# Antimatter Quantum Interferometry

## Abstract

**:**

## 1. Introduction

_{dB}= h/p [1]. This relation, together with the uncertainty principle and the superposition principle, is at the heart of quantum mechanics. These principles have now been tested in an overwhelming variety of experiments over more than 100 years.

_{2}[8], and up to the complexity of fullerene [9].

## 2. Antimatter

^{+}e

^{-}bound system), was discovered by M. Deutsch in 1951 [21]. It is constituted by an electron and a positron and has been the subject of intense investigation in the last decades, holding the promise to allow tests of fundamental laws (see [22] and references therein).

## 3. Antimatter Interferometry

^{−5}and virtually no antiparticle can survive in the environment because of immediate annihilation with ordinary matter. For these reasons, controlled sources of antiparticles are restricted to high-energy accelerators or radioactive sources. Interferometry also requires antimatter at relatively low energies, suitable for controlled propagation or even confinement, as is the case for the above-mentioned Antiproton Decelerator or the radioactive

^{22}Na positron sources.

^{4}particles per second. In comparison, electron sources can easily reach the mA range—11 orders of magnitude higher!

## 4. Types of Interferometry

- The wavelength of the radiation (the de Broglie wavelength of the particle) $\lambda $.
- The periodicity of the grating used to evidence the diffraction/interference effect $d$.
- The longitudinal scale $L$ that is related to the integrating distance or to the observation distance.

_{T}is a measure of the dominance of the transverse scale, while D

_{L}indicates the level of longitudinal dominance. If, D

_{T}is big in such a way as to also predominate over D

_{L}then

_{L}which dominates D

_{T}, then one has

- $L<<{L}_{T}$: moiré regime, where particles behave like classical bullets (deflectometry).
- $L\text{}\approx \text{}{L}_{T}$: Talbot–Lau regime, where particles start to show interference.
- $L>>{L}_{T}$: Fraunhofer regime, where the usual far-field approximation holds.

_{T}is satisfied. However, the Fraunhofer interference will require a good initial collimation of the beam.

^{+}emitter

^{22}Na source. Antiprotons are available at particle accelerators since they will need to be produced at very high energy. The Antiproton Decelerator at CERN is the only machine dedicated to the production of antiprotons at the MeV scales or below that can prove adequate for interferometry.

## 5. The Experiment

^{22}Na radioactive source followed by a beam line, an interferometer and a nuclear emulsion detector were used.

## 6. Results

_{max}− I

_{min})/(I

_{max}+ I

_{min}) as a function of the energy, which corresponds to changing the wavelength of the positrons. The result of such a study for energies 8, 9, 11, 14, 16 keV is shown in Figure 4. It clearly indicates the quantum mechanical origin of the effect which is energy dependent. By contrast, in the moiré regime no such behavior is expected since the particles would behave classically.

^{4}per second, generated by the time-incoherent

^{22}Na source, and the transit time through the interferometer is 10

^{−8}s, this turns out to be a single-particle experiment, being therefore the antimatter version of the celebrated Merli–Missiroli–Pozzi single electron result [11].

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The relevant quantities in an interferometric measurement with gratings are the wavelength of the particle/radiation, the period of the gratings d and the distance scale between gratings $L$. A detector might be located at some distance (similar to $L$) from the second grating. The coherently illuminated area from the first to the second grating is also shown.

**Figure 2.**Scheme of the QUPLAS-0 detector experimental configuration. The collimated positron beam propagates through the interferometer, consisting of two gratings and the emulsion detector (tilted by 45°, see text). The interference pattern is collected in the emulsion. A Ge detector is used to monitor the positron beamline through the 511-keV gammas generated by positron annihilation.

**Figure 3.**The contrast (I

_{maz}− I

_{min})/(I

_{max}+ I

_{min}) is shown on the left (

**A**) as a function of the longitudinal coordinate y. It is maximum for the resonant energy of 14 keV for which the actual interference pattern is shown in the insert. Other energies are visible albeit with a reduced contrast. On the right (

**B**), the transverse position of the interference patterns on the emulsion is shown.

**Figure 4.**Visibility of the Talbot–Lau interference pattern as a function of energy (wavelength) in QUPLAS-0. The dependence on E is the smoking-gun proof of the quantum mechanical origin of the effect. The classical moiré effect (orange dashed line) would in fact have been achromatic.

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**MDPI and ACS Style**

Giammarchi, M.
Antimatter Quantum Interferometry. *Symmetry* **2019**, *11*, 1247.
https://doi.org/10.3390/sym11101247

**AMA Style**

Giammarchi M.
Antimatter Quantum Interferometry. *Symmetry*. 2019; 11(10):1247.
https://doi.org/10.3390/sym11101247

**Chicago/Turabian Style**

Giammarchi, Marco.
2019. "Antimatter Quantum Interferometry" *Symmetry* 11, no. 10: 1247.
https://doi.org/10.3390/sym11101247