Microwave spectroscopy of radio-frequency-dressedRb87

Abstract

We study the hyperfine spectrum of atoms of 87 Rb dressed by a radio-frequency field, and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant side bands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum, using a semi-classical model in the low field limit and the Rotating Wave Approximation for alkali-like species in general and 87 Rb atoms in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.

Bi-chromatic adiabatic shells for atom interferometry

“…To do this, we load the bi-chromatic shell trap for several pairs of ω 1 and ω 2 and then we fit Lorentzian curves to the number of atoms transferred to the upper state as we scan the microwave frequency ω MW /2π. By finding the combination of ω 1 and ω 2 that gives the minimum line-width, we can thus match the two traps (see figure 2(a)), at which point we observe a reduction in line-width by of the order of ×10 with respect to the mono-chromatic shell (measured elsewhere [29]).…”

“…The solution of this Hamiltonian for a weak MW-field that acts as a probe on the RF-dressed energy levels leads to inter-manifold transitions [28][29][30] on a spectrum of 7 groups (spaced by the RF-dressing frequency) of 5 transitions (spaced by the RF-dressing Rabi frequency), when the initial state is [29] for a detailed study). Concretely, the transition with n=0, k=0 is coincident with the hyperfine splitting [29]. In practice, this transition is shifted both by the nonlinear dependence of the eigenenergies on the magnetic field and on the difference in magnitude of g 1 and g 2 .…”

“…We explain these multi-photon transitions with a semi-classical two-level toy model in appendix C. An analysis on the complete microwave spectrum between rfdressed ultra-cold Rubidium 87 Zeeman sub-levels can be found in [29]. In this work, we focus only on the transition from -ñ 1, 1 | to ñ 2, 1 | .…”

Hafele and Keating on a chip: Sagnac interferometry with a single clock

“…Another consequence is the emergence of groups of transitions to quasienergy levels that are separated by multiples of the RF-dressing frequency, ω RF . 21 Each group occurs near one of the seven possible bare transition frequencies, and these reflect the standard selection rules for microwave polarisation. Even numbered groups n = 0, ±2 may be addressed with π-polarised MW, and odd numbered groups n = ±1, ±3 with σ-polarisation.…”

“…Additional aspects include the possibility of low-noise dispersive detection, 20 and also a complex spectrum of hyperfine multi-photon transitions that combine RF-photons from the dressing fields with additional microwave driving. 21 The principle of RF-dressed potentials 22 is to combine static B DC with time-dependent B RF (t) magnetic fields that drive atomic spin-flips. Neglecting the internal structure of an atom and within the weak field regime, the Hamiltonian for an atom with total spin F interacting with a static and single-frequency RF-field of arbitrary polarisation is given by…”