Diffractive Orbits in an Open Microwave Billiard

Abstract

We demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge strongly influence the conduction spectrum of this resonator, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Recently, Katine et al. studied the transmission behavior of an open quantum billiard in the context of a two dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure [1]. Their resonator was formed by a wall with a small aperture, called a quantum point contact (QPC), and an arc-shaped reflector. A schematic of this resonator is shown in Fig. 1. The voltage on the reflector could be varied, effectively moving the reflector towards or away from the wall. Their measurements showed a series of conductance peaks, analogous to those seen in a Fabry-Perot, as the reflector position was varied.As we discuss below, the resonator considered here represents a new class of billiards, to our knowledge not previously studied in the literature. That is, the billiard is geometrically open, but in the stable regime, it is classically closed. In the unstable regime, the resonance properties of the billiard are determined in large part by diffraction.The resonator shown in Fig. 1 has two distinct modes of operation. When the center of curvature of the reflector is to the left of the wall (the regime studied in [1]), then all classical paths starting from the QPC that hit the reflector remain forever in the region between wall and the reflector: the dynamics is stable and the periodic orbits can be semiclassically quantized. Each quantized mode of the resonator can be characterized by two quantum numbers (n, m), which represent the number of radial and angular nodes respectively. As the reflectorwall separation is varied, the conductance exhibits a peak each time one of these quantized modes is allowed.

Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities

“…05.45.Mt, 32.80.Rm Understanding the properties of long-lived, quasi-bound states in open mesoscopic systems is of central importance for many research subjects, e.g. semiconductor ballistic quantum dots [1,2,3,4], photoionization of Rydberg atoms [5], microwave systems [6,7], quantum chaos [8], and optical microcavities [9,10,11,12,13,14,15]. In several of these studies the long-lived states are scarred.…”

“…Mode D is localized along two symmetry-related rays connecting the corners of the cavity. Such kind of rays are called diffractive rays [6].…”

Sharing Quantum States

“…An additional arc-shaped gate is situated ∼2 μm away from the dot with its focal point at the tunnel barrier of the dot. Thus, applying a voltage V cav generates an electronic mirror that confines quantized ballistic cavity modes with increased weight at the tunnel barrier [3]. Notably, we designed a cavity gate with a relatively small opening angle of 45°in order to confine only fundamental one-dimensional modes; i.e., high angular-momentum modes leak out into the drain.…”

“…DOI: 10.1103/PhysRevLett.115.166603 PACS numbers: 73.23.-b, 73.21.La, 85.75.-d Quantum physics has profited enormously from combining optical cavities and atoms into a quantum engineering platform, where atoms mediate interactions among photons and photons communicate information between atoms [1]. In mesoscopic physics, the constituents of the optical success story have been independently realized: (i) prototypes of electronic cavities were implemented through structuring of a two-dimensional electron gas (2DEG) [2,3], yielding extended fermionic modes akin to quantum corrals on metal surfaces [4,5], and (ii) artificial atoms in the form of quantum dots have been studied, unraveling numerous interesting phenomena such as the Coulomb blockade [6] and the Kondo effect [7,8]. The combination of several dots into controlled quantum bits (qubits) has been demonstrated [9,10], thus promoting the next challenge of introducing coherent coupling between distant qubits without relying on nearest-neighbor exchange.…”

Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers

“…It's known for instance from the study of open microwave resonators, that in the regime where there are no stable periodic orbits, orbits that diffract off the sharp edges of the resonator can have a strong influence on the spectrum and wavefunctions. 63 Similarly, the analysis of the spiral billiard suggests that for the formation of a notch-emitting high-Q mode, a mechanism beyond geometric optics (such as diffraction) is necessary. If a wavepacket of cylindrical waves with dominantly negative components were injected into the system, the notch, which is discontinuous on the scale of a wavelength, would diffract a small part of the amplitude into positively rotating components above the critical angle, which would eventually be emitted from the notch.…”