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Register a new userChiral state-conversion without encircling an exceptional point
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Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We show that a slow enough variation of parameters, even away from the systems exceptional point, can also lead to a robust asymmetric state exchange. To study this process, we consider a prototypical two-level non-Hermitian Hamiltonian with a constant coupling between elements. Closed form solutions are obtained when the amplification/attenuation coefficients in this arrangement are varied in conjunction with the resonance detuning along a circular contour. Using asymptotic expansions, this input-independent mode conversion is theoretically proven to take place irrespective of whether the exceptional point is enclosed or not upon encirclement. Our results significantly broaden the range of parameter space required for the experimental realization of such chiral mode conversion processes.
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We calculate analytically the geometric phases that the eigenvectors of a parametric dissipative two-state system described by a complex symmetric Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a parameter setting where the two eigenvalues and the corresponding eigenvectors of the Hamiltonian coalesce. We show that it can be encircled on a path along which the eigenvectors remain approximately real and discuss a microwave cavity experiment, where such an encircling of an EP was realized. Since the wavefunctions remain approximately real, they could be reconstructed from the nodal lines of the recorded spatial intensity distributions of the electric fields inside the resonator. We measured the geometric phases that occur when an EP is encircled four times and thus confirmed that for our system an EP is a branch point of fourth order.
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omni-polarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.
Electromagnetically induced transparency, as a quantum interference effect to eliminate optical absorption in an opaque medium, has found extensive applications in slow light generation, optical storage, frequency conversion, optical quantum memory as well as enhanced nonlinear interactions at the few-photon level in all kinds of systems. Recently, there have been great interests in exceptional points, a spectral singularity that could be reached by tuning various parameters in open systems, to render unusual features to the physical systems, such as optical states with chirality. Here we theoretically and experimentally study transparency and absorption modulated by chiral optical states at exceptional points in an indirectly-coupled resonator system. By tuning one resonator to an exceptional point, transparency or absorption occurs depending on the chirality of the eigenstate. Our results demonstrate a new strategy to manipulate the light flow and the spectra of a photonic resonator system by exploiting a discrete optical state associated with specific chirality at an exceptional point as a unique control bit, which opens up a new horizon of controlling slow light using optical states. Compatible with the idea of state control in quantum gate operation, this strategy hence bridges optical computing and storage.
We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to a planar waveguide, and a small non-separable perturbation depending on both transverse coordinates. It is assumed that the spectrum of the unperturbed planar waveguide features an exceptional point (EP), while the perturbation drives the system into the unbroken phase. Slightly below the EP, the waveguide sustains two-component envelope solitons. We derive one-dimensional equations for the slowly varying envelopes of the components and show their stable propagation. When both traverse directions are taken into account within the framework of the original model, the obtained two-component bright solitons become metastable and persist over remarkably long propagation distances.
As one fundamental property of light, the orbital angular momentum (OAM) of photon has elicited widespread interest. Here, we theoretically demonstrate that the OAM conversion of light without any spin state can occur in homogeneous and isotropic medium when a specially tailored locally linearly polarized (STLLP) beam is strongly focused by a high numerical aperture (NA) objective lens. Through a high NA objective lens, the STLLP beams can generate identical twin foci with tunable distance between them controlled by input state of polarization. Such process admits partial OAM conversion from linear state to conjugate OAM states, giving rise to helical phases with opposite directions for each focus of the longitudinal component in the focal field.
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