Observation of Resonance Trapping in an Open Microwave Cavity

Abstract

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.PACS numbers: 03.65.Nk, 84.40.Az, 85.30.Vw Since more than ten years, interference phenomena in open quantum systems have been studied theoretically in the framework of different models. Common to all these studies is the appearance of different time scales as soon as the resonance states start to overlap see [1] and the recent papers [2] with references therein). Some of the states align with the decay channels and become short-lived while the remaining ones decouple to a great deal from the continuum and become long-lived (trapped). Due to this phenomenon, the number of relevant states will, in the short-time scale, be reduced while the system as a whole becomes dynamically stabilized. The phenomenologically introduced doorway states in nuclear physics provide an example for the alignment of the short-lived states with the channels [3]. Calculations for microwave resonators showed that the trapped resonance states can be identified in the time-delay function and that short-lived collective modes are formed at large openings of the resonator [4]. Resonance narrowing is inherent also in the Fano formalism [5]. Similar effects have been found in the linewidths in a semiconductor microcavity with variable strength of normal-mode coupling [6]. In spite of the many theoretical studies, the effect of resonance trapping has not yet been verified unambigously in an experiment. A theoretical study of neutron resonances in nuclei as a function of the interaction of a doorway state with narrow resonances [7] allowed only to draw the conclusion that resonance trapping is not in contradiction with experimental data. For a clear experimental demonstration of the trapping effect, the coupling strength to the decay channels should be tunable, which was not possible in all above mentioned experiments.The mechanism of resonance trapping can be illustrated best on the basis of a schematical model. In an open quantum system the resonance states are allowed to decay, i. e. their energies are complex,The Hamilton operator is non-hermitian,Here H 0 describes the N discrete states of the closed quantum system coupled to K decay channels by the N × K matrix V . H 0 and V V † are hermitian and α is a real parameter for the total coupling strength between the closed system and the channels. The complex eigenvalues of H give the energy positions E R and widths Γ R of the resonance states. Studies on the basis of this model were perfo...

Effective coupling for open billiards

“…Nevertheless, fluctuations around the mean value g = 1 should in general be largest for small energies and can possibly result locally in overcritical coupling. This might be an explanation for the observed resonance trapping in billiards [15,16,17,18].…”

“…They are relevant as theoretical models for understanding the transport properties of mesoscopic semiconductor structures [13] or experimental results on microwave scattering in flat resonators [14,15]. Also signatures of resonance trapping were recently observed in billiards both, numerically [16,17,18] and in microwave resonator experiments [15].…”

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

“…(14). The integration contour C is shown by the brown, clockwise-oriented circle just inside the unit circle in Fig.…”

“…In many such familiar circumstances, we can generally think of these processes as following a simple exponential decay law. We note from the outset that the exponential decay is associated with the resonance in quantum mechanics [1][2][3][4][5][6][7][8][9][10][11][12][13][14], which can be thought of as a generalized eigenstate that resides outside the ordinary Hilbert space [2-4, 8, 12, 15-19].…”

Exploring quantum dynamics in an open many-body system: transition to superradiance

“…3. This phenomenon was discovered in numerical simulations [20,21], see also [22,23], was studied in molecular and atomic physics [24,25,26] and observed in experiments with microwave cavities [27]. The fact that the underlying physics is analogous to the Dicke coherent state [9] was explained in Refs.…”