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Review of Scientific Instruments

Quantum-based microwave power measurements: Proof-of-concept experiment

T. P. Crowley, Elizabeth A. Donley, Thomas P. Heavner

Published Jul 27, 2004• 38 citations
Publisher

Abstract

We present an initial proof-of-concept experiment to measure microwave power based on quantum-mechanical principles. Ground-state cesium atoms exposed to microwaves at 9.192 631 770 GHz oscillate between two hyperfine states at a rate that is proportional to the rf magnetic field strength. This provides a quantum-based method of measuring rf field strength that depends only on the fundamental parameters in the proportionality constant. A small fountain apparatus was used to prepare laser-cooled cesium atoms in a single hyperfine state, which were then launched through a cylindrical cavity operating in the TE011 mode. After passing through the cavity, the fraction of atoms in the two hyperfine states was measured. Rabi oscillations between the two states were observed as a function of microwave field strength. The scaling with field strength and with time in the cavity agreed with theory to within 0.4%. The field strength in the cavity was used, together with measured S parameters, to determine the microwave power incident at a reference plane outside the fountain apparatus. The difference between the quantum-based microwave power measurement and a traditional microwave power measurement was less than 5% of the measured power.

DOI
10.1063/1.1771501

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We present an initial proof-of-concept experiment to measure microwave power based on quantum-mechanical principles. Ground-state cesium atoms exposed to microwaves at 9.192 631 770 GHz oscillate between two hyperfine states at a rate that is proportional to the rf magnetic field strength. This provides a quantum-based method of measuring rf field strength that depends only on the fundamental parameters in the proportionality constant. A small fountain apparatus was used to prepare laser-cooled cesium atoms in a single hyperfine state, which were then launched through a cylindrical cavity operating in the TE011 mode. After passing through the cavity, the fraction of atoms in the two hyperfine states was measured. Rabi oscillations between the two states were observed as a function of microwave field strength. The scaling with field strength and with time in the cavity agreed with theory to within 0.4%. The field strength in the cavity was used, together with measured S parameters, to determine the microwave power incident at a reference plane outside the fountain apparatus. The difference between the quantum-based microwave power measurement and a traditional microwave power measurement was less than 5% of the measured power.
Quantum-mechanics-based measurement of microwave magnetic field strength has been suggested and has attracted considerable research interest. Such measurements exploit the fact that the Rabi frequency, which indicates the degree of combination between atoms and microwaves, is proportional to the magnetic field strength of the microwaves interacting with the atoms. This new method is expected to facilitate realization of a quantum-based electromagnetic sensor that minimally perturbs the microwaves, being both nonmetal and wireless. This paper demonstrates measurement of the microwave magnetic field strength at a 9.2-GHz frequency using the Rabi frequency of cesium-133 atoms. The microwaves are radiated from a horn antenna.
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.
Microwave emission has been observed at the ground-state hyperfine transition frequency of a cesium atomic vapor driven into a nonabsorbing state by means of coherent population trapping. The coherent emission observed is due to the oscillating magnetization generated by the coherence, which is induced between the ground-state hyperfine levels when they are coupled to an excited state by means of two laser radiations via a \ensuremath{\Lambda} scheme. The experiments described were done in a quartz cell containing buffer gases such as neon and nitrogen, reducing the linewidth through the Dicke effect. The cell was placed inside a microwave cavity tuned at 9.2 GHz, the ground-state hyperfine frequency of cesium, and a power output of the order of 100 fW was measured in the case where nitrogen was used as the buffer gas.
We present an atom-based approach for determining microwave electric and magnetic fields by using a single rubidium vapor cell in a microwave waveguide. For a 87Rb cascade three-level system employed in our experiment, a weak probe laser driving the lower transition, 5S1/2→5P3/2, is first used to measure the microwave magnetic field based on the atomic Rabi resonance. When a counter-propagating strong coupling laser is subsequently turned on to drive the Rydberg transition, 5P3/2→67D5/2, the same probe laser is then used as a Rydberg electromagnetically induced transparency (EIT) probe to measure the microwave electric field by investigating the resonant microwave dressed Autler-Townes splitting (ATS). By tuning the hyperfine transition frequency of the ground state using an experimentally feasible static magnetic field, we first achieved a measurement of the microwave electric and magnetic field strength at the same microwave frequency of 6.916 GHz. Based on the ideal relationship between the electric and magnetic field components, we obtained the equivalent microwave magnetic fields by fitting the inversion to the measured microwave electric fields, which demonstrated that the results were in agreement with the experimental measurement of the microwave magnetic fields in the same microwave power range. This study provides new experimental evidence for quantum-based microwave measurements of electric and magnetic fields by a single sensor in the same system.
We demonstrate the feasibility of a novel microwave power standard based on the electromagnetic interaction with laser-cooled atoms. Under the effect of the radiation, the internal state populations undergo a Rabi flopping oscillation. Measurement of the oscillation frequency allows the determination of the electromagnetic field strength. The measurements are made over a dynamic range of 18 dB and the standard deviation of the measurements is about 0.3%. The field strength was linear with the Rabi frequency within the accuracy of our measurements.