Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number $n$ in the range between 25 and 35, have been deflected by 90$^\circ$, decelerated and loaded into off-axis electric traps at initial densities of $\approx 10^6$ atoms/cm$^{-3}$ and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 K and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as $n^{-4}$ and corresponding closely to the natural lifetimes of the initially prepared Rydberg-Stark states. The decay rate was found to continually decrease over time and to reach an almost $n$-independent rate of more than (1 ms)$^{-1}$ after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. TheComment: 36 pages, 18 figure

Rydberg states of helium in electric and magnetic fields of arbitrary relative orientation

A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ($n$ = 30, $B \leq$ 120 mT and $F$ = 0 - 78 V/cm ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different $m_l$ values and pronounced $m_l$-mixing effects at all angles between the electric and magnetic field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.Comment: 16 pages, 18 figure

Slow and velocity-tunable beams of metastable He2_2 by multistage Zeeman deceleration

Metastable helium molecules (He$_2^*$) have been generated by striking a discharge in a supersonic expansion of helium gas from a pulsed valve. When operating the pulsed valve at room temperature, 77K, and 10K, the mean velocity of the supersonic beam was measured to be 1900m/s, 980m/s, and 530m/s, respectively. A 55-stage Zeeman decelerator operated in a phase-stable manner was then used to further reduce the beam velocity and tune it in the range between 100 and 150m/s. The internal-state distribution of the decelerated sample was established by photoionization spectroscopy.Comment: 10 pages, 7 figure

Fluorescence-lifetime-limited trapping of Rydberg helium atoms on a chip

Metastable (1s)(2s) $^3{\rm S}_1$ helium atoms produced in a supersonic beam were excited to Rydberg-Stark states (with $n$ in the $27-30$ range) in a cryogenic environment and subsequently decelerated by, and trapped above, a surface-electrode decelerator. In the trapping experiments, the Rydberg atoms were brought to rest in 75~$\mu$s and over a distance of 33~mm and kept stationary for times $t_{\mathrm{trap}}$ in the $0-525$~$\mu$s range, before being re-accelerated for detection by pulsed field ionization. The use of a home-built valve producing short gas pulses with a duration of about 20~$\mu$s enabled the reduction of losses arising from collisions with atoms in the trailing part of the gas pulses. Cooling the decelerator to 4.7~K further suppressed losses by transitions induced by blackbody radiation and by collisions with atoms desorbing from the decelerator surface. The main contribution (60\%) to the atom loss during deceleration is attributed to the escape out of the decelerator moving traps of atoms having energies higher than the trap saddle point, spontaneous emission and collisions with atoms in the trailing part of the gas pulses causing each only about 20\% of the atom loss. At 4.7 K, the atom losses in the trapping phase of the experiments were found to be almost exclusively caused by spontaneous emission and the trap lifetimes were found to correspond to the natural lifetimes of the Rydberg-Stark states. Increasing the temperature to 100 K enhanced the trap losses by transitions stimulated by blackbody radiation

Metrology of Rydberg states of the hydrogen atom

We present a method to precisly measure the frequencies of transitions to high-$n$ Rydberg states of the hydrogen atom which are not subject to uncontrolled systematic shifts caused by stray electric fields. The method consists in recording Stark spectra of the field-insensitive $k=0$ Stark states and the field-sensitive $k=\pm2$ Stark states, which are used to calibrate the electric field strength. We illustrate this method with measurements of transitions from the $2\,\text{s}(f=0\text{ and } 1)$ hyperfine levels in the presence of intentionally applied electric fields with strengths in the range between $0.4$ and $1.6\,$Vcm$^{-1}$. The slightly field-dependent $k=0$ level energies are corrected with a precisely calculated shift to obtain the corresponding Bohr energies $\left(-cR_{\mathrm{H}}/n^2\right)$. The energy difference between $n=20$ and $n=24$ obtained with our method agrees with Bohr's formula within the $10\,$kHz experimental uncertainty. We also determined the hyperfine splitting of the $2\,\text{s}$ state by taking the difference between transition frequencies from the $2\,\text{s}(f=0 \text{ and }1)$ levels to the $n=20,k=0$ Stark states. Our results demonstrate the possibility of carrying out precision measurements in high-$n$ hydrogenic quantum states

