Observation of Quantum Capacitance in the Cooper-Pair Transistor

Abstract

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 anti-crossing caused by the Josephson coupling. It depends parametrically on the gate voltage and is dual to the Josephson inductance. Furthermore, it's magnitude may be substantially larger than C geom . We have been able to detect C Q in our CPT, by measuring the in-phase and quadrature rf-signal reflected from a resonant circuit in which the CPT is embedded.C Q can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.

Charge and Spin State Readout of a Double Quantum Dot Coupled to a Resonator

“…This SET was coupled to an impedance matching rf resonant circuit to form an rf-SET which had dramatically improved sensitivity and bandwidth [8]. Similarly, an rf-QPC has also been realised for broadband charge detection of semiconductor quantum dot devices [9,10].More recently, state readout of a superconducting charge qubit has been accomplished by directly coupling it to a microwave resonant circuit [11][12][13]. Working in the dispersive regime where the resonator and qubit bandgap energies are detuned, the qubit has a state-dependent 'quantum capacitance' which causes a shift in the resonator frequency [14].…”

Inverse Landau-Zener-Stückelberg problem for qubit-resonator systems

“…The appearance of the interferogram depends on several factors: the values of the qubit parameters, the model for the dissipative environment (such as Eqs. (13,14) and the parameters α and B), the value of the bias current (which distorts the shape of the resonances, as demonstrated in Ref. [17]).…”

“…Let us assume that the qubit's state is known (i.e., this is measured by a device whose details we do not consider here for simplicity; see Refs. [12,13,16,24] for different realizations of the ways to probe the qubit's state). Given the known qubit state, we aim to find the Hamiltonian's parameters.…”

“…11 The impact of the qubit on the resonator's frequency shift can be described in terms of the so-called quantum capacitance, as studied for the qubits in Refs. [12,13]. The quantum capacitance is defined as the derivative of the average charge on the qubit with respect to the applied voltage.…”

Josephson charge qubits: a brief review

“…Thus, the readout process is extremely simple. Alternative readout schemes include the switching of a large Josephson junction [6], a radio-frequency SET [7], dispersive measurements [35,36], as well as quantum capacitance readout [37,38].…”