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Rydberg-Atom Interferometry

James Palmer

Published Mar 28, 2020• 0 citations

Abstract

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.

Related papers

Matter-wave interferometry with atoms in high Rydberg states

J. E. Palmer, S. D. Hogan

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.

arXiv:1907.07649•Molecular Physics•Apr 24, 2019•9 citations

Electric Rydberg-Atom Interferometry

J. E. Palmer, S. D. Hogan

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.

arXiv:1907.01234•Physical Review Letters•Jun 27, 2019•22 citations

Matter-wave interferometry with atoms in high Rydberg states

Palmer, JE, S. D. Hogan

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.

•Jan 1, 2019•6 citations

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

J. D. R. Tommey, S. D. Hogan

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.

Physical Review A•Sep 3, 2021•8 citations

A coherent electric analogue of the Stern-Gerlach experiment

S. D. Hogan, F. O. Eyles

A coherent electric analogue of the Stern-Gerlach experiment has been performed with helium atoms in Rydberg states. The atoms, travelling in pulsed supersonic beams, were prepared in superpositions of Rydberg states with different static electric dipole polarisabilities using pulses of microwave radiation. State-dependent forces were then exerted on them, transverse to their direction of propagation, using inhomogeneous electric fields. These fields were generated between a pair of electrodes in a wedge configuration. The forces applied resulted in the coherent evolution of each atomic wavepacket into a superposition of spatially separated momentum states. The classical paths of least action associated with these momentum states evolved over time up to a separation of ∼2 nm. The coherent evolution of the atoms, and hence the superposition of atomic wavepackets in this ‘half-loop’ electric Rydberg-atom interferometer, was monitored by measuring the internal Rydberg state populations at the end of each measurement cycle. The experimental data are in good quantitative agreement with the results of semiclassical calculations of the phase evolution of the atomic superposition states which account for contributions from Stark shifts, the momentum differences between the classical paths of least action through the apparatus, and the spatial separation of the atomic wavepackets.

Molecular Physics•Jul 30, 2026•0 citations

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

D. Chan, J. D. D. Martin

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.

arXiv:2306.06776•Physical Review A•Jan 12, 2024•1 citation

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.

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.

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.

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.

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.

A coherent electric analogue of the Stern-Gerlach experiment has been performed with helium atoms in Rydberg states. The atoms, travelling in pulsed supersonic beams, were prepared in superpositions of Rydberg states with different static electric dipole polarisabilities using pulses of microwave radiation. State-dependent forces were then exerted on them, transverse to their direction of propagation, using inhomogeneous electric fields. These fields were generated between a pair of electrodes in a wedge configuration. The forces applied resulted in the coherent evolution of each atomic wavepacket into a superposition of spatially separated momentum states. The classical paths of least action associated with these momentum states evolved over time up to a separation of ∼2 nm. The coherent evolution of the atoms, and hence the superposition of atomic wavepackets in this ‘half-loop’ electric Rydberg-atom interferometer, was monitored by measuring the internal Rydberg state populations at the end of each measurement cycle. The experimental data are in good quantitative agreement with the results of semiclassical calculations of the phase evolution of the atomic superposition states which account for contributions from Stark shifts, the momentum differences between the classical paths of least action through the apparatus, and the spatial separation of the atomic wavepackets.

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.