Parity-time-antisymmetric atomic lattices without gain

Abstract

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 (P T ) 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.

Perfect absorption and no reflection in disordered photonic crystals

“…In particular, for φ d = ±π/4 and p = 0, δ ds (z) turns out to be a sine function of z, i.e., in quadrature with the atomic density distribution N j (z) along the optical lattice. In this case, the correlated modulations in N j (z) and δ ds (z) result in a P T -antisymmetric susceptibility with its real (imaginary) part being an odd (even) function of the position z [2,43]. This implies, in particular, both that the system is a pseudo-Hermitian one [46] and that it satisfies the spatial Kramers-Kronig relations [3].…”

“…Such atoms are driven into the four-level N configuration by three coherent fields of frequencies (real amplitudes) ω p (E p ), ω c (E c ), and ω d (E d ) [2,43] [see Fig. 1 …”

“…Note that the dressing field comprises a red-detuned traveling-wave (TW) component and a blue-detuned standing-wave (SW) component so as to yield a small space-dependent dynamic shift [43], mismatch between the optical lattice (black solid curve) and the space-periodic dynamic shift δ ds (z) (red dashed curve) arising, respectively, from the dipole-trap beams and from the dressing field beams. In particular, for φ d = ±π/4 and p = 0, δ ds (z) turns out to be a sine function of z, i.e., in quadrature with the atomic density distribution N j (z) along the optical lattice.…”

“…More specifically, we use a lossy atomic crystal lattice with a P T -antisymmetric or more general non-Hermitian susceptibility [2,43,44], known to exhibit both URL and CPA, to assess the robustness of these two phenomena against (i) uncorrelated and (ii) self-correlated random fluctuations in the typical structural or geometric lattice parameters [45]. Disorder archetypes in the width (d) of the atomic density distribution within a unit cell and in the period (a) of the cold-atomic lattice for each unit cell are briefly illustrated in Sec.…”

Unidirectional reflectionless light propagation at exceptional points

“…Studies showed that light propagation in optical lattices of driven cold atoms with PT-antisymmetric susceptibilities, i.e. χ(z) = −χ * (−z), exhibited EPs (also known as non-Hermitian degeneracies), at which complete unidirectional reflectionless light propagation was observed [91,92].…”