We have studied microwave response of a high-mobility two-dimensional electron system (2DES) contacted by two side electrodes. Using kinetic inductance of the 2DES and inter-electrode capacitance, we have constructed a subwavelength 2D plasmonic resonator. We have shown that the resonant frequency of this circuit can be controlled by 2D electron density, external magnetic field, or size of the electrodes. This opens up possibilities for using arrays of plasmonic circuits as tunable components in different frequency ranges.
We report on theoretical investigations of frequency dependent quantum capacitance. It is found that at finite frequency a quantum capacitor can be characterized by a classical RLC circuit with three parameters: a static electrochemical capacitance, a charge relaxation resistance, and a quantum inductance. The quantum inductance is proportional to the characteristic time scale of electron dynamics and due to its existence, the time dependent current can accumulate a phase delay and becomes lagging behind the applied ac voltage, leading to a negative effective capacitance.
We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/ωC_B$ also an inductive term $iωL_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(ϕ)$ at fixed $ϕ=0$. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described.
The Hamiltonian of a charge qubit, which consists of two Josephson junctions is found within well known quantum mechanical procedure. The inductance of the qubit is included from the very beginning. It allows a selfconsistent derivation of the current operator in a two state basis. It is shown that the current operator has nonzero nondiagonal matrix elements both in the charge and the eigenstate basis. It is also shown that the interaction of the qubit with its own LC resonator has a noticeable influence on the qubit energies. The influence of the junctions asymmetry and the gate capacitance o…
Here we investigate high frequency AC transport through narrow graphene nanoribbons with topgate potentials that form a localized quantum dot. We show that as a consequence of the finite dwell time of an electron inside the quantum dot (QD), the QD behaves like a classical inductor at sufficiently high frequencies ω\gtrsim50 GHz. When the geometric capacitance of the topgate and the quantum capacitance of the nanoribbon are accounted for, the admittance of the device behaves like a classical serial RLC circuit with resonant frequencies ω\sim100-900 GHz and Q-factors greater than 10^{6}. These …
Individual electrons in graphene behave as massless quasiparticles. In surprising twist, it is inferred from plasmonic investigations that collectively excited graphene electrons must exhibit non-zero mass and its inertial acceleration is essential for graphene plasmonics. Despite such importance, this collective mass has defied direct unequivocal measurement. It may be directly measured by accelerating it with a time-varying voltage and quantifying the phase delay of the resulting current; this voltage-current phase relation would manifest as kinetic inductance, representing the collective in…
Three-dimensional (3D) semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with its linear energy dispersion. In analogy to two-dimensional (2D) Dirac semimetals, such as graphene, Cd3As2, a 3D semimetal, has shown ultra-high mobility, large Fermi velocity, and has been hypothesized to support plasmons at terahertz frequencies. In this work, we demonstrate synthesis of high-quality large-area Cd3As2 thin-films through thermal evaporation as well as the experimental realization of plasmonic structures consisting of periodic arrays of Cd3As…
We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, the sub-gap charge transport takes place via slow tunneling of quasiparticles that link two Josephson-coupled charge manifolds. In between the quasiparticle tunneling events, the CPT behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage. This capacitance has two parts, the geometric capacitance, C_geom, and the quantum capacitance C_Q. The latter is due to the level a…
Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of…
We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical SQUIDs, with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, it…
We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate $1/τ$ from the nonlinearity scales with the fourth power of frequency $ω$, while the ph…
The device applications of plasmonic systems such as graphene and two dimensional electron gases (2DEGs) in III-V heterostructures include terahertz detectors, mixers, oscillators and modulators. These two dimensional (2D) plasmonic systems are not only well-suited for device integration, but also enable the broad tunability of underdamped plasma excitations via an applied electric field. We present demonstrations of the coherent coupling of multiple voltage tuned GaAs/AlGaAs 2D plasmonic resonators under terahertz irradiation. By utilizing a plasmonic homodyne mixing mechanism to downconvert …
We analyze dynamic properties of vertical graphene-base hot-electron transistors (GB-HETs) and consider their operation as detectors of terahertz (THz) radiation using the developed device model. The GB-HET model accounts for the tunneling electron injection from the emitter, electron propagation across the barrier layers with the partial capture into the GB, and the self-consistent oscillations of the electric potential and the hole density in the GB (plasma oscillations), as well as the quantum capacitance and the electron transit-time effects. Using the proposed device model, we calculate t…
Ultra strong coupling is studied in a modulation-doped parabolic potential well coupled to an inductance-capacitance resonant circuit. In this system, in accordance to Kohn's theorem, strong reduction of the energy level separation caused by the electron-electron interaction compensates the depolarization shift. As a result, a very large ratio of 27% of the Rabi frequency to the center resonance frequency as well as a polariton gap of width 2? ? 670GHz are observed, suggesting parabolic quantum wells as the system of choice in order to explore the ultra-strong coupling regime.
A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer and one small loop, and three Josephson junctions. The contributions to relaxation (T_1) and dephasing (T_ϕ) arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We use a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimens…
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systems are strongly detuned, theory attributes the shift to an effective resonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readou…
