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Physical Chemistry Chemical Physics

Trapping cold molecular hydrogen

Ch. Seiler, S. D. Hogan, Frédéric Merkt

Published Jan 1, 2011• 42 citations
Publisher

Abstract

Translationally cold H(2) molecules excited to non-penetrating |M(J)| = 3 Rydberg states of principal quantum number in the range 21-37 have been decelerated and trapped using time-dependent inhomogeneous electric fields. The |M(J)| = 3 Rydberg states were prepared from the X (1)Σ(+)(u)(v = 0, J = 0) ground state using a resonant three-photon excitation sequence via the B (1)Σ(+)(u)(v = 3, J = 1) and I (1)Π(g) (v = 0, J = 2) intermediate states and circularly polarized laser radiation. The circular polarization of the vacuum ultraviolet radiation used for the B ← X transition was generated by resonance-enhanced four-wave mixing in xenon and the degree of circular polarization was determined to be 96%. To analyse the deceleration and trapping experiments, the Stark effect in Rydberg states of molecular hydrogen was calculated using a matrix diagonalization procedure similar to that presented by Yamakita et al., J. Chem. Phys., 2004, 121, 1419. Particular attention was given to the prediction of zero-field positions of low-l states and of avoided crossings between Rydberg-Stark states with different values of |M(J)|. The calculated Stark maps and probabilities for diabatic traversal of the avoided crossings were used as input to Monte-Carlo particle-trajectory simulations. These simulations provide a quantitatively satisfactory description of the experimental data and demonstrate that particle loss caused by adiabatic traversals of avoided crossings between adjacent |M(J)| = 3 Stark states of H(2) is small at principal quantum numbers beyond n = 25. The main source of trap losses was found to be from collisional processes. Predissociation following the absorption of blackbody radiation is estimated to be the second most important trap-loss mechanism at room temperature, and trap loss by spontaneous emission is negligible under our experimental conditions.

DOI
10.1039/c1cp21276a

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Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.

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Translationally cold H(2) molecules excited to non-penetrating |M(J)| = 3 Rydberg states of principal quantum number in the range 21-37 have been decelerated and trapped using time-dependent inhomogeneous electric fields. The |M(J)| = 3 Rydberg states were prepared from the X (1)Σ(+)(u)(v = 0, J = 0) ground state using a resonant three-photon excitation sequence via the B (1)Σ(+)(u)(v = 3, J = 1) and I (1)Π(g) (v = 0, J = 2) intermediate states and circularly polarized laser radiation. The circular polarization of the vacuum ultraviolet radiation used for the B ← X transition was generated by resonance-enhanced four-wave mixing in xenon and the degree of circular polarization was determined to be 96%. To analyse the deceleration and trapping experiments, the Stark effect in Rydberg states of molecular hydrogen was calculated using a matrix diagonalization procedure similar to that presented by Yamakita et al., J. Chem. Phys., 2004, 121, 1419. Particular attention was given to the prediction of zero-field positions of low-l states and of avoided crossings between Rydberg-Stark states with different values of |M(J)|. The calculated Stark maps and probabilities for diabatic traversal of the avoided crossings were used as input to Monte-Carlo particle-trajectory simulations. These simulations provide a quantitatively satisfactory description of the experimental data and demonstrate that particle loss caused by adiabatic traversals of avoided crossings between adjacent |M(J)| = 3 Stark states of H(2) is small at principal quantum numbers beyond n = 25. The main source of trap losses was found to be from collisional processes. Predissociation following the absorption of blackbody radiation is estimated to be the second most important trap-loss mechanism at room temperature, and trap loss by spontaneous emission is negligible under our experimental conditions.
Abstract 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 ◦ , decelerated and loaded into off-axis electric traps at initial densities of ≈ 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 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. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared Rydberg–Stark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg–Stark states of higher ∣ m ∣ values. While searching for such a mechanism, we discovered that resonant dipole–dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher ∣ m ∣ values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole–dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative processes that the observed decay of the population of Rydberg atoms in the trap could be satisfactorily reproduced for all n values studied experimentally.
The interaction between inhomogeneous electric fields and the large electric dipole moments of atoms and molecules in Rydberg states of high principal quantum number can be used to efficiently accelerate and decelerate atoms and molecules in the gas phase. We describe here how hydrogen atoms and molecules initially moving with velocities of ∼600 m/s in supersonic beams can be decelerated to zero velocity and loaded into electric traps. The long observation times that are made possible by the electrostatic trapping enables one to study slow relaxation processes. Experiments are presented in which we have observed photoionization processes and transitions between Rydberg states induced by blackbody radiation at temperatures between 10 K and 300 K on a time scale of several milliseconds. Comparison of these processes in Rydberg states of H and H(2) suggests the importance, in H(2), of collisional processes and of the process of blackbody-radiation-induced predissociation.
Hydrogen atoms in supersonic expansions with velocities in the range from 700to800m∕s700\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}800\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}700to800m∕s have been excited to Rydberg-Stark states with principal quantum number nnn between 20 and 40, decelerated to zero velocity in the lab frame using time-dependent inhomogeneous electric fields, and trapped in a two-dimensional electrostatic trap with an initial density of $\ensuremath{\approx}5\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The motion of the atomic cloud in the trap was observed by measuring the times of flight and images of the H+{\mathrm{H}}^{+}H+ ions produced by pulsed field ionization. The velocity distribution of the trapped atoms can be described by an effective temperature of 350mK350\phantom{\rule{0.3em}{0ex}}\mathrm{mK}350mK. The decay of the population of trapped atoms does not follow a single-exponential behavior and has contributions from radiative and collisional processes.
Hydrogen and deuterium Rydberg atoms, initially moving at velocities of 600 and 560 m s −1 , respectively, in pulsed supersonic beams, have been decelerated and electrostatically trapped following adiabatic 90° deflection from their initial axis of propagation to minimize collisions with the trailing edge of the gas pulses. The time evolution of the potential energy surfaces, over which the atoms undergoing deceleration travel during the trap-loading process, is analogous to that of a moving electrodynamic trap. It has been studied in the laboratory-fixed frame of reference and in the continuously moving frame of reference defined by the instantaneous position of the electric-field minimum around which the atoms are located. The importance of the quadratic Stark effect in the deceleration of samples in Rydberg states with principal quantum numbers above 35 has also been investigated by comparison of experimental results with predictions resulting from the numerical calculation of particle trajectories. The data presented for deuterium atoms represent the first application of Rydberg–Stark deceleration and trapping for this atom. Comparison of the rate of loss of n = 30 H and D atoms from the trap enables one to conclude that it is not affected by the particle dynamics during deceleration and trap loading.
N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10 ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.
Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.