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arXiv:1901.06805 · Physical Review Letters

Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms

Yue Jiang, Yefeng Mei, Ying Zuo, Yanhua Zhai, Jensen Li, Jianming Wen, Shengwang Du

Published Nov 8, 2019• 123 citations
arXivHTMLPDF

Abstract

Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch.

DOI
10.1103/physrevlett.123.193604

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Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch.
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Abstract A wide class of non-Hermitian Hamiltonians can possess entirely real eigenvalues when they have parity-time (PT) symmetric potentials. Recently, this family of non-Hermitian systems has attracted considerable attention in diverse areas of physics due to their extraordinary properties, especially in optical systems based on solid-state materials, such as coupled gain–loss waveguides and microcavities. Considering the desired refractive index can be effectively manipulated through atomic coherence, it is important to realize such non-Hermitian optical potentials and further investigate their distinct properties in atomic systems. In this paper, we review the recent theoretical and experimental progress of non-Hermitian optics with coherently prepared multi-level atomic configurations. The realizations of (anti-) PT symmetry with different schemes have extensively demonstrated the special optical properties of non-Hermitian optical systems with atomic coherence.
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Phase-dependent PT\boldsymbol{\mathcal{PT}}PT -, non-PT\boldsymbol{\mathcal{PT}}PT -, and anti-PT\boldsymbol{\mathcal{PT}}PT -symmetry
We propose a scheme to realize -, non- -, and anti- -symmetry in an ensemble of four-level double-lambda configuration. We find that the ensemble of atoms exhibits either symmetry, non-symmetry and antisymmetry of parity-time in terms of the refractive index modulation. Such fascinating modulation of real and imaginary parts of refractive index is attained via the relative phase ( ϕ ) of the optical fields. The control of spatial modulations of refractive index then leads to the control of -, non- -, and anti- -symmetry via the relative phase of the optical fields. Such interesting and controllable system via relative phase may open a new way in observing -, non- -, and anti- -symmetry with gain-loss contrast in atomic systems.
We propose a scheme to realize parity-time (PT) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation contributed by an assisted field, the optical lattice potential provided by a far-detuned laser field, and the optical gain resulted from an incoherent pumping can be used to construct a PT-symmetric complex optical potential for probe field propagation in a controllable way. Comparing with previous study, the present scheme uses only a single atomic species and hence is easy for the physical realization of PT-symmetric Hamiltonian via atomic coherence.