A continuous beam monochromator for matter waves

Eur. Phys. J. D (2024) 78 :39 https://doi.org/10.1140/epjd/s10053-024-00829-3 THE EUROPEAN PHYSICAL JOURNAL D Regular Article - Cold Matter and Quantum Gases A continuous beam monochromator for matter waves Johannes Fiedlera and Bodil Holst Department of Physics and Technology, University of Bergen, Allégaten 55, 5007 Bergen, Norway Received 22 January 2024 / Accepted 15 March 2024 / Published online 4 April 2024 © The Author(s) 2024 Abstract. Atom and, of late, molecule interferometers find application in both the crucible of fundamental research and industrial pursuits. A prevalent methodology in the construction of atom interferometers involves the utilisation of gratings fashioned from laser beams. While this approach imparts commendable precision, it is hampered by its incapacity to attain exceedingly short wavelengths and its dependence on intricate laser systems for operational efficacy. All applications require the control of matter waves, particularly the particle’s velocity. In this manuscript, we propose a continuous beam monochromator scheme reaching enormously high velocity purification with speed ratios in the order of 103 based on atom-surface diffraction. Beyond these high purifications, the proposed scheme simplifies the application by reducing the degree of freedom to a single angle, selecting the wanted particle’s velocity. 1 Introduction Atom interferometry is one of the advanced investigation techniques in modern physics[1,2] covering a wide range from fundamental research, such as the transition between the classical and the quantum world due to high mass [3] or slower particles [4,5], via as well as magnetic and gravity sensing [6,7], quantum metrology [8], atomic clocks [9], dark matter and gravitational wave detectors [10] also in space [11,12] to matter-wave lithography [13,14]. Recently, portable atom gravimeters for geophysical investigations, such as prospecting and oil survey, have become commercially available [15]. Atom interferometers are also proposed as accelerometers for sub-sea navigation in submarines and underwater drones [7,16]. However, reaching the envisaged accuracy requires either a velocity-sensitive measurement or an accurate velocity preselection. Velocitysensitive measurements are challenging but realisable [5, 17,18]. A measure for the wave’s monochromaticity is speed ratios (ratio between velocity v and velocity spread Δv, v/Δv). To reach large speed ratios, one needs control of the particle’s trajectories [17,19] and a low particle flux [5] to distinguish each particle. An alternative to a velocity-sensitive measurement is velocity preselection, enabling high-contrast interferences. Here, we differentiate between two principles: (a) changing the momentum of particles with the wrong velocity (momentum) or (b) removing the particles with a different momentum. a Velocity-dependent accelerating or decelerating particles within a particle beam have been realised by the Rydberg–Stark decelerator, a chain of quadrupoles creating an inhomogeneous field that couples differently to the dipoles moving with different velocities [20–22]. Thus, this technique is restricted to particles with a permanent dipole moment. Another possibility is the Zeeman slower, which works analogously to the Stark effect but uses magnetic fields coupled to the spin-polarised magnetic moment. The more straightforward solution is removing the particles from the beam with a velocity different from the target velocity, which can be realised using two choppers, which only transmit particles with a velocity matching the time window for the chopper openings. This technique has been realised in various configurations and setups, e.g., a cascade of choppers [23] or a helical gearwheel [24,25]. However, it has the apparent disadvantage that a continuous beam will be pulsed. A further possibility, removing particles with an unwanted velocity from a beam, uses atomic mirrors, which has been demonstrated experimentally [26] as well as the slowing of atomic beams, the so-called atomic paddle [27], Stark effect decelerator [28] and Zeeman slower [29]. Here, we present a novel approach to velocity selection, which enables a continuous beam with speed ratios up to several hundred by exploiting the recently proposed reflective atom interferometer [30]. The example presented here is for a helium beam scattering off hydrogen-passivated Si(111) [31]. However, the proposed device can be adapted to other materials and atomic beams. The reflection direction is velocity- e-mail: johannes.fi[email protected] (corresponding author) 123 39 Page 2 of 6 Eur. Phys. J. D (2024) 78 :39 sensitive depending on the surface structure. Thus, by sending the reflected (diffracted) beam through a pinhole, the particles with a velocity outside a specific range will be blocked, and the beam’s speed ratio will be enhanced. The velocity-dependent beam spread is increased using three reflections instead of one (simple reflection scheme). Experimentally, this is made possible by the monolithic nature of the atom interferometer, which ensures that the reflective surfaces do not move relative to each other. 2 The monochromator The proposed monochromator for matter waves is based on the reflective atom interferometer introduced in Ref. [30], which consists of two parallel structured plates cut into a single crystal. It requires two parallel nano-structured planar surfaces, which can be achieved by cutting a monolithic crystal, such as silicon, and chemically dipping the Si(111) crystal in an HF solution [32]. The incoming beam is diffracted three times within the device before leaving. For each diffraction, the incidence ϑinc and reflection angles ϑout are related by Bragg’s law   λdB ϑout = arcsin sin ϑinc + n , aS (1) with the diffraction order n, the de-Broglie wavelength λdB = 2π/p = 2π/(mv), the reduced Planck constant , the particle’s mass m and velocity v, and the lattice constant of the structured surface aS . Due to the structure of this equation, the three internal diffractions ni lead to a total diffraction order for the entire device N = n1 + n2 + n3 . Figure 1 illustrates the situation. In previous work [30], we have seen a strong dependency of the diffraction orders’ positions on the incoming beam’s wavelength, which motivated the further consideration of the device to act as a monochromator. In the following, we will first consider the relation between the incidence and reflection angle with respect to velocity deviations. One of these angles should be fixed for practical applications, where we used the outgoing angle ϑout . Thus, we first analyse the optimal incidence angle concerning a strong velocity dependence. Afterwards, we derive conditions for the device’s dimensions, expressed in the length-to-separation ratio d/s, allowing for an almost arbitrary scaling of the device. All given examples consider a helium beam in a monolithic Si(111)H(1×1) device according to Ref. [30]. 2.1 Optimal incidence ang (...truncated)