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Europhysics Letters (EPL)

Phase-dependent $\boldsymbol{\mathcal{PT}}$ -, non-$\boldsymbol{\mathcal{PT}}$ -, and anti-$\boldsymbol{\mathcal{PT}}$ -symmetry

Ziauddin Ziauddin

Published Dec 12, 2018• 4 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/124/41001

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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 an all-optical-control scheme to simultaneously realize parity-time (𝒫𝒯)-symmetric and 𝒫𝒯-antisymmetric susceptibilities along the propagation direction of light by applying an external magnetic field. Through the light-atom interaction within a double-Λ configuration, the resulting position-dependent susceptibilities for the interacting fields can be manipulated through the relative phase between them. In particular, for the probe field, one can switch its refractive index from the 𝒫𝒯-symmetry to 𝒫𝒯-antisymmetry by just varying the phase. Based on the quantum interference among transition channels in a closed loop, analytical formulas are also derived to illustrate the conditions for 𝒫𝒯-symmetry and 𝒫𝒯-antisymmetry.
PT\cal{PT}PT -symmetry in Rydberg atoms
We propose a scheme to realize parity-time ( PT )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87 Rb atoms in a four-level inverted Y -type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from PT -symmetry to non- PT -symmetry via different external parameters, i.e. , coupling field detuning, probe field intensity and control field intensity.
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.
Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time (PT)(PT)(PT) space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.
We study an ensemble of ultracold atoms trapped in the one-dimensional optical lattices under the N level configuration to examine the absorption and dispersion properties modulated into different ways along the lattice direction z. We find these trapped atoms with a Gaussian density distribution in each period may exhibit either symmetry χp(z)=χp*(-z) or antisymmetry χp(z)=-χp*(-z) of parity-time (PT) in terms of the probe susceptibility. Such intriguing twofold modulations of real (χ'p) and imaginary (χ″p) susceptibilities with a π/2 phase shift are attained by spatially modulating intensities or frequencies of one driving field in a suitable way. The PT-symmetric or PT-antisymmetric atomic lattices correspond in fact to complex photonic crystals and may be extended to develop functional devices like photonic diodes and transistors, a task impossible for real photonic crystals.
Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The prevous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in nonlinear optical interactions based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe 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.