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Optica Quantum

Cavity-free Δ-type coherent population trapping for microwave sensing

ido friedman, Shmuel Sternklar, Eliran Talker

Published Jul 6, 2026• 0 citations
Publisher

Abstract

We present a combined experimental and theoretical study of a cavity-free Δ-type coherent population trapping (CPT) system interacting with an external microwave field under realistic operating conditions. Two optical fields establish a Λ-type CPT resonance in a warm 85 Rb vapor cell, while an independently generated microwave field couples the hyperfine ground states and closes the Δ loop. Unlike previous implementations, the microwave field is neither resonantly enhanced nor phase-locked to the optical fields. These results establish the CPT contrast as a direct optical readout of the applied microwave field. At microwave resonance, the normalized contrast varies linearly with the microwave Rabi frequency, with a slope of 0.171 ± 0.021. Since the microwave Rabi frequency is proportional to the microwave magnetic-field amplitude, this response corresponds to a microwave-field component sensitivity of 3 ±0.36nT/Hz under the present experimental conditions. For finite microwave detuning, the CPT resonance exhibits asymmetric spectral shifts, producing a dispersive-like response that can be used for frequency-sensitive microwave detection. This cavity-free architecture enables interaction with uncontrolled external microwave fields and establishes a practical platform for future CPT-based microwave sensing under realistic operating conditions.

DOI
10.1364/opticaq.589568

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We present a combined experimental and theoretical study of a cavity-free Δ-type coherent population trapping (CPT) system interacting with an external microwave field under realistic operating conditions. Two optical fields establish a Λ-type CPT resonance in a warm 85 Rb vapor cell, while an independently generated microwave field couples the hyperfine ground states and closes the Δ loop. Unlike previous implementations, the microwave field is neither resonantly enhanced nor phase-locked to the optical fields. These results establish the CPT contrast as a direct optical readout of the applied microwave field. At microwave resonance, the normalized contrast varies linearly with the microwave Rabi frequency, with a slope of 0.171 ± 0.021. Since the microwave Rabi frequency is proportional to the microwave magnetic-field amplitude, this response corresponds to a microwave-field component sensitivity of 3 ±0.36nT/Hz under the present experimental conditions. For finite microwave detuning, the CPT resonance exhibits asymmetric spectral shifts, producing a dispersive-like response that can be used for frequency-sensitive microwave detection. This cavity-free architecture enables interaction with uncontrolled external microwave fields and establishes a practical platform for future CPT-based microwave sensing under realistic operating conditions.
We investigated experimentally and theoretically a cavity-free microwave field that couples the two ground states of a Λ-type atomic system, thereby forming a closed Δ configuration. In this regime, the absence of cavity-imposed phase matching leads to a strong sensitivity of the ground-state coherence to the microwave field parameters. We observe that the coherent population trapping (CPT) resonance exhibits a pronounced dependence on the microwave power and detuning, resulting in measurable changes in resonance contrast, linewidth, and center frequency. To explain these effects, we develop a numerical density-matrix model in which the ground-state coherence explicitly incorporates the microwave coupling strength, capturing the essential physics of this no-phase-matching Δ system. The excellent agreement between theory and experiment establishes a simple and robust framework for microwave control of cavity-free Δ-type atomic systems, with direct implications for compact atomic clocks and quantum-enhanced quantum sensing platforms.
Coherent population trapping (CPT) resonance signals have promise in a wide range of applications involving precision sensing. Generally, the CPT phenomenon occurs in a three-level Λ system with a bichromatic phase-coherent light fields. We theoretically and experimentally studied an Rb vapor-cell-based atomic system involving bichromatic CPT optical fields and an external microwave (MW) field simultaneously. In such a mixing scheme, the coherence of the ground states could be controlled either by the Rabi frequency of the microwave field or by the relative phase between the optical fields and the MW field. Moreover, we investigated the Rabi resonance in this mixing scheme. The Rabi frequency of the MW field can be measured SI (International System of Units)-traceably based on the Rabi resonance lineshape, and thus holds the potential to realize intensity stabilization of the optical field in this system. Simple theoretical models and numerical calculations are also presented to explain the experimental results. There is scope to use the proposed technique in future development of SI-traceable optical field strength standards.
We report a phase-sensitive microwave detection setup for spectroscopy of coherent population trapping (CPT) resonance in a Cs vapor cell. In this scheme, the optically carried microwave interrogation signal that interacts with atoms is detected by a fast photodiode at the cell output and is then mixed with the local oscillator microwave signal itself. This detection scheme produces at the output of the microwave mixer a dispersive CPT signal that can be directly used for correction of the local oscillator frequency onto the atomic resonance. The evolution of the dispersive CPT resonance signal with the laser power is briefly reported. With this detection scheme, we demonstrate the operation of a CPT atomic clock with a short-term fractional frequency stability of 1 × 10 − 11 at 1 s, which is in good agreement with the slope of the frequency discriminator and the residual microwave phase noise of the setup.
We present a microwave frequency standard based on coherent population trapping (CPT) in the 87Rb D1 line. The CPT spectrum is obtained using two Raman lasers with a 6.8 GHz frequency offset by injection locking of a master laser to a slave laser. We have constructed an atomic clock employing a 5 cm long Rb vapor cell confined with 6.67 kPa neon buffer gas at 70 °C. Using this system, we improve the CPT contrast through the elimination of undesired off-resonant fields created by the direct modulation method. We measured the frequency shift of the CPT signal as a function of the temperature of the Rb cell and estimated it to be approximately 1.3 ×10−9/K. The frequency of a 10 MHz crystal oscillator has been stabilized to the CPT spectrum between the two ground states in 87Rb. The relative frequency stability is approximately 2.3×10−12 for an average time of 68 s.
The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.
An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at <20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two mF=0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5×10-11 τ-1/2(1 s<τ<2000 s). The best stability of 6.4×10-13 is reached at an integration time of τ=2000 s. This stability is sufficient for many high-precision applications. Frequency-shift measurements were made to evaluate the frequency dependencies on the operation parameters.