coherent superposition of states, while ensuring that the momenta of these components were equal at the end of the process to enable matter-wave interference to be observed. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼ 320 nm and displacements of up to 150 pm were observed between the pairs of matter-wave components at the end of the interferometry sequences.
An electric analogue of the longitudinal Stern-Gerlach matter-wave interferometer has been realized for atoms in Rydberg states with high principal quantum number n. The experiments were performed with He atoms prepared in coherent superpositions of the n=55 and n=56 circular Rydberg states in a zero electric field by a π/2 pulse of resonant microwave radiation. These atoms were subjected to a pulsed inhomogeneous electric field to generate a superposition of momentum states before a π pulse was applied to invert the internal states. The same pulsed inhomogeneous electric field was then reapplied for a second time to transform the motional states to have equal momenta before a further π/2 pulse was employed to interrogate the final Rydberg state populations. This Hahn-echo microwave pulse sequence, interspersed with a pair of equivalent inhomogeneous electric field pulses, yielded two spatially separated matter waves. Interferences between these matter waves were observed as oscillations in the final Rydberg state populations as the amplitude of the pulsed electric field gradients was adjusted.
Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.