Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry

Abstract

The Landauer-Büttiker formalism establishes an equivalence between the electrical conduction through a device, e. g. a quantum dot, and the transmission. Guided by this analogy we perform transmission measurements through three-port microwave graphs with orthogonal, unitary, and symplectic symmetry thus mimicking three-terminal voltage drop devices. One of the ports is placed as input and a second one as output, while a third port is used as a probe. Analytical predictions show good agreement with the measurements in the presence of orthogonal and unitary symmetries, provided that the absorption and the influence of the coupling port are taken into account. The symplectic symmetry is realized in specifically designed graphs mimicking spin 1/2 systems. Again a good agreement between experiment and theory is found. For the symplectic case the results are marginally sensitive to absorption and coupling strength of the port, in contrast to the orthogonal and unitary case. 73.21.Hb, 72.10.Fk Wave transport and wave scattering phenomena have been of great interest in the last decades, both from experimental and theoretical points of view (see for instance Ref.[1]). Apart from the intrinsic importance in the complex scattering in a particular medium, the interest also comes from the equivalence between physical systems belonging to completely different areas, in which the dimensions of the systems may differ by several orders of magnitude [2]. One of these equivalences occurs in mesoscopic quantum systems, where the electrical conduction reduces to a scattering problem through the Landauer-Büttiker formalism [3][4][5]. Following this line, classical analogies of quantum systems have been used as auxiliary tools to understand the properties of the conductance of electronic devices in two-terminal configurations [6][7][8][9][10]. A plethora of chaotic scattering experiments in presence of time reversal invariance (TRI) and no spin 1/2 have been performed [7,8,[10][11][12][13][14][15][16], while very few experimental studies regarding absence of TRI are reported [7,8,17,18]. Furthermore, due to its intrinsic complexity, there are no scattering experiments up to now for systems with TRI and spin 1/2, where the signatures of the symplectic ensemble are expected, though there is one study of the spectral statistics in Au nanoparticles obeying this symmetry [19]. Moreover, very recently the appearance of a microwave experiment showing the signatures of the symplectic symmetry [20,21] for eigenvalue statistics has opened the possibility to study transport in the presence of this symmetry.Multiterminal devices are good candidates to provide experimental realizations for the three symmetry classes: Device Terminal 1 Terminal 2 Terminal 3 Junction FIG. 1. Sketch of a three-terminal setting that allows the measurement of the voltage along a device. The device carries a current while the vertical wire measures the voltage drop. Thin lines represent perfect conductors connected to sources of voltages V1, V2, and V3.orthogonal, un...

Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry

“…where S 0 is the scattering matrix of the junction that accounts for the coupling to the probe. In fact, S 0 can be obtained from the experiment [24,31], it reads as…”

“…5, where we observe that they do not reach the value 1. The dissipation parameter γ can be quantified by fitting the autocorrelation function C 11 (t) of the 11 element of the scattering ma- trix [4,24,33]…”

“…Multiterminal systems have also been studied in [15][16][17][18][19][20][21][22][23]. Among them three-terminal systems have been considered in which the voltage drop along the system is the observable of interest [24,25]. While two of the terminals are connected to fixed electronic reservoirs to feed the system, the third one is used as a probe that tunes the voltage drop.…”

“…More recently, an experiment with microwave graphs has been performed for an asymmetric configuration, where the probe is located on one side of a chaotic graph [24]. Analytical and numerical procedures were carried out to compute f .…”

Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

“…Wave-chaotic phenomena have been studied in various systems, ranging from 1D graphs [1][2][3][4][5], 2D billiards [6][7][8][9][10][11][12] to 3D enclosures [13][14][15][16][17][18]. The statistical properties of many system quantities, such as the closed system eigenvalues and the open system scattering/impedance matrices, exhibit universal characteristics, which only depend on general symmetries (e.g., time-reversal, symplectic) and the degree of system loss.…”