Ultracold metastable helium: Ramsey fringes and atom interferometry

Abstract

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/M He [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 S 1 state and 20 ms for the 2 1 S 0 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][4][5]. To help solving 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 S 1 -2 1 S 0 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.

Long-lived quantum coherent dynamics of a $Λ$-system driven by a thermal environment

“…We finally turn to the question of experimental observability of Fano coherences. We suggest metastable He(2 3 S 1 ) atoms [49,50] as a readily realizable Λ-system, in which to observe noise-induced coherent dynamics. The Λ-system is formed by the m = ±1 Zeeman sublevels of the metastable 3 S state and the nondegenerate excited 3 P 0 state as shown in Fig.…”

“…As in the case of isotropic incoherent excitation considered above, the coherences exhibit quantum beats with frequency ∆ and lifetime 1/(Qr). The coherent evolution could be probed by applying a π/2 radiofrequency pulse (as part of the standard Ramsey sequence [3,50]) to convert the coherences to the populations of the m = ±1 atomic states, which could be measured by state-selective photoionization [49,50].…”

“…The steady-state populations and coherences [48] ρ (SS) gigi = (r + γ)∆ 2 + r 2 γ (3r + 2γ)∆ 2 + 2r 2 γ ρ R(SS) g1g2 = − r 2 γ (3r + 2γ)∆ 2 + 2r 2 γ (7) deviate from the values expected in thermal equilibrium [ρ (SS,th) gigi = (r + γ)/(3r + 2γ)]. As in the case of the V-system [29], this could be used to detect Fano coherences by measuring the deviation of steady-state populations from their equilibrium values via, e.g, stateselective photoionization [49,50].…”

Bloch oscillations with a metastable helium Bose-Einstein condensate

“…It was recently suggested that metastable helium (He * ) (which can be made into a Bose-Einstein condensate [20]) is a promising candidate for atom interferometry experiments [21], for several reasons: Due to its low mass, it can be accelerated fast and efficiently, allowing fast separation of finite-size wave packets and easy detection of different momentum states. For example, helium atoms that differ by two-photon momenta separate 20 times faster than rubidium.…”

“…Position-sensitive detectors can be used to make a full three-dimensional reconstruction of the atomic cloud [22,23] which helps to diagnose systematic effects. Another advantage of He * is its low second-order Zeeman shift of 2.3 mHz/G 2 [21] (2 times smaller than for 88 Sr and ∼10 5 times smaller than for Rb and Cs [24,25]), relaxing the required magnetic field control. For recoil measurements, an added advantage is that the mass of helium is known with a 20 times higher accuracy than that of Rb, Cs, or Sr [26,27].…”