Nonlinear graphene quantum capacitors for electro-optics

Abstract

Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride, respectively, as the electrodes and the insulating dielectric, a strongly nonlinear behavior at zero bias and small voltages is obtained. When the temperature is sufficiently low, the strong nonlinear interaction emerging from the quantum capacitance exhibits a diverse range of phenomena. The proposed structure could take over the functionalities of nonlinear elements in many cryogenic quantum systems, and in particular, quantum electrooptics. It is shown that ultrastrong coupling is easily reached with small number of pump photons at temperatures around 1 K and capacitor areas of the order of 1 μm 2 . A measure of anharmonicity is defined and as potential applications, a qubit design as well as schemes for non-reciprocal devices such as an electromagnetic frequency circulator are discussed. 20 Josephson junctions, despite their strong nonlinearity, normally operate at very small currents, which limits their maximum total photon occupation number. Moreover, they occasionally need to be biased by either a direct current (DC) magnetic field or electric current. As for the nonlinear capacitors, Graphene has been used in optomechanics as the mechanical element in the form of a drum capacitor.

CUBIT: Capacitive qUantum BIT

“…where α is the contribution of JJs, and τ is the characteristic time of nonlinear interaction for the quantum capacitor [4]. This value has already been estimated theoretically [4] for a weakly nonlinear regime, which is not obviously a matter of interest in qubit design. The reason is that the anharmonicity should actually be large to guarantee two-level operation of the oscillator, strictly allowing no more than 1 photon at the qubit frequency ω to survive in the oscillator.…”

“…Since the limiting cases and truncated expansions may not be sufficiently accurate, the anharmonicity was studied with a completely numerical approach, where limiting expressions of the type reported in the previous study [4] no longer hold true and significantly deviate from exact values. The numerical computations are rather elaborate; therefore, instead of a description of the entire algorithm and minor details, the Mathematica calculation packages have been made freely available to readers as Supplementary Information.…”

CUBIT: Capacitive qUantum BIT

“…For the BN thickness of 3nm to 70nm, the contribution of geometric parallel plate capacitance of the structure has been shown that can be neglected [2], and the quantum capacitance is given by…”

“…It is found that A rapidly increases with the temperature decreasing and also is a strong function of the capacitance area [1], and at temperatures of a few 0.1K easily yield strong nonlinearity. Signal can be fed into the qubit oscillator by inductive or capacitive coupling similar to the qubits based on JJs [2]. of or enhancement in the anharmonicity of A, leaving nonlinear terms of sixth and higher orders.…”

“…We discuss a new type of qubit with integrability, based on a nonlinear Quantum Capacitor (QC) made of the two-dimensional materials [1], Graphene (Gr) and Boron Nitride (BN). Without exception, all existing superconducting qubits [2][3][4] rely on the nonlinear inductance of Josephson Junctions (JJs). Here, the nonlinear inductance is replaced by the nonlinear capacitance coming from two Gr monolayers separated by a multilayer BN, which acts as a potential barrier and forms a parallel plate capacitance [1].…”