Single Charge Tunneling

Abstract

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Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling

“…The last term in the Hamiltonian, the Josephson term, couples the tunneling Cooper pairs to the photons in the resonator. The superconducting phase operatorθ can be expressed in the charge eigenbasis as [74,75]…”

“…where λ = πe 2 Z/h (where we reinstated the Planck constant), here Z denotes the impedance of the microwave resonator. We note that ifφ can be replaced by a classical variable ϕ(t), a unitary transformation of the Hamiltonian (withÛ = exp[−iϕ(t)N ]) removes ϕ(t) from the Josephson term and results in the usual capacitive coupling 2eN (V +V Ω ), where 2eV Ω = ∂ t ϕ(t) [74,75]. The goal of the engine is to extract energy stored in the resonator to drive charge (in the form of Cooper pairs) against the external voltage bias.…”

Physical Implementations of Quantum Absorption Refrigerators

“…The Hamiltonian in Eq. (30) is just the sum of the noninteracting resonators, which define the Hamiltonians of the subsystems asĤ j = E jâ † jâ j , plus the Josephson Hamiltonian which is determined by the cosine of the phase difference across the junction [53,57]. Here the phase difference includes the fluxes of the resonators as well as the external voltage.…”

“…Here the phase difference includes the fluxes of the resonators as well as the external voltage. Physically, the Cooper pairs that tunnel across the junction can exchange photons with the resonators to make up for the difference in chemical potential across the junction [57][58][59][60][61]. This results in the highly nonlinear interaction between the resonators.…”

Photon-assisted dynamical Coulomb blockade in a tunnel junction

“…Since the statistics of the electron tunneling across the barrier is driven by V , it follows that next electrons have less probability to cross the barrier [1]. When two tunnel junctions are in series, thus defining a conducting island between the two insulating barriers, a complete blocking of electron transport may occur at very low temperature k B T ≪ e 2 /C, referred to as Coulomb blockade [2]. With one junction only, the charge accumulated in the contacts leaks continuously into the rest of the circuit, leading to a progressive recovery of the possibility to have subsequent tunneling events [3].…”