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 $3 \text{K}$. The experiments were carried out with a skimmed supersonic beam of metastable $(1\text{s})^1(2\text{s})^1\, {}^1\text{S}_0$ helium atoms excited with laser radiation to $n\text{p}$ 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 $250 \mu\text{m}$. Short-lived $n\text{p}$ Rydberg levels were coherently transferred to the long-lived $n\text{s}$ 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 $n\text{s}$ Rydberg levels 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 build-up of stray fields was minimized by controlling the temperature of the surface and monitoring the partial pressures of H$_2$O, N$_2$, O$_2$ and CO$_2$ in the experimental chamber during the cool-down. Compensation of the stray electric fields to levels below $100 \text{mV}/\text{cm}$ was achieved over a region of $6 \text{mm}$ along the beam-propagation direction which, for the $1770 \text{m}/\text{s}$ beam velocity, implies the possibility to preserve the coherence of the atomic sample for several microseconds above the cold surfaces.Comment: 12 pages, 10 figure

Imaging-assisted single-photon Doppler-free laser spectroscopy and the ionization energy of metastable triplet helium

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation which exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities - and thus their Doppler shifts. With the example of spectra of (1\mathrm{s})(n\mathrm{p})\,^3\mathrm{P}_{0-2}\leftarrow (1\mathrm{s})(2\mathrm{s})\,^3\mathrm{S}_1 transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1 MHz in the UV. Using a retro-reflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental (Clausen et al., Phys. Rev. Lett. 127 093001 (2021)) and high-level theoretical (Patk\'os et al., Phys. Rev. A 103 042809 (2021)) values of this quantity

Multistage Zeeman deceleration of metastable neon

A supersonic beam of metastable neon atoms has been decelerated by exploiting the interaction between the magnetic moment of the atoms and time-dependent inhomogeneous magnetic fields in a multistage Zeeman decelerator. Using 91 deceleration solenoids, the atoms were decelerated from an initial velocity of 580m/s to final velocities as low as 105m/s, corresponding to a removal of more than 95% of their initial kinetic energy. The phase-space distribution of the cold, decelerated atoms was characterized by time-of-flight and imaging measurements, from which a temperature of 10mK was obtained in the moving frame of the decelerated sample. In combination with particle-trajectory simulations, these measurements allowed the phase-space acceptance of the decelerator to be quantified. The degree of isotope separation that can be achieved by multistage Zeeman deceleration was also studied by performing experiments with pulse sequences generated for $^{20}$Ne and $^{22}$Ne.Comment: 16 pages, 15 figure

Die Ausbreitung des Eem-Meeres in Nordwestdeutschland

Neuere Kartier- und Bohrergebnisse machen eine teilweise Revision der bisherigen Ansichten über die Ausbreitung des Eem-Meeres notwendig. Nach Dechend (1958) und Sindowski (1958, 1965) erreichte das Eem-Meer während seines Höchststandes ungefähr die heutige Küstenlinie. Im Bereich der ostfriesischen Küste haben die Arbeiten von Barckhausen (1984) und Barckhausen & Streif (1978) einige kleinere Veränderungen des eemzeitlichen Küstenverlaufs ergeben. Im Elbe-Weser-Dreieck muß die Küstenlinie des Eem-Meeres um bis zu 22 km in die Hadelner Bucht verlegt werden. Sie entspricht dadurch der maximalen Ausbreitung des holozänen Meeres vom Subboreal bis Subatlantikum.researc

New method to study ion-molecule reactions at low temperatures and application to the H2+_2^+ + H2_2 →\rightarrow H3+_3^+ + H reaction

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the ${\rm H}_2^+ + {\rm H}_2\rightarrow {\rm H}_3^+ + {\rm H}$ reaction with the ${\rm H}_2^+$ ion prepared in a single rovibrational state at collision energies in the range $E_{\rm col}/k_{\rm B} = 5$-60 K. To reach such low collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H$_2$ molecules and the second is a supersonic beam of H$_2$ molecules excited to Rydberg-Stark states of principal quantum number $n$ selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10$^\circ$. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state ${\rm H}_2$ beam and by adapting the electric-potential functions to the electrodes of the deflector. The collision energy is varied down to below $E_{\rm col}/k_{\rm B}= 10$ K, i.e., below $E_{\rm col}\approx 1$ meV, with an energy resolution of 100 $\mu$eV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical-Langevin-capture model in the collision-energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studyingComment: 39 pages, 10 figure