Electric field metrology for SI traceability: Systematic measurement uncertainties in electromagnetically induced transparency in atomic vapor

Abstract

We investigate the relationship between the Rabi frequency (X RF , related to the applied electric field) and Autler-Townes (AT) splitting, when performing atom-based radio-frequency (RF) electric (E) field strength measurements using Rydberg states and electromagnetically induced transparency (EIT) in an atomic vapor. The AT splitting satisfies, under certain conditions, a well-defined linear relationship with the applied RF field amplitude. The EIT/AT-based E-field measurement approach derived from these principles is currently being investigated by several groups around the world as a means to develop a new SI-traceable RF E-field measurement technique. We establish conditions under which the measured AT-splitting is an approximately linear function of the RF electric field. A quantitative description of systematic deviations from the linear relationship is key to exploiting EIT/AT-based atomic-vapor spectroscopy for SI-traceable field measurement. We show that the linear relationship is valid and can be used to determine the E-field strength, with minimal error, as long as the EIT linewidth is small compared to the AT-splitting. We also discuss interesting aspects of the thermal dependence (i.e., hot-versus cold-atom) of this EIT-AT technique. An analysis of the transition from coldto hot-atom EIT in a Doppler-mismatched cascade system reveals a significant change of the dependence of the EIT linewidth on the optical Rabi frequencies and of the AT-splitting on X RF .

Transition from electromagnetically induced transparency to Autler–Townes splitting in cold cesium atoms

“…These trends for γ ATS are also borne out by calculating the separation between the pair of non-dark eigenstates of the (decay-free) Hamiltonian in equation (1), when setting all detunings to zero. Calculations similar to those shown in figures 2 and 3 can be performed at any atom temperature(see [32] and references therein), and for both cascade and Λ-type three-level atoms. In the hot-atom cases (i.e., in vapor cells), the difference between coupler and probe wavelengths determines the size of residual Doppler shifts, which in turn determines the visibilities and detailed shapes of EIT and ATS spectra.…”

“…In the hot-atom cases (i.e., in vapor cells), the difference between coupler and probe wavelengths determines the size of residual Doppler shifts, which in turn determines the visibilities and detailed shapes of EIT and ATS spectra. In hot gases γ EIT generally tends to be larger than in the cold-atom case, in particular in weak coupler and probe fields, and follows a different scaling (see figure 7 in [32]).…”

“…We numerically solve the equations (1)-(3) to obtain the absorption coefficient α for a range of values of Ω c and Ω p , including the case of a strong probe, Ω p Γ eg . The result is averaged over the thermal velocity distribution in the gas [32]; under our conditions (T=100-200 μK) the thermal motion is marginally important. In the calculation we also assume γ r =0, which is admissible due to our very low experimental probe intensities and the low principal quantum number of the utilized Rydberg state.…”

“…Exploiting the fact that Rydberg atoms strongly couple to radio-frequency(RF) fields, Rydberg EIT and ATS effects are used to realize precise measurements of such fields [27][28][29][30][31]. Holloway et al [32] have investigated the relationship between the Rabi frequency of resonant RF transitions between Rydberg states and the resultant ATS splitting in Rydberg-EIT spectra measured in room-temperature atomic vapor. In related work, the enhancement and suppression of multi-wave mixing (MWM) in five-level systems [33] has been studied, and the effect of Rydbergatom interactions was explored [34].…”

“…We introduce two parameters, the Rydberg-EIT linewidth, γ EIT , and the AT spilitting, γ ATS , to characterize the EIT to ATS transition. In our model, we calculate spectra using methods provided in [32] to study the dependence of γ EIT and γ ATS on the Rabi frequencies of both the probe and coupling transitions. The transition between EIT and ATS effect is linked to a qualitative change in behavior of γ EIT and γ ATS as a function of coupler and probe Rabi frequencies.…”