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Optics Express

Rabi resonance in coherent population trapping: microwave mixing scheme

Xiaochi Liu, Ya-Nan Lv, Songbai Kang, Chang‐Ling Zou, Junyi Duan, Ning Ru, Jifeng Qu

Published Jan 1, 2021• 13 citations
Publisher

Abstract

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.

DOI
10.1364/oe.412139

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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 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.
Coherent population trapping (CPT) is extensively studied for future vapor cell clocks of high frequency stability. In the constructive polarization modulation CPT scheme, a bichromatic laser field with polarization and phase synchronously modulated is applied on an atomic medium. A high contrast CPT signal is observed in this so-called double-modulation configuration, due to the fact that the atomic population does not leak to the extreme Zeeman states, and that the two CPT dark states, which are produced successively by the alternate polarizations, add constructively. Here, we experimentally investigate CPT signal dynamics first in the usual configuration, a single circular polarization. The double-modulation scheme is then addressed in both cases: one pulse Rabi interaction and two pulses Ramsey interaction. The impact and the optimization of the experimental parameters involved in the time sequence are reviewed. We show that a simple seven-level model explains the experimental observations. The double-modulation scheme yields a high contrast similar to the one of other high contrast configurations like push-pull optical pumping or crossed linear polarization scheme, with a setup allowing a higher compactness. The constructive polarization modulation is attractive for atomic clock, atomic magnetometer, and high precision spectroscopy applications.
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 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.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
A lin⊥lin quasi-bichromatic light can be employed to realize a double-Λ coherent population trapping (CPT) resonance configuration, thereby enabling a CPT atomic clock with improved performance. A method for generating such light is proposed, in which two lasers with different linewidths are used to achieve a microwave frequency separation of several gigahertz. The effects of the optical injection ratio from the master extended-cavity diode laser into the slave vertical-cavity surface-emitting laser and the microwave power modulating the slave laser on the locking range were systematically investigated. The influence of both the injection ratio and microwave power on the contrast, linewidth, and the ratio of contrast to linewidth of the CPT signal is also studied. To enhance the trapping efficiency, single-pass and multi-pass interactions between the lin⊥lin quasi-bichromatic light and 87Rb atoms are investigated, with near-purely coherent states achieved under multi-pass interactions. Our scheme offers a promising solution for high-performance atomic clock applications.