Tunneling proximity resonances: interplay between symmetry and dissipation

Abstract

We report the first observation of bound-state proximity resonances in coupled dielectric resonators. The proximity resonances arise from the combined action of symmetry and dissipation. We argue that the large ratio between the widths is a distinctive signature of the multidimensional nature of the system. Our experiments shed light on the properties of 2D tunneling in the presence of a dissipative environment.Tunneling and dissipation are ubiquitous phenomena in physics. A detailed understanding of their combined action would be highly desirable given the relevance of the problem for atomic physics, condensed matter physics, chemistry and biology [1]. However, the incorporation of dissipative effects is by no means trivial. Due to limitations of the available analytical and computational methods, up-to-date descriptions are still restricted to a few manageable cases, the prototype situation involving a bistable potential in 1D [2].In this Letter we report the observation of novel aspects of tunneling in 2D potentials and its interplay with classical dissipation. In experiments utilizing microwave dielectric resonators, we find that symmetry not only plays a crucial role while shaping the eigenstates of the system, but also influences the way they couple to the external environment acquiring a finite width. In the observed resonance multiplets, we find that one of the members is extremely sharp due to the symmetry of the configuration. The large ratios of the observed widths appear to be a peculiar consequence of the multidimensional nature of the system. The experiments were carried out using M gT i dielectric cylinders placed between two parallel copper plates, 30 cm square, separated by a gap l = 6.38 mm (Fig. 1). The disks had diameter D = 12.65 mm and dielectric constant ε r = 16. After establishing input/output coupling to the near field of the resonators by inserting coax lines terminated by loops, measurements of the transmission amplitude as a function of the frequency were performed using an HP8510B network analyzer.The eigenvalue problem of a single dielectric resonator can be solved analytically by regarding the system as a waveguide along the direction z orthogonal to the plates [3]. The entire field configuration can be derived from * Electronic addresses: kpance@sagar-3.physics.neu.edu; vlorenza@mit.edu; srinivas@neu.edu. the knowledge of the longitudinal components {H z , E z } alone, that separately obey the Helmoltz equation:Here, r = (φ, ρ, z) in cylindrical coordinates and k = √ ε r (ω/c) denotes the medium wave number for a mode at frequency ω = 2πf (ε r = 1 outside the dielectric). For perfectly conducting walls, boundary conditions require k z = pπ/l, p integer. We have verified through explicit measurements of the field profile that p ≥ 1, and all modes are evanescent with a decay constant close to the expected value κ r = k 2 z − ω 2 /c 2 [4]. A generic mode of the dielectric is classified according to its azimuthal, radial and vertical quantum numbers (m, n, p). If m = 0, the mode has ...

Directional Emission, Increased Free Spectral Range, and Mode $Q$-Factors in 2-D Wavelength-Scale Optical Microcavity Structures

“…Photonic molecules (i.e., clusters of closely-located electromagnetically-coupled microcavities [29][30][31][32][33][34][35]) offer higher design flexibility than deformed microdisk resonators. Careful control of the mutual coupling between individual resonators forming photonic molecules makes possible manipulation of their modal frequencies and quality factors.…”

“…When individual microdisks are brought close to each other, in place of every double-degenerate WG-mode in their optical spectrum there appears a number (equal to double the number of cavities) of coupled photonic molecule supermodes [29]. Properly designed and optimally tuned photonic molecule configurations have been shown to enable efficient WG-mode degeneracy splitting accompanied by a significant enhancement of the Q-factor of non-degenerate molecule modes [31,34,35]. However, the non-degenerate modes studied before in various symmetrical configurations do not produce directional emission patterns.…”

“…Nevertheless, highly directional emission patterns have also been demonstrated in optically-large double-disk molecules operating on high-azimuthal-order WG modes [36]. Precise positioning of the cavities in the optimized configuration can be achieved with modern fabrication techniques [30], and the estimates of the sensitivity of photonic molecule characteristics to size and position disorder can be found in [37] and [31]. It should also be noted that while TE and TM spectra of photonic molecules of the same configuration have similar features that are mainly determined by the symmetry properties of the molecular geometry and inter-cavity coupling distances [34], their emission patterns can differ drastically [37].…”

Photonic molecules made of matched and mismatched microcavities: new functionalities of microlasers and optoelectronic components

“…One of the most striking examples of the advantages offered by photonic molecules is a possibility of building quasisingle-mode structures with significantly (up to 50-fold) enhanced quality factors [12,13]. This can be done by arranging identical WG-mode microcavities into high-symmetry photonic molecule structures such as triangles [12,14], squares [12,13], hexagons and circular loops [15] and by carefully tuning the inter-cavity coupling distances. Modal characteristics of a hexagonal-shaped photonic molecule are presented in Fig.…”

Photonic Molecules and Spectral Engineering

“…Furthermore, the optical interactions between photonic atoms may be tuned to enhance select modes in PM structures and to shape their angular emission profiles [8,[33][34][35][36], paving the way to realizing low-threshold single-mode microlasers with high collection efficiency. It should be noted that many of the above-mentioned applications of PMs to be discussed in this chapter have well-known analogs in the field of microwave and millimeter-wave engineering [37][38][39][40][41]. However, it was recently discovered that PM structures may also serve as simulators of quantum many-body physics, yielding unique insights into new physical regimes in quantum optics and promising applications in quantum information processing [42].…”