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Register a new userBehavior of Shannon entropy around an exceptional point in an open microcavity
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We have investigated the Shannon entropy around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy had an extreme value at the EP in the parameter space. The Shannon entropies showed discontinuity across a specific line in the parameter space, directly related to the occurrence of exchange of the Shannon entropy as well as the mode patterns with that line as a boundary. This feature results in a nontrivial topological structure of the Shannon entropy surfaces.
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We report on the detection of free nanoparticles in a micromachined, open-access Fabry-Perot microcavity. With a mirror separation of $130,mu$m, a radius of curvature of $1.3,$mm, and a beam waist of $12,mu$m, the mode volume of our symmetric infrared cavity is smaller than $15,$pL. The small beam waist, together with a finesse exceeding 34,000, enables the detection of nano-scale dielectric particles in high vacuum. This device allows monitoring of the motion of individual $150,$nm radius silica nanospheres in real time. We observe strong coupling between the particles and the cavity field, a precondition for optomechanical control. We discuss the prospects for optical cooling and detection of dielectric particles smaller than $10,$nm in radius and $1times10^7,$amu in mass.
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 develop a quantum mechanical method of measuring the Newtonian constant of gravitation, G. In this method, an optomechanical system consisting of two cavities and two membrane resonators is used. The added source mass would induce the shifts of the eigenfrequencies of the supermodes. Via detecting the shifts, we can perform our measurement of G. Furthermore, our system can features exceptional point (EP) which are branch point singularities of the spectrum and eigenfunctions. In the paper, we demonstrate that operating the system at EP can enhance our measurement of G. In addition, we derive the relationship between EP enlarged eigenfrequency shift and the Newtonian constant. This work provides a way to engineer EP-assisted optomechanical devices for applications in the field of precision measurement of G
The relation between the Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system give equivalent effects to the Shannon entropy.
Exceptional points (EPs) associated with a square-root singularity have been found in many non-Hermitian systems. In most of the studies, the EPs found are isotropic meaning that the same singular behavior is obtained independent of the direction from which they are approached in the parameter space. In this work, we demonstrate both theoretically and experimentally the existence of an anisotropic EP in an acoustic system that shows different singular behaviors when the anisotropic EP is approached from different directions in the parameter space. Such an anisotropic EP arises from the coalescence of two square-root EPs having the same chirality.
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