Characterizing the local vectorial electric field near an atom chip using Rydberg-state spectroscopy

We use the sensitive response to electric fields of Rydberg atoms to characterize all three vector components of the local electric field close to an atom-chip surface. We measured Stark-Zeeman maps of $S$ and $D$ Rydberg states using an elongated cloud of ultracold rubidium atoms (temperature $T\sim 2.5\mu \mathrm{K}$) trapped magnetically $100\mu \mathrm{m}$ from the chip surface. The spectroscopy of $S$ states yields a calibration for the generated local electric field at the position of the atoms. The values for different components of the field are extracted from the more complex response of $D$ states to the combined electric and magnetic fields. From the analysis we find residual fields in the two uncompensated directions of $0.0\pm 0.2$ and $1.98\pm 0.09$ V/cm. This method also allows us to extract a value for the relevant field gradient along the long axis of the cloud. The manipulation of electric fields and the magnetic trapping are both done using on-chip wires, making this setup a promising candidate to observe Rydberg-mediated interactions on a chip.

Figure 1

(a) Calculated Stark map of the $28D_{5/2}$ state of ${}^{87}\mathrm{Rb}$ in a magnetic field of $B=3.4$ G. The red and black lines correspond to the cases when the magnetic field is perpendicular and parallel to the electric field, respectively. At zero electric field each line represents the sublevel $m_j=5/2,3/2,1/2,-1/2,-3/2,-5/2$ from top to bottom, respectively. In the $\vec{E}\perp \vec{B}$ configuration, for the two uppermost states the initial downshift is followed by an increase in energy, thus creating an initial dip in the Stark map. This is an additional feature compared to the $\vec{E}\parallel \vec{B}$ case, and it can be used to extract information on different electric-field components. (b) Detail of the shift of the two uppermost sublevels for various stray field configurations in the case where the applied electric field ${\vec{E}}_{ap}\perp \vec{B}$. Here, we use an orthogonal coordinate system ($x,u,v$) with $x$ along the direction of the magnetic field and $u$ along the direction of the applied electric field ${\vec{E}}_{ap}$; $v$ is perpendicular to both $x$ and $u$ (see Fig. 2 for a graphic description of the experimental field directions). The plot illustrates the sensitivity of the Stark-Zeeman map to different field configurations; see text for details.

Figure 2

(a) Sketch of the experimental geometry: We excite ${}^{87}\mathrm{Rb}$ atoms to a Rydberg level using a two-photon excitation scheme with two counterpropagating 780- and 480-nm lasers. The atoms are magnetically trapped in vacuum $\sim 100\mu \mathrm{m}$ below the surface of an atom chip. The numbering of the on-chip wires is indicated in the inset. The excitation is done along the axial direction of the cloud during magnetic trapping. The gray arrows indicate a coordinate system composed of different field components; both $(x,y,z)$ and $(x,u,v)$ are orthogonal systems. Namely, we call the stray electric field along the long direction of the cloud the parallel component $E_x$ (along the direction of the $x$ axis). We apply a voltage to wire 4 that changes the field ($E_{ap}$ along the direction of the $u$ axis) at the position of the atoms so we can generate Stark maps. The produced field is perpendicular to the $B$ field and lies in the $yz$ plane. The stray field in the third direction, labeled $E_v$ (along the direction of the $v$ axis), is in the $yz$ plane and orthogonal to $E_u$. (b) Laser scheme for the Rydberg excitation. The intermediate state detuning from the $5P_{3/2}$ state is 100 MHz towards the blue.

Figure 3

Measured Stark shift and broadening for the $30S$ state. We use these measurements to calibrate the actual applied electric field we are generating at the position of the atoms. The plot shows the resonance shift of the Rydberg signal at different applied voltages. The vertical bars are the measured FWHM of each feature obtained from a Gaussian fit. We fit two quadratic functions to the data in order to obtain the parameters in Eq. (2); see the main text for details.

Figure 4

The $28D_{5/2}$-state Stark map of two different sublevels: The top and bottom curves are the $m_j=5/2$ and $m_j=3/2$ sublevels (ZEL), respectively. The color scale indicates the normalized number of atoms, normalized to the number of atoms measured when the Rydberg excitation lasers are off resonance. The measurements were taken outside the dark red area. We deliberately saturated the upper sublevel in order to be able to see the other one, which has a much smaller coupling strength. The white lines are the resulting fitted curves for the resonance position of each sublevel where the parallel and perpendicular electric fields are used as fitting parameters (from the fit we get $E_x=0$ V/cm and $E_v=1.98$ V/cm, respectively; see main text for details).

Figure 5

Rydberg loss spectroscopy of the $28D_{5/2}$ state for different applied fields. (a) The top state in Fig. 1 considering the voltage-to-field conversion. The color scale indicates the normalized atom number in each spectrum; measurements are performed outside the uniform dark red area. The dashed white line shows the resulting fitted curve, obtained using only the data within the area of the solid white line (below 15 V/cm). (b) At $E_{ap}\sim 19$ V/cm the Rydberg feature is asymmetric due to the presence of field gradients. Therefore, a skewed Gaussian (solid curve) is fit to the data. A small asymmetry is observed around 0 V/cm; it is due to a slow residual drift of the cavity to which the Rydberg lasers are locked [26]. (c) The measurement of the FWHM of the loss feature at different temperatures at an applied electric field of $E_{ap}\sim 12$ V/cm where the Rydberg feature is symmetric.