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arXiv:2202.10458 · Physical Review A

Quantum squeezing of slow-light dark solitons via electromagnetically induced transparency

Jinzhong Zhu, Guoxiang Huang

Published Mar 18, 2022• 8 citations
arXivHTMLPDF

Abstract

We consider the quantum effect of slow-light dark soliton (SLDS) in a cold atomic gas with defocusing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are biorthogonal and constitute a complete biorthonormalized basis, useful for the calculation on the quantum fluctuations of the SLDS. We demonstrate that, due to the large Kerr nonlinearity contributed from the EIT effect, a significant quantum squeezing of the SLDS can be realized; the squeezing efficiency can be manipulated by the Kerr nonlinearity and the soliton's amplitude, which can be much higher than that of bright solitons. Our work contributes to efforts for developing quantum nonlinear optics and non-Hermitian physics and for possible applications in quantum information processing and precision measurements.

DOI
10.1103/physreva.105.033515

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We consider the quantum effect of slow-light dark soliton (SLDS) in a cold atomic gas with defocusing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are biorthogonal and constitute a complete biorthonormalized basis, useful for the calculation on the quantum fluctuations of the SLDS. We demonstrate that, due to the large Kerr nonlinearity contributed from the EIT effect, a significant quantum squeezing of the SLDS can be realized; the squeezing efficiency can be manipulated by the Kerr nonlinearity and the soliton's amplitude, which can be much higher than that of bright solitons. Our work contributes to efforts for developing quantum nonlinear optics and non-Hermitian physics and for possible applications in quantum information processing and precision measurements.
We investigate the quantum squeezing of slow-light solitons generated in a $\mathrm{\ensuremath{\Lambda}}$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). Starting from the Heisenberg-Langevin and Maxwell equations governing the quantum dynamics of atoms and probe laser field, we derive a quantum nonlinear Schr\"odinger equation controlling the evolution of the probe-field envelope. By using a direct perturbation approach to diagonalize the effective Hamiltonian (where the atomic variables have been eliminated), we carry out a detailed calculation on the quantum fluctuations of a slow-light soliton, expanded as a superposition of the complete and orthonormalized set of eigenfunctions obtained by solving the Bogoliubov-de Gennes (BdG) equations describing the quantum fluctuations. We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.
We present a scheme to realize simultaneous quantum squeezing of light polarizations and atomic spins via a perturbed double electromagnetically induced transparency (DEIT) in a cold four-level atomic ensemble coupled with a probe laser pulse of two polarization components. We derive two coupled quantum nonlinear Schr\"odinger equations from Maxwell-Heisenberg-Langevin equations describing the quantum dynamics of the atoms and the probe pulse and develop a quantum theory of vector optical soliton (VOS), which have ultraslow propagation velocity and extremely low generation power. We solve the non-Hermitian eigenvalue problem describing the quantum fluctuations on the background of the VOS and rigorously prove that all fluctuation eigenmodes (including continuous modes and four zero modes) obtained constitute a biorthonormal and complete set. We find that, due to the giant self- and cross-Kerr nonlinearities contributed by the perturbed DEIT, a large polarization squeezing of the probe pulse can be realized. We also find that, together with the polarization squeezing of the probe pulses, a significant squeezing of atomic spins also occurs simultaneously. The results of the simultaneous squeezing of light polarizations and atomic spins by using only a coherent probe pulse reported here opens a route for uncovering the unique property of the quantum interface between light and atomic ensembles and also for applications in quantum information and precision measurement.
We investigate the formation and propagation of vector vortex solitons (VS) and unipolar soliton (US) in a cold atomic gas with Bessel lattices (BLs). The system we consider is a cold, coherent atomic gas with a tripod or multipod level configuration. Dueing to the giant enhancement of Kerr nonlinearity contributed by electromagnetically induced transparency (EIT), a vector weak vortex soliton can be effectively formed with ultraslow propagating velocity. Furthermore, we demonstrate that the characteristics of 2D VS and US can be controlled and manipulated via adjusting BLs. The results predicted here may be used to design all-optical switching at very low light level.
Abstract We propose a scheme to realize the manipulation of a weak signal pulse by ultraslow optical soliton in a coherent inverted-Y-type atomic system via double electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations, we derive nonlinear equations governing the spatial-temporal evolution of the probe and signal pulse envelopes. We show the giant enhancement of optical Kerr nonlinearity can be obtained under the condition of the double EIT, which results in the generation of a (2+1)-dimension optical soliton and can realize the manipulation of a weak signal pulse. Applying a far-detuned laser field to the system, we find that a weak signal pulse can be trapped by a (3+1)-dimension light bullet. In particular, the trajectories of the light bullet and trapped signal pulse can be manipulated and controlled by introducing a Stern–Gerlach gradient magnetic field. The results predicted here may not only open a route for the study of weak-light nonlinear optics but also have potential applications in the precision measurements and optical information processing and transmission.
We study electromagnetically induced transparency (EIT) and nonlinear pulse propagation in a resonant atomic gas confined in a microwaveguide. We find that the quantum-interference effect in this system can be greatly enhanced due to the reduction of the mode volume of the optical field. In particular, compared with atomic gases in free space, the EIT transparency window in the present confined system can be much wider and deeper, the group velocity of the probe field can be much slower, and the Kerr nonlinearity of the system can be much stronger. We show that a more efficient production of ultraslow optical solitons in the present system may be achieved with much slower propagating velocity and lower generation power. Features of EIT and pulse propagation in the present system are very promising for practical applications in optical information processing and transmission.