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IEEE MTT-S International Microwave Symposium digest

Development of a quantum based microwave power measurement

T. P. Crowley, Elizabeth A. Donley, Thomas P. Heavner, John R. Juroshek, Bill F. Riddle

Published Aug 27, 2003• 1 citation
Publisher

Abstract

An initial proof-of-principle experiment to measure microwave power based on quantum mechanical principles is presented. An RF magnetic field causes laser-cooled cesium atoms to oscillate between two hyperfine levels at a rate proportional to the field strength. The populations vary as predicted with relative microwave intensity and duration.

DOI
10.1109/mwsym.2003.1212640

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•Jan 1, 2013•4 citations
An initial proof-of-principle experiment to measure microwave power based on quantum mechanical principles is presented. An RF magnetic field causes laser-cooled cesium atoms to oscillate between two hyperfine levels at a rate proportional to the field strength. The populations vary as predicted with relative microwave intensity and duration.
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.
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 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.
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.
In this work, the theoretical and measurement results have been reported of microwave E-field sensing using an atomic spectroscopy instead of conventional methods (using antennae) under practice till date. This method is based on interaction of microwave with the Rb atoms excited to the Rydberg states by using two laser beams. This significantly new technique may get accepted internationally as a new primary standard for accurate and precise measurements of various Radio-Frequency parameters such as E-field, power, radiation pressure etc as it provides traceability to physical constants and SI units. The atomic model is also studied theoretically and Optical Bloch equations of the same are reported. It has been shown that microwave E-field strength is measured by studying the frequency difference between the peaks in laser transmission curve. The ability of atoms to sense E-field is shown by varying the power and distance of the antenna from atomic cell. In addition, results are shown for weak RF field detection by detuning the RF field by MHz order.
In the past several years, the field of optomechanics has progressed from proof-of-principle experiments to the realization of mechanical oscillators and measurements in the quantum regime. Mechanical oscillators are of great interest because they can have small dissipation rates, can couple to many different systems of interest, and are the fundamental elements of ultrasensitive force detectors. Coupling these mechanical oscillators to microwave or optical fields provides a twofold advantage. Firstly, information about mechanical position can be encoded in the interrogating field, enabling sensitive readout of the mechanical oscillator. Secondly, the radiation pressure force of that field can be used to control the state of the mechanical oscillator. Including a high-quality microwave or optical cavity enhances both of these effects, as the field strength is resonantly increased.\nThe major questions in the field of optomechanics in the last several years have dealt with using mechanical oscillators for ultrasensitive measurements and as tools for quantum information. Both of these goals have the prerequisite that we be able to read out the motion of the mechanical oscillator in a quantum efficient manner. To that end, we developed a nearly shot-noise limited microwave interferometer capable of measuring mechanical motion with an imprecision below that at the standard quantum limit. This achievement is not only a critical improvement for the electromechanical experiments we do, but is also an important tool for any experiment that encodes the information of interest in microwave fields. In order to use mechanical oscillators as tools for quantum information, the mechanical oscillator must also be cooled into the quantum regime and fully controllable by the interrogating fields. To this end, we used the radiation pressure of microwave fields to cool our macroscopic mechanical oscillator to less than one phonon. We also demonstrated coherent transfer between itinerant microwave states and the mechanical oscillator, even for incident fields with less than one photon of energy.\nThese accomplishments have set the foundation for further experiments to extend the quantum information abilities of optomechanical systems, couple diverse quantum systems via a mechanical intermediary, and potentially explore the foundations of quantum mechanics at macroscopic scales.