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arXiv:2407.19384 · Physical Review Letters

Generation of Neutron Airy Beams

Dusan Sarenac, Owen Lailey, Melissa E. Henderson, Huseyin Ekinci, Charles W. Clark, David G. Cory, Lisa DeBeer‐Schmitt, M. G. Huber, Jonathan Stuart White, Kirill Zhernenkov, Dmitry A. Pushin

Published Apr 17, 2025• 12 citations
arXivHTMLPDF

Abstract

The Airy wave packet is a solution to the potential-free Schrödinger equation that exhibits remarkable properties such as self-acceleration, nondiffraction, and self-healing. Although Airy beams are now routinely realized with electromagnetic waves and electrons, the implementation with neutrons has remained elusive due to small transverse coherence lengths, low fluence rates, and the absence of neutron lenses. In this Letter, we overcome these challenges through a holographic approach and present the first experimental demonstration of neutron Airy beams. The presented techniques pave the way for fundamental physics studies with Airy beams of nonelementary particles, the development of novel neutron optics components, and the realization of neutron Airy-vortex beams.

DOI
10.1103/physrevlett.134.153401

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In 1979, Berry and Balazs [M V Berry and N L Balazs 1979 Am. J. Phys. 47 264] obtained a strict solution of the Schrödinger equation with Airy function used as the initial condition, and described the wave function represented by such solution as the Airy wave-packets. They discovered that infinite Airy wave-packet has unique properties such as non-spreading and free acceleration, proving that it is the only nontrivial non-spreading solution of the time-dependent Schrödinger equation in one dimension. However, the observing of the finite Airy beam seems to be more meaningful since wave-packets in reality is inevitably band limited. A certain form of finite Airy beam was investigated by Siviloglou et al. in 2007 [Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901; Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979]. They noted that the Airy wave packet still exhibits its most exotic feature, i.e., its trend toward free acceleration. While in the present paper we discuss the properties of Airy beam in a few steps further and propose several conclusions. On the one hand, a theoretic explanation is given to solve the matter of the centre of mass of infinite Airy beam. On the other hand, deeper research is conducted on the unique properties of finite Airy beam. Another form of finite Airy beam is discussed by reduction to absurdity, and its field distribution is put forward by numerical simulation. We find that the trajectory of the centroid holds its position, which means that the beam cannot accelerate freely as a whole. Ultimately, we have the conclusion that finite Airy beam can neither freely accelerate nor be non-diffractive.

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Following their discovery in the late 1970s, optical Airy beams have found numerous applications in technologies such as microscopy and optical trapping, many of which are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recent advancements have shown that Airy beams can also be produced using matter waves with many of the same unique characteristics of their optical counterparts. We present here a study of the recovery time of damaged matter Airy wave packets in free space and a nonlinear Kerr-type medium. We show that in free space the recovery time increases approximately linearly with mass and is independent of other kinematical parameters such as momentum, velocity, and spatial width. In the Kerr-type medium, recovery time is decreased compared to free space and does not scale linearly with mass. In order to study matter Airy beams, we introduce the Path Integral Quantum Trajectory (PIQTr) model as a new computational tool for the study of non-relativistic, quantum mechanical wave packets and demonstrate its effectiveness in dealing with heavy particle dynamics.

