Ultracold metastable helium: Ramsey fringes and atom interferometry

Appl. Phys. B (2016) 122:289 DOI 10.1007/s00340-016-6563-0 Ultracold metastable helium: Ramsey fringes and atom interferometry W. Vassen1 · R. P. M. J. W. Notermans1 · R. J. Rengelink1 · R. F. H. J. van der Beek1 Received: 16 June 2016 / Accepted: 4 November 2016 / Published online: 26 November 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract We report on interference studies in the internal and external degrees of freedom of metastable triplet helium atoms trapped near quantum degeneracy in a 1.5 µm optical dipole trap. Applying a single π/2 rf pulse we demonstrate that 50% of the atoms initially in the m = +1 state can be transferred to the magnetic field insensitive m = 0 state. Two π/2 pulses with varying time delay allow a Ramsey-type measurement of the Zeeman shift for a high precision measurement of the 2 3 S1–2 1 S0 transition frequency. We show that this method also allows strong suppression of mean-field effects on the measurement of the Zeeman shift, which is necessary to reach the accuracy goal of 0.1 kHz on the absolute transition frequencies. Theoretically the feasibility of using metastable triplet helium atoms in the m = 0 state for atom interferometry is studied demonstrating favorable conditions, compared to the alkali atoms that are used traditionally, for a non-QED determination of the fine structure constant. 1 Introduction The helium atom has a long history as testing ground for fundamental atomic physics. With two electrons, helium is a three-body system and the nonrelativistic Schrödinger This article is part of the topical collection “Enlightening the World with the Laser” - Honoring T. W. Hänsch guest edited by Tilman Esslinger, Nathalie Picqué, and Thomas Udem. * W. Vassen 1 LaserLaB, Department of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands equation cannot be solved exactly. Level energies are therefore more difficult to calculate than for atomic hydrogen showing a more stringent test of atomic physics theory. Calculations of level energies and transition frequencies have pushed our understanding of atomic physics since the twenties of last century. A major breakthrough occurred in the nineties with the advent of variational calculations in a double basis set in correlated form for the electrons, adding relativistic and quantum electrodynamics (QED) terms in orders of the fine structure constant α and the reduced electron to helium mass ratio µ/MHe [1, 2]. As nonrelativistic calculations can now be performed to virtually arbitrary precision, measurements of level energies nowadays are sensitive to QED and nuclear size effects. As these effects are strongest for S-states and small principle quantum number n, the n 1,3 S states are theoretically the most promising to test QED. In particular the n = 2 states are important for high-resolution spectroscopy as these also show long lifetimes, 7800 s for the 2 3 S1 state and 20 ms for the 2 1 S0 state (natural linewidth 8 Hz), while the 2 3 P state has, for an allowed electric dipole transition, a relatively long lifetime of 98 ns (natural linewidth 1.6 MHz). A helium level scheme is shown in Fig. 1. Transition frequencies in helium can nowadays be measured more accurately than calculated, where the theoretical limitation is in the calculation of high-order QED terms. This hampers extraction of the charge radius of the helium nucleus (the alpha-particle for 4 He and the helion for 3 He) from transition frequencies with an accuracy that can compete with other experiments. However, in calculating transition isotope shifts between 4 He and 3 He, QED terms cancel to a large extent, allowing very accurate extraction of the difference in the (squared) nuclear charge radii of the alpha-particle and the helion. This is particularly interesting in relation to the proton size puzzle [3–5]. To help solving 13 289 Page 2 of 11 E [eV] W. Vassen et al. He+ 24 1s3s 23 1s3p 1s3d 1s3p 1s3d 1s2p τ ≈ 98 ns 1s3s 22 21 20 0 1s2p τ ≈ 0.5 ns 887 nm 1s2s τ ≈ 20 ms 1557 nm 1083 nm 1s2s τ ≈ 7800 s (1s)2 1 S 1 P Singlet states (para-helium) D 1 S 3 3 3 P D Triplet states (ortho-helium) Fig. 1  Level scheme, lifetimes and transition wavelengths for lowlying n 1,3 LJ states of helium (n < 4). The 2 3 S1 and 2 1 S0 states are metastable and can be populated in a dc discharge. The 2 3 S1 state is the ground state of orthohelium and is the starting point of experimental work in this paper the proton size puzzle, Lamb shift measurements have recently been performed in muonic 4 He+ and 3 He+ ions, from which results are expected soon. The projected accuracy of the muonic helium experiments is around 0.5 am (0.03% relative accuracy in the nuclear charge radius) [4]. For electronic helium and assuming point nuclei, Pachucki and Yerokhin [6] have performed QED calculations of the isotope shift with an accuracy of 0.7 and 3.9 kHz for, respectively, the 2 3 S1–2 1 S0 transition at 1557 nm and the 2 3 S1–2 3 P transition at 1083 nm. These QED limited accuracies allow extraction of the squared nuclear charge radius difference with an accuracy that will be similar to values deduced from the muonic helium experiments if the experimental accuracy of the isotope shift is of similar or higher accuracy. Presently, for the 2 3 S1–2 1 S0 transition, the accuracy is 2.4 kHz [7] while for the 2 3 S1–2 3 P transition the isotope shift accuracy is 3.2 kHz [8, 9]. Surprisingly, a four standard deviation difference exists between the nuclear charge radius difference extracted from both measurements. The possibility to accurately calculate level energies and wavefunctions has allowed confrontation with several other experimental results. Radiative lifetimes of the 2 3 S1 and 2 1 P1 states have been measured in cold clouds of helium atoms initially prepared in the metastable 2 3 S1 state of 4 He [10, 11], showing good agreement with theory. Also molecular potentials for two metastable helium atoms can be calculated very accurately in some cases. This has allowed a stringent test of quantum chemistry calculations 13 from a measurement of the s-wave scattering length a between two m = +1 atoms in the metastable 2 3 S1 state, atheory = 7.567 (24) nm [12, 13], while aexp = 7.512 (5) nm [14]. Examples of other confrontations between experiment and theory for cold collisions between metastable helium atoms can be found in Ref. [15]. Helium atoms in the metastable 2 3 S1 state (He*) are also very interesting from the perspective of atomic matter wave physics. Being light, superposition states with different momenta spatially separate fast and detection of He* atoms can be performed on a microchannel plate (MCP) detector with high efficiency [15]. Actually one of the first experiments on atom interferometry (Young’s double slit experiment) was performed with a beam of He* atoms [16]. Transversal Bragg scatter (...truncated)