Two-dimensional imaging of electromagnetic fields via light sheet fluorescence imaging with Rydberg atoms

Abstract

The ability to image electromagnetic fields holds key scientific and industrial applications, including electromagnetic compatibility, diagnostics of high-frequency devices, and experimental scientific work involving field interactions. Generally electric and magnetic field measurements require conductive elements which significantly distort the field. However, electromagnetic fields can be measured without altering the field via the shift they induce on Rydberg states of alkali atoms in atomic vapor, which are highly sensitive to electric fields. Previous field measurements using Rydberg atoms utilized electromagnetically induced transparency to read out the shift on the states induced by the fields, but did not provide spatial resolution. In this work, we demonstrate that electromagnetically induced transparency can be spatially resolved by imaging the fluorescence of the atoms. We demonstrate that this can be used to image $\sim$ V/cm scale electric fields in the DC-GHz range and $\sim$ mT scale static magnetic fields, with minimal distortion to the fields. We also demonstrate the ability to image $\sim$ 5 mV/cm scale fields for resonant microwave radiation and measure standing waves generated by the partial reflection of the vapor cell walls in this regime. With additional processing techniques like lock-in detection, we predict that our sensitivities could reach down to nV/cm levels. We perform this field imaging with a spatial resolution of 160 $μ$m, limited by our imaging system, and estimate the fundamental resolution limitation to be 5 $μ$m.

Figures (8)

• Figure 1: The fluorescence measurement scheme.a, The energy level diagram for $^{85}$Rb used in the measurement. b, The experimental setup for spatially resolved fluorescence measurement. c, The CCD image of the light sheet is recorded as the coupling laser is scanned ($\Delta f_c$). The resulting change in fluorescence $\Delta \mathcal{F}$ of a 2$\times$2 pixel average in the vapor cell (representing a 160$\times$160 $\mu$m area) is shown in black. d, The NIST logo is constructed of copper over a 1.6 mm thick circuit board with a conductive ground plane underneath. e, The geometry is replicated in a finite element model. f, The fluorescence is imaged in an 11$\times$11$\times$45 mm cell placed above the letters, with the beam placed 2.5 mm above the letters. 1 V$_\textrm{pk}$ at 30 MHz is applied to the letters. The inset shows the spectrum taken from a group of (2$\times$2) that were averaged to achieve sufficient signal to noise. The electric field strength is found by fitting the spectrum to the Eq. \ref{['eq:ACStarkFit']}. g, The field is measured at all points in the cell by fitting each point. h, The simulated field strength at 2.5 mm above the letters given by the finite element model.
• Figure 1: Response of the EIT spectrum to non-resonant electric fields.a, The dynamic polarizability $\alpha$ is plotted for the relevant levels (legend in $\textbf{b}$) over a range of drive frequencies $f_\textrm{applied}$. b, A Stark map showing the change in the energy of each $m_J$ sub-level of the Rydberg states for various static electric field strengths.
• Figure 2: Shielding of low frequency electric fields by the vapor cell. An electric field at a fixed amplitude of 0.71 V$_\mathrm{RMS}$ is applied using electrodes placed 11 mm apart on either side of the cell. The applied frequency $f_\textrm{applied}$ is then scanned, and an EIT spectrum is measured (left) at various $f_\textrm{applied}$ (blue) and fit (black) to find the electric field strength. This is repeated for many $f_\textrm{applied}$ and the rolloff at low frequencies is mapped (right). The data is fitted to an exponential fit and the cutoff frequency is found to be 1.0$\pm$0.6 MHz.
• Figure 2: Spatial resolution limiting effects.a, The parallax resolution $r_\textrm{parallax}$ arises from the finite thickness of the beam resulting in a horizontal width corresponding to a vertical slice of the beam when projected onto the camera aperture. b, The thermal resolution $r_\textrm{th}$ arises from the atoms moving between absorbing and emitting radiation.
• Figure 3: Fluorescence images of standing waves in a parallel wire transmission line. The finite element model (a) and actual transmission line (b) are shown. The fluorescence imaging is performed in the plane definied by the leads. b, The vapor cell used in this dataset contained a patch of charges opposite the stem of the vapor cell. This is imaged to demonstrate DC field sensing capabilities inside of the vapor cell, illustrating the ability to image fields due to localized charges. c-h, A signal at 15 dBm is applied and the resulting fields are shown at 1 GHz (simulation c, measured d), 5 GHz (e,f), and 10 GHz (g,h).