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Physical Review A

Resonant Rydberg-atom–microwave-field interactions in the ultrastrong-driving regime: Beyond the rotating-wave approximation

J. D. R. Tommey, S. D. Hogan

Published Nov 25, 2019• 4 citations
Publisher

Abstract

The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number $n=105$ in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the $1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}\ensuremath{\rightarrow}1s105p\phantom{\rule{0.16em}{0ex}}^{3}P$ transition, were identified from Autler-Townes splittings of the $1s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.

DOI
10.1103/physreva.100.053417

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The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number n=105n=105n=105 in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the 1s105s3S1\ensuremath→1s105p3P1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}\ensuremath{\rightarrow}1s105p\phantom{\rule{0.16em}{0ex}}^{3}P1s105s3S1​\ensuremath→1s105p3P transition, were identified from Autler-Townes splittings of the 1s3p3P2\ensuremath→1s105s3S11s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s3p3P2​\ensuremath→1s105s3S1​ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.
We study the ultrastrong driving of Rydberg excitons in Cu2_22​O by a microwave field. The effect of the field is studied using optical absorption spectroscopy, and through the observation of sidebands on the transmitted laser light. A model based on Floquet theory is constructed to study the system beyond the rotating wave approximation. We obtain near quantitative agreement between theory and experiment across a 16-fold range of microwave field strengths spanning from the perturbative to the ultrastrong driving regime. Compared to Rydberg atoms, the large non-radiative widths of Rydberg excitons leads to new behaviour such as the emergence of an absorption continuum without ionization.
Abstract We study the ultrastrong driving of Rydberg excitons in Cu2O by a microwave field. The effect of the field is studied using optical absorption spectroscopy, and through the observation of sidebands on the transmitted laser light. A model based on Floquet theory is constructed to study the system beyond the rotating wave approximation. We obtain near quantitative agreement between theory and experiment across a 16-fold range of microwave field strengths spanning from the perturbative to the deep strong driving regime. Compared to Rydberg atoms, the large non-radiative widths of Rydberg excitons leads to new behaviour such as the emergence of an absorption continuum without ionization.
Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s ^{3}S_{1} Rydberg level by two-color two-photon laser excitation from the metastable 1s2s ^{3}S_{1} level. Two-photon microwave transitions between the 1s55s ^{3}S_{1} and 1s56s ^{3}S_{1} levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the atom-resonator coupling was studied by time-domain measurements of Rabi oscillations.
An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6S 1 / 2-6P 3 / 2-66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 → 65 P 1 / 2 transition. Microwave field induced AT splitting, f A T, is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W. The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.
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.
The coherent interaction between ensembles of helium Rydberg atoms and microwave fields in the vicinity of a solid-state coplanar waveguide is reported. Rydberg-Rydberg transitions, at frequencies between 25 and 38 GHz, have been studied for states with principal quantum numbers in the range 30-35 by selective electric-field ionization. An experimental apparatus cooled to 100 K was used to reduce effects of blackbody radiation. Inhomogeneous, stray electric fields emanating from the surface of the waveguide have been characterized in frequency- and time-resolved measurements and coherence times of the Rydberg atoms on the order of 250 ns have been determined. These results represent a key element in the development of an experimental architecture to interface Rydberg atoms with solid-state devices.