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Physical Review A

Dark-state-induced transparency and the ultranarrow spectrum

Ting-Qian Zhou, Yue Chang, Li‐Ping Yang

Published Mar 13, 2025• 3 citations
Publisher

Abstract

Ultranarrow scattering spectra have important applications in precision measurements. Here, we show that the dark state of two atoms coupled to a one-dimensional (1D) waveguide leads to an ultranarrow transparency window with a width significantly smaller than the spontaneous decay rate of the atoms. Specifically, the position of this transparency dip is linearly proportional to the atom-atom distance. This ultranarrow dip can measure the atom-atom distance with an accuracy of one percent of the resonant wavelength. Additionally, the dip depth is highly sensitive to the atom-atom detuning, which could be used to measure small magnetic-field gradients at the nanoscale. The sign of the detuning can be further determined by measuring the second-order correlation function of the reflected photons.

DOI
10.1103/physreva.111.033708

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Ultranarrow scattering spectra have important applications in precision measurements. Here, we show that the dark state of two atoms coupled to a one-dimensional (1D) waveguide leads to an ultranarrow transparency window with a width significantly smaller than the spontaneous decay rate of the atoms. Specifically, the position of this transparency dip is linearly proportional to the atom-atom distance. This ultranarrow dip can measure the atom-atom distance with an accuracy of one percent of the resonant wavelength. Additionally, the dip depth is highly sensitive to the atom-atom detuning, which could be used to measure small magnetic-field gradients at the nanoscale. The sign of the detuning can be further determined by measuring the second-order correlation function of the reflected photons.
A scheme for obtaining a tunable ultranarrow linewidth of a cavity due to an embedded four-level atomic medium with double-dark resonances is proposed. It is shown that the steep dispersion induced by double-dark resonances in the transparency window leads to the ultranarrow transmission peak. Compared with the case of a single-dark resonance system, the linewidth can be narrowed even by one order under proper conditions. Furthermore, the position of the ultranarrow peak can be engineered by varying the detuning of the control field.
Magnetically induced optical transparency (MIOT) is a technique to realize the narrow transmission spectrum in a cavity quantum electrodynamics system, which is demonstrated in a recent experiment of cold 88Sr^{88}\mathrm{Sr}88Sr atoms in an optical cavity [M. N. Winchester, M. A. Norcia, J. R. K. Cline, and J. K. Thompson, Phys. Rev. Lett. 118, 263601 (2017)]. In this experiment, MIOT induces a new narrow transmission window for the probe beam, which is highly immune to the fluctuation of the cavity mode frequency. The linewidth of this transmission window approaches the decay rate of the electronic 3P1^{3}P_{1}3P1​ state [about $(2\ensuremath{\pi})\phantom{\rule{0.28em}{0ex}}7.5\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}]$ and is much less than the uncertainty of the cavity mode frequency [about $(2\ensuremath{\pi})\phantom{\rule{0.28em}{0ex}}150\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}]$. In this paper, we propose an approach to further reduce the linewidth of this MIOT-induced transmission window, with the help of two Raman beams which couple the electronic 3P1^{3}P_{1}3P1​ state to the 3S1^{3}S_{1}3S1​ state, and the 3S1^{3}S_{1}3S1​ state to the 3P0^{3}P_{0}3P0​ state, respectively. With this approach, one can reduce the transmission linewidth by orders of magnitude. Moreover, the peak value of the relative transmission power or the transmission rate of the probe beam is almost unchanged by the Raman beams, and the peak position is insensitive to the average frequency of the two Raman beams.
We investigate the single-photon propagation in the one-dimensional waveguide coupled to NNN two-level atoms. For a waveguide coupled to NNN distant atoms, the transparency can be induced by coherent interaction at resonance for an eveneveneven numbernumbernumber of NNN, while for an oddoddodd numbernumbernumber of NNN, the photon can be fully reflected. We then can switch the photon transport by controlling the atomic number. For a waveguide coupled to a small atomic ensemble of NNN atoms in the same position, the transparency disappears, and the photonic transport property displays a jump behavior near the resonance point.
We have shown that an ultranarrow dark region can be associated with the feature of significant amount of vaccuum-Rabi splitting in the absorption spectrum of a weak coherent field probing a two-level atom strongly coupled to two degenerate cavity-modes with preselected polarizations. The cavity-induced transparency is produced by the decay-interference of the two independent cavity modes interacting with the same reservoir. It has been shown that the resonant probe transparency is independent of the individual decay rates of the cavity modes. The present model exhibits the possibility of obtaining the narrow dark transparency associated with the significant amount of Rabi splitting in the absorption spectrum with the appreciable value of the cavity-losses.
When an ensemble of quantum emitters interacts with a common radiation field, their emission becomes collective, giving rise to superradiant and subradiant states, characterized by broadened and narrowed linewidths. In this work, we propose to harness subradiant states for quantum metrology; such states naturally arise in subwavelength-spaced atomic arrays in free space and in small ensembles of emitters coupled to one-dimensional waveguides. We demonstrate that their collective optical response yields sharp, narrow features in the transmittance spectrum, which can be used to enhance sensitivity to external perturbations. This improved sensitivity can be applied to atomic clock operation, spatially resolved imaging of emitter positions, and enables precise detection of both global and spatially varying detunings (such as those induced by electromagnetic fields or gravitational gradients).
Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level $\ensuremath{\Lambda}$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\ensuremath{\Omega}}_{\ensuremath{\mu}}$, as in standard EIT systems. Tunneling between the wells at the frequency ggg provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by ggg. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.