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arXiv:1012.3910 · New Journal of Physics

Experimental proposal for measuring the Gouy phase of matter waves

I. G. da Paz, Pablo L. Saldanha, Maria Carolina Nemes, J. G. Peixoto de Faria

Published Dec 8, 2011• 33 citations
arXivHTMLPDF

Abstract

The Schrödinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment that allows for direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed, and shown to be completely under control within present-day technology. We also discuss how this finding can open the possibility of using the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.

DOI
10.1088/1367-2630/13/12/125005

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•Mar 28, 2020•0 citations
The Schrödinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment that allows for direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed, and shown to be completely under control within present-day technology. We also discuss how this finding can open the possibility of using the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.
In this thesis, we study theoretical and experimental aspects of the Gouy phase in matter waves. We show that this phase is related to the covariance between position and momentum and can be indirectly extracted from interferometric experiments. Next, we analyze a diffraction experiment with macro-molecules realized by Zeilingers group [1] and we show that the existence of a Gouy phase is compatible with those experimental data. Similar to the Gouy phase for classical electromagnetic waves, it is shown that a beam of matter waves suffers a phase anomaly around the focus of a quantum lens. An experimental proposal to measure this phase is presented with experimental parameters viable to current technology. We hope this work motivates studies of the theoretical problem, open a few years ago, and forexperiments that lead us to an understanding deeper and more realistic of the Gouy phase for mixed states of matter waves and light. At the end, we present our conclusions.
Abstract Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.
The influence of space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyze in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the Earth or alternatively of two parallel oriented lead blocks. It appears that for the lead blocks the detection should be possible with realistic modifications of existing devices within the near future. For the Earth's gravitational field the experimental difficulties are too big. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. The calculation makes use of Fermi coordinates. In the second part we calculate the shift of the Ramsey fringes for the two different sources of curvature and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.
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.