Manipulating Rydberg atoms close to surfaces at cryogenic temperatures

Helium atoms in Rydberg states have been manipulated coherently with microwave radiation pulses near a gold surface and near a superconducting NbTiN surface at a temperature of $3\mathrm{K}$. The experiments were carried out with a skimmed supersonic beam of metastable ${\left(1s\right)}^1{\left(2s\right)}^1{}^1{S}_0$ helium atoms excited with laser radiation to $np$ Rydberg levels with principal quantum number $n$ between 30 and 40. The separation between the cold surface and the center of the collimated beam is adjustable down to $250\mu \mathrm{m}$. Short-lived $np$ Rydberg states were coherently transferred to the long-lived $ns$ state to avoid radiative decay of the Rydberg atoms between the photoexcitation region and the region above the cold surfaces. Further coherent manipulation of the $ns$ Rydberg states with pulsed microwave radiation above the surfaces enabled measurements of stray electric fields and allowed us to study the decoherence of the atomic ensemble. Adsorption of residual gas onto the surfaces and the resulting slow buildup of stray fields was minimized by controlling the temperature of the surface and monitoring the partial pressures of ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and $\mathrm{C}{\mathrm{O}}_2$ in the experimental chamber during the cool-down procedure. Compensation of the stray electric fields to levels below $100\mathrm{mV}/\mathrm{cm}$ was achieved over a region of $6\mathrm{mm}$ along the beam-propagation direction which, for the $1770\text{-m}/\mathrm{s}$ beam velocity, implies the possibility to preserve the coherence of the atomic sample for several microseconds above the cold surfaces.

Figure 1

Schematic view of the experimental setup consisting of the source chamber, the cryogenic chamber, and the ultra-high-vacuum-compatible experimental chamber (see text for details).

Figure 2

(a) Schematic of the excitation sequence. The blue arrow indicates the laser-induced transition from the ${\left(1s\right)}^1{\left(2s\right)}^1{}^1{S}_0$ metastable state of He to a specific state of the $np$ Rydberg series. The thick red arrows indicate transitions between $np$ and $ns$ states stimulated by pulsed microwave radiation. (b) Time sequence and length of the radiation pulses.

Figure 3

(a) Spectrum of the $31p\to 31s$ transition of singlet helium recorded with a 160-ns-long microwave pulse. The red line is a fit of $P_{p\to s}^s$ [see Eq. (1)]. (b) Spectrum of the $31s\to 31p$ transition recorded with a second 160-ns-long microwave pulse at a delay of $t=8\mu \mathrm{s}$. The red line is a fit of the expected $s$-state population $P_{s\to p}^s$ [see Eq. (2)], taking into account a Gaussian distribution of transition frequencies arising from the Stark effect caused by the stray field. The dashed vertical lines correspond to the calculated field-free frequency. Detunings are specified relative to the fitted line center.

Figure 4

(a) Measured transition frequency as a function of the applied electric potential difference $V$ to electrode 3 (bottom horizontal axis) and the corresponding parallel electric field $F_{\parallel }$ (top horizontal axis). The uncertainties of the transition frequencies are of the order of the size of the dots. The vertical bars correspond to the widths (FWHM) of the lines in MHz and the red line is a quadratic fit of the Stark shift in Eq. (3). (b) Population in the $34s$ state as a function of the time delay $t$ (bottom axis) and the detuning ${\Delta }_0$ from the field-free transition frequency (left axis). The blue areas indicate low $34s$ state population and the green areas show the positions of the electrodes 2 and 3. This provides a map of the stray electric field strength along the propagation axis (top axis) in the sample region with the right axis indicating the electric field $F$, determined from the fitted transition frequencies (white dots).

Figure 5

(a) Measurement of stray fields above the chip surface (yellow horizontal box) using the $34s\leftrightarrow 34p$ Stark shifts for atoms moving at a mean distance of $250\mu \mathrm{m}$ above the surface. The dots indicate the central positions of the transitions and the vertical bars indicate the corresponding width of the transitions. The data points indicate the measurement preformed without (red points) or with (black diamonds) stray-field compensation. Vertical green bars indicate the position of electrodes 2 and 3. (b) Spectrum of the $34s\leftrightarrow 34p$ transition with the stray-field compensation at a delay of $6\mu \mathrm{s}$. (c) Simulation of the direction of a compensation field without stray fields from the surface. The sample holder is depicted by the yellow bar and the electrodes by the green bars.

Figure 6

(a) Rabi oscillations measured as a function of microwave amplitude $\propto \sqrt{P_{\mu }}$ and detuning ${\Delta }_0$ from the field-free resonance frequency of the $34s\leftrightarrow 34p$ transition of singlet He, for a Rydberg atom cloud moving at a mean distance of $250\mu \mathrm{m}$ above the gold surface. (b) Corresponding simulation as described in the text. $\eta$ is varied linearly from 0 to 1 when the experimentally set amplitude at the microwave source is varied as the square root of the power between 0 and $5\mathrm{mW}$. In (a) and (b), the color scale indicating the population ranges from $0.14$ (blue) to 1 (dark red). (c) Measured (black dots) and simulated (red line) Rabi oscillations at the detuning indicated by the dashed vertical line in (a). The vertical scale is normalized to the maximum field-ionization signal of the $34s$ Rydberg state observed at a detuning ${\Delta }_0=-4.9\mathrm{MHz}$ and microwave amplitudes below $0.04\sqrt{\mathrm{W}}$.

Figure 7

(a) Population $P_{s\to p}^s$ as a function of microwave pulse length $\delta t$ versus detuning ${\Delta }_0$ from the field-free resonance frequency of the $34s\leftrightarrow 34p$ transition of singlet He. The Rydberg atom cloud is moving with a center-of-mass position of about $250\mu \mathrm{m}$ above the NbTiN surface. (b) Corresponding simulation as described in the text. (c) Observed (black dots) and simulated (red line) Rabi oscillations at a detuning of ${\Delta }_0=-2\mathrm{MHz}$.

Figure 8

(a) Temperatures of the sample holder (dashed blue line) and $30\text{-K}$ stage (solid red line) during the cooling procedure. The green lines indicate the temperatures at which critical gases freeze out. The blue lines show temperatures at which the sample holder is stabilized. (b) Typical pressures measured in the cryogenic chamber (dotted black line) and the partial pressures of H${}_2$O (solid yellow line) and N${}_2$ (dashed red line) measured in the experimental chamber. The features at positions labeled a – d are discussed in the text.

Figure 9

Spectra of the $\left[{\mathrm{He}}^{+}\right]np\leftarrow {\left(1s\right)}^1{\left(2s\right)}^1{}^1{S}_0$ Rydberg series of He recorded when (a) the residual gas adsorbed and charges build up in the matrix of frozen material, and when (b) the adsorption process onto the sample surface was suppressed. (c) Evolution of the field-induced shift of the ionization threshold ($-\Delta E_{\mathrm{I}}$) versus time, with (full blue circles) and without (open red circles) suppression of adsorption of residual gas onto the sample surface.

Figure 10

Measurement of the position and width of the He${}^{*}$ beam above the chip surface with an imaging MCP. Image obtained without (a) and with (c) collimating adjustable aperture. The intensity profiles along the vertical lines in panels (a) and (c) are displayed in panels (b) and (d), respectively (see text for details). The color scale in (a) and (c) corresponds to the minimal (blue) and maximal (red) value of each measurement.