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arXiv:1109.5543 · Physical Review B

Coherent superconducting quantum pump

Felix Hoehne, Yu. A. Pashkin, O. V. Astafiev, Mikko Möttönen, Jukka P Pekola, Jaw-Shen Tsai

Published Apr 5, 2012• 5 citations
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Abstract

We demonstrate nonadiabatic charge pumping utilizing a sequence of coherent oscillations between a superconducting island and two reservoirs. The pumping rate for each elementary cycle is limited by the coupling between the island and the reservoirs given by the Josephson energy. Our experimental and theoretical studies show that relaxation can be employed to reset the pump in