It is shown that the coherence created by a resonance transverse superhigh-frequency (SHF) field induces, under the action of a longitudinal SHF and transverse radio-frequency (RF) nonresonance fields, the Zeeman coherences on two adjacent allowed Δ m = 1 transitions. Under the action of an RF transverse field these coherences induce further a coherence on a forbidden Δ m = 2 transition. The resonance behavior of such coherence was earlier observed experimentally when the RF-field frequency coincided with the Δ m = 2 transition frequency. The theoretical conclusions are in quantitative agreement with the experiment.
We demonstrate the accurate determination of the magnetic strength of a microwave field utilizing the dressed cesium atom as a sensor. A bias magnetic field is initially used to split the Zeeman levels of the ground state. Its value is carefully selected to ensure that the microwave field to be measured is closely resonant to a pair of selected hyperfine Zeeman levels ( | F = 3 , m F = 3 ⟩ and | F = 4 , m F = 4 ⟩ ), while other states are neglected. This approach significantly simplifies the interaction model. A weak radio-frequency magnetic field is utilized to drive atoms away from the specified magnetic quantum number state to its neighbor, whose population imbalance is supervised by optical readout. The long atomic transverse relaxation time due to the antirelaxation coatings of alkali-metal-vapor cells makes it possible to precisely depict the interaction between atoms and the microwave field. Consequently, the microwave field can be accurately determined with an uncertainty of less than 1% even beyond 100 nT, corresponding to a radio-frequency spectral line broadening less than 100 Hz. The features we have identified enable us to expand the possibilities of developing new metrology for measuring microwave fields in an alternative way.
We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the
D Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved
nFJ fine-structure levels in fields up to 120 mG, where the transition into
nF7/2 displays a thee-peak Zeeman pattern, while
nF5/2 shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.
We have discovered an interference which results in the vanishing of some electric dipole transition amplitudes. A transition-matrix element
T between certain
S and
P sublevels with the same value of
MF vanishes when an applied magnetic field satisfies ${X}_{s}+{X}_{p}=\ensuremath{-}2{M}_{F}$, where $X={\ensuremath{\mu}}_{B}{g}_{J}\frac{B}{A}$, and
A is the hfs constant. There must be an avoided crossing between the two states of the same
MF which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply
MF<0 and
I>J. We observed the vanishing of
T in
23Na for one of the $\ensuremath{\Delta}{M}_{F}=0$ optical transitions of the $3{S}_{\frac{1}{2}}(F=1)\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}(F=1)$ manifold. Absorption of cw laser light was monitored by observing total fluorescence perpendicular to both the atomic and laser beams, and absorption vanished near an applied field of 155 G.
T vanishes for a large number of cases including rf and microwave frequencies and is a rather general consequence of angular momentum selection rules and perturbation theory. This phenomenon may have application in optical pumping, Lamb-shift measurements, and atomic weak neutral-current experiments.