Determination of microwave magnetic field based on dressed cesium atoms

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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mrow><a:mo stretchy="false">|</a:mo></a:mrow><a:mi>F</a:mi><a:mo>=</a:mo><a:mn>3</a:mn><a:mo>,</a:mo><a:msub><a:mi>m</a:mi><a:mi>F</a:mi></a:msub><a:mo>=</a:mo><a:mn>3</a:mn><a:mo fence="false" stretchy="false">⟩</a:mo></a:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:mrow><g:mo stretchy="false">|</g:mo></g:mrow><g:mi>F</g:mi><g:mo>=</g:mo><g:mn>4</g:mn><g:mo>,</g:mo><g:msub><g:mi>m</g:mi><g:mi>F</g:mi></g:msub><g:mo>=</g:mo><g:mn>4</g:mn><g:mo fence="false" stretchy="false">⟩</g:mo></g:math>), 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.