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The Airy wave packet is a solution to the potential-free Schrödinger equation that exhibits remarkable properties such as self-acceleration, nondiffraction, and self-healing. Although Airy beams are now routinely realized with electromagnetic waves and electrons, the implementation with neutrons has remained elusive due to small transverse coherence lengths, low fluence rates, and the absence of neutron lenses. In this Letter, we overcome these challenges through a holographic approach and present the first experimental demonstration of neutron Airy beams. The presented techniques pave the way for fundamental physics studies with Airy beams of nonelementary particles, the development of novel neutron optics components, and the realization of neutron Airy-vortex beams.
In 1979, Berry and Balazs [M V Berry and N L Balazs 1979 Am. J. Phys. 47 264] obtained a strict solution of the Schrödinger equation with Airy function used as the initial condition, and described the wave function represented by such solution as the Airy wave-packets. They discovered that infinite Airy wave-packet has unique properties such as non-spreading and free acceleration, proving that it is the only nontrivial non-spreading solution of the time-dependent Schrödinger equation in one dimension. However, the observing of the finite Airy beam seems to be more meaningful since wave-packets in reality is inevitably band limited. A certain form of finite Airy beam was investigated by Siviloglou et al. in 2007 [Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901; Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979]. They noted that the Airy wave packet still exhibits its most exotic feature, i.e., its trend toward free acceleration. While in the present paper we discuss the properties of Airy beam in a few steps further and propose several conclusions. On the one hand, a theoretic explanation is given to solve the matter of the centre of mass of infinite Airy beam. On the other hand, deeper research is conducted on the unique properties of finite Airy beam. Another form of finite Airy beam is discussed by reduction to absurdity, and its field distribution is put forward by numerical simulation. We find that the trajectory of the centroid holds its position, which means that the beam cannot accelerate freely as a whole. Ultimately, we have the conclusion that finite Airy beam can neither freely accelerate nor be non-diffractive.
Airy beams have been studied in an optical context since their discovery in the late 1970s and have found numerous applications in technologies such as microscopy and optical trapping. Many of these applications are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recently, Airy beams have been produced using electrons and these matter waves exhibit many of the same unique characteristics of their optical counterparts. We use our Path Integral Quantum Trajectory (PIQTr) model to present a study of the reflection and transmission of matter Airy wave packets. Like the more familiar Gaussian wave packets, Airy beams have a Gaussian momentum distribution. However, despite this similarity, Airy beams show unique features for transmission and reflection.
Following their discovery in the late 1970s, optical Airy beams have found numerous applications in technologies such as microscopy and optical trapping, many of which are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recent advancements have shown that Airy beams can also be produced using matter waves with many of the same unique characteristics of their optical counterparts. We present here a study of the recovery time of damaged matter Airy wave packets in free space and a nonlinear Kerr-type medium. We show that in free space the recovery time increases approximately linearly with mass and is independent of other kinematical parameters such as momentum, velocity, and spatial width. In the Kerr-type medium, recovery time is decreased compared to free space and does not scale linearly with mass. In order to study matter Airy beams, we introduce the Path Integral Quantum Trajectory (PIQTr) model as a new computational tool for the study of non-relativistic, quantum mechanical wave packets and demonstrate its effectiveness in dealing with heavy particle dynamics.
Airy vortex beams, which integrate orbital angular momentum with diffraction-resistant and self-accelerating characteristics of Airy beams, offer unique capabilities for high-capacity optical communication and high-resolution imaging. Here, we experimentally demonstrate the generation and manipulation of frequency-converted Airy vortex beams through four-wave mixing in hot Rb vapor. A 780 nm vortex beam and a 776 nm two-dimensional Airy beam coherently participate in the four-wave mixing process, generating a 420 nm output beam that combines the orbital angular momentum of the vortex beam with the spatial structure of the Airy beam. The generated beam exhibits pronounced quasi-nondiffracting propagation and self-acceleration, with an intensity decay rate reduced by a factor of ∼1.88 relative to the input vortex beam and a transverse acceleration ∼1.84 times that of the input Airy beam. Moreover, both the intensity and the spatial profile of the generated beam are flexibly manipulated by varying the Rb vapor temperature and the pump beam power. This work provides a versatile approach for generating and controlling structured light at what we believe are new wavelengths, opening opportunities for short-wavelength optical manipulation and optical information processing.
Self-healing of an Airy beam during propagation is of fundamental interest and also promises important applications. Despite many studies of Airy beams in the quantum regime, it is unclear whether an Airy beam only including a single photon can heal after passing an obstacle because the photon may be blocked. Here we experimentally observe self-healing of a heralded single-photon Airy beam. Our observation implies that an Airy wave packet is robust against obstacle caused distortion and can restore even at the single-photon level.