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Journal of Physics B Atomic Molecular and Optical Physics

Cooling of Rydberg during radiative cascade

C L Taylor, Jingjing Zhang, F. Robicheaux

Published Nov 17, 2006• 23 citations
Publisher

Abstract

We have simulated the centre-of-mass motion of Rydberg anti-hydrogen atoms in spatially varying magnetic fields. We find that a population of anti-hydrogen can lose substantial centre-of-mass kinetic energy during the radiative cascade to the ground state. The loss of energy is due to the change in magnetic moment when photons are emitted and is akin to adiabatic cooling. We also simulate the pattern of anti-hydrogen hits on the walls of the trap and find that the existence of trapped Rydberg atoms leads to a distinctive distribution along the trap axis.

DOI
10.1088/0953-4075/39/23/012

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We have simulated the centre-of-mass motion of Rydberg anti-hydrogen atoms in spatially varying magnetic fields. We find that a population of anti-hydrogen can lose substantial centre-of-mass kinetic energy during the radiative cascade to the ground state. The loss of energy is due to the change in magnetic moment when photons are emitted and is akin to adiabatic cooling. We also simulate the pattern of anti-hydrogen hits on the walls of the trap and find that the existence of trapped Rydberg atoms leads to a distinctive distribution along the trap axis.
We have simulated the motion of a Rydberg hydrogen atom in electric and magnetic fields that have a strong position dependence. The orientation and strengths of the fields depend strongly on the spatial position of the atom. The angle between the fields could take on any value. We use the quantum energy levels for a Rydberg state in electric and magnetic fields to derive a spatially dependent potential energy for the centre-of-mass motion of the atom. We compute the radiative decay rate into states with low principal quantum numbers. After the decay, the atom could be trapped using the magnetic moment of the electron. We present results for a specific trap geometry which could be experimentally realized.
We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to 4T4\phantom{\rule{0.3em}{0ex}}\mathrm{T}4T. We have followed the radiative cascade from completely l,ml,ml,m mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\ensuremath{\mid}m\ensuremath{\mid}\ensuremath{\sim}n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\ensuremath{\lesssim}20$. For higher nnn manifolds, the electrons in the most negative mmm states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\ensuremath{\sim}35$ generated in antihydrogen experiments at 4K4\phantom{\rule{0.3em}{0ex}}\mathrm{K}4K will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative mmm states due to the fact that only $\ensuremath{\mid}\ensuremath{\Delta}m\ensuremath{\mid}+\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\pi}\ensuremath{\mid}=1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\ensuremath{\mid}m\ensuremath{\mid}$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\ensuremath{\gtrsim}20$.
Cold circular Rydberg atoms are produced and magnetically trapped. The trap is characterized by direct spatial imaging of ion distributions, ion counting, and state-selective field ionization. At room temperature, we observe about 70% of the trapped atoms remaining after 6 ms. We measure a trap oscillation frequency increase of the circular Rydberg atom trap relative to the ground-state atom trap due to the larger magnetic moment of the circular Rydberg atoms. Simulations of the center-of-mass and internal-state evolution of circular states in our magnetic trap are performed and results are in good agreement with experimental observations.
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.
A new method for cooling atomic hydrogen down to 100 µK or below is suggested. The method exploits the unique properties of atomic hydrogen, which are the following: atomic hydrogen does not condense at temperatures as low as 20 µK and cannot be heated by IR radiation in the absence of atom-wall collisions. Therefore, the most efficient and well-known gas cooling technique can be employed, namely, the adiabatic expansion of the volume occupied by the gas (this approach is used in a gas-expansion machine). It is suggested to adiabatically expand the volume of a magnetic trap containing atomic hydrogen.