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Register a new userConnecting Berrys phase and the pumped charge in a Cooper pair pump
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The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. when $E_{mathrm{J}}lesssim E_{mathrm{C}}$. It is also known that Berrys phase is related to the pumped charge induced by the adiabatical variation of the eigenstates. We show explicitly that pumped charge in Cooper pair pump can be understood as a partial derivative of Berrys phase with respect to the phase difference $phi$ across the array. The phase fluctuations always present in real experiments can also be taken into account, although only approximately. Thus the measurement of the pumped current gives reliable, yet indirect, information on Berrys phase. As closing remarks, we give the differential relation between Berrys phase and the pumped charge, and state that the mathematical results are valid for any observable expressible as a partial derivative of the Hamiltonian.
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We propose a method to perform accurate and fast charge pumping in superconducting nanocircuits. Combining topological properties and quantum control techniques based on shortcuts to adiabaticity, we show that it is theoretically possible to achieve perfectly quantised charge pumping at any finite-speed driving. Model-specific errors may still arise due the difficulty of implementing the exact control. We thus assess this and other practical issues in a specific system comprised of three Josephson junctions. Using realistic system parameters, we show that our scheme can improve the pumping accuracy of this device by various orders of magnitude. Possible metrological perspectives are discussed.
We study adiabatic charge transfer in a superconducting Cooper pair pump, focusing on the influence of current measurement on coherence. We investigate the limit where the Josephson coupling energy $E_J$ between the various parts of the system is small compared to the Coulomb charging energy $E_C$. In this case the charge transferred in a pumping cycle $Q_P sim 2e$, the charge of one Cooper pair: the main contribution is due to incoherent Cooper pair tunneling. We are particularly interested in the quantum correction to $Q_P$, which is due to coherent tunneling of pairs across the pump and which depends on the superconducting phase difference $phi_0$ between the electrodes: $1-Q_P/(2e) sim (E_J/E_C) cos phi_0$. A measurement of $Q_P$ tends to destroy the phase coherence. We first study an arbitrary measuring circuit and then specific examples and show that coherent Cooper pair transfer can in principle be detected using an inductively shunted ammeter.
We have experimentally studied the behaviour of the so-called Cooper pair pump (CPP) with three Josephson junctions, in the limit of small Josephson coupling EJ < EC. These experiments show that the CPP can be operated as a traditional turnstile device yielding a gate-induced current 2ef in the direction of the bias voltage, by applying an RF-signal with frequency f to the two gates in phase, while residing at the degeneracy node of the gate plane. Accuracy of the CPP during this kind of operation was about 3% and the fundamental Landau-Zener limit was observed to lie above 20 MHz. We have also measured the current pumped through the array by rotating around the degeneracy node in the gate plane. We show that this reproduces the turnstile-kind of behavior. To overcome the contradiction between the obtained e-periodic DC-modulation and a pure 2e-behaviour in the RF-measurements, we base our observations on a general principle that the system always minimises its energy. It suggests that if the excess quasiparticles in the system have a freedom to tunnel, they will organize themselves to the configuration yielding the highest current.
This paper is devoted to an analysis of the experiment by Nakamura {it et al.} (Nature {bf 398}, 786 (1999)) on the quantum state control in Josephson junctions devices. By considering the relevant processes involved in the detection of the charge state of the box and a realistic description of the gate pulse we are able to analyze some aspects of the experiment (like the amplitude of the measurement current) in a quantitative way.
The advent of quantum optical techniques based on superconducting circuits has opened new regimes in the study of the non-linear interaction of light with matter. Of particular interest has been the creation of non-classical states of light, which are essential for continuous-variable quantum information processing, and could enable quantum-enhanced measurement sensitivity. Here we demonstrate a device consisting of a superconducting artificial atom, the Cooper pair transistor, embedded in a superconducting microwave cavity that may offer a path toward simple, continual production of non-classical photons. By applying a dc voltage to the atom, we use the ac Josephson effect to inject photons into the cavity. The backaction of the photons on single-Cooper-pair tunneling events results in a new regime of simultaneous quantum coherent transport of Cooper pairs and microwave photons. This single-pair Josephson laser offers great potential for the production of amplitude-squeezed photon states and a rich environment for the study of the quantum dynamics of nonlinear systems.
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