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Physical Review A

Circular states of atomic hydrogen

Robert Lutwak, Jeffrey Holley, Pin Peter Chang, Scott N. Paine, Daniel Kleppner, Theodore W. Ducas

Published Aug 1, 1997• 61 citations
Publisher

Abstract

We describe the creation of circular states of hydrogen by adiabatic transfer of a Rydberg state in crossed electric and magnetic fields, and also by adiabatic passage in a rotating microwave field. The latter method permits rapid switching between the two circular states of a given $n$ manifold. The two methods are demonstrated experimentally, and results are presented of an analysis of the field ionization properties of the circular states. An application for the circular states is illustrated by millimeter-wave resonance in hydrogen of the $n=29\ensuremath{\rightarrow}n=30$ transition.

DOI
10.1103/physreva.56.1443

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We describe the creation of circular states of hydrogen by adiabatic transfer of a Rydberg state in crossed electric and magnetic fields, and also by adiabatic passage in a rotating microwave field. The latter method permits rapid switching between the two circular states of a given nnn manifold. The two methods are demonstrated experimentally, and results are presented of an analysis of the field ionization properties of the circular states. An application for the circular states is illustrated by millimeter-wave resonance in hydrogen of the n=29\ensuremath→n=30n=29\ensuremath{\rightarrow}n=30n=29\ensuremath→n=30 transition.
Helium atoms have been prepared in the circular $|n=55,\ensuremath{\ell}=54,{m}_{\ensuremath{\ell}}=+54\ensuremath{\rangle}$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially traveling in pulsed supersonic beams, were photoexcited from the metastable 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ level to the outermost, ${m}_{\ensuremath{\ell}}=0$ Rydberg-Stark state with n=55n=55n=55 in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with ${m}_{\ensuremath{\ell}}=+54$ defined with respect to the magnetic-field quantization axis. The circular states were detected by ramped electric-field ionization along the magnetic-field axis. The dependence of the circular state production efficiency on the strength of the excitation electric field, and the electric-field switch-off time was studied, and microwave spectroscopy of the circular-to-circular $|55,54,+54\ensuremath{\rangle}\ensuremath{\rightarrow}|56,55,+55\ensuremath{\rangle}$ transition at $\ensuremath{\sim}38.5$ GHz was performed.
We describe an experimental method of producing circular Rydberg states using a circularly polarized microwave field. A Na sss state is excited in the circularly polarized microwave field, and as the field is turned off, it makes an adiabatic rapid passage through a multiphoton resonance and evolves adiabatically into the circular state. Minimal optical selectivity is required and the field can be turned off quickly.
Circular Rydberg states with n=70n=70n=70 have been prepared in helium using a modified version of the crossed-fields method. This approach to the preparation of high-nnn circular Rydberg states overcomes limitations of the standard crossed-fields method which arise at this, and higher, values of nnn. The experiments were performed with atoms traveling in pulsed supersonic beams that were initially laser photoexcited from the metastable 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ level to the 1s73s3S11s73s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s73s3S1​ level by resonance-enhanced two-color two-photon excitation in a magnetic field of 16.154 G. These excited atoms were then polarized using a perpendicular electric field of 0.844 V/cm, and transferred by a pulse of microwave radiation to the state that, when adiabatically depolarized, evolves into the n=70n=70n=70 circular state in zero electric field. The excited atoms were detected by state-selective electric field ionization. Each step of the circular state preparation process was validated by comparison with the calculated atomic energy-level structure in the perpendicular electric and magnetic fields used. Of the atoms initially excited to the 1s73s3S11s73s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s73s3S1​ level, $\ensuremath{\sim}80%$ were transferred to the n=70n=70n=70 circular state. At these high values of $n, \mathrm{\ensuremath{\Delta}}n=1$ circular-to-circular Rydberg state transitions occur at frequencies below 20 GHz. Consequently, atoms in these states, and the circular state preparation process presented here, are well suited to hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.
Circular atoms, i.e., Rydberg atoms with maximum angular momentum, are semiclassical atoms of great interest for Rydberg constant metrology and QED tests. Following a suggestion by Delande and Gay, we have prepared circular atoms by a new method, involving the adiabatic switching of crossed electric and magnetic fields. The method, which is demonstrated for Rydberg states of lithium (principal quantum number n=20to25n=20 \mathrm{to} 25n=20to25, is applicable over a wide variety of experiment conditions.
The authors propose to prepare oriented circular Rydberg states in atoms (i.e. states where one valence electron has spherical quantum numbers: m=l=n-1>>1) by combining the specific advantages of the adiabatic crossed-field method, recently tested in alkali and alkaline earth atoms, and of the adiabatic RF field method whose principle was described in 1986. The formal equivalence of the two methods is pointed out. Their association is made possible by considering the dynamical symmetry of the Coulomb potential. In order to illustrate the new process, calculations have been performed for the manifold n=5 of hydrogen.
We discuss three proposed schemes of initializing circular-state Rydberg atoms via optical couplings provided by the ponderomotive effect in contrast to the current circularization methods that utilize electric-dipole interactions. In our first proposed method, a radial optical trap consisting of two Laguerre-Gaussian beams of opposite winding numbers transfers orbital angular momentum to the Rydberg atom, providing a first-order coherent coupling between an F state and a circular state. Additionally, we propose a one-dimensional ponderomotive optical lattice modulated at rf frequencies, providing quadrupolelike couplings in the hydrogenic manifold for rapid adiabatic passage through a series of intermediate Rydberg states into the circular state. For the third proposed scheme, a two-dimensional ponderomotive optical lattice with a time-orbiting trap center induces effectively the same coupling as a ${\ensuremath{\sigma}}^{+}$- or ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized rf field of tunable purity for all-optical rapid adiabatic passage into the circular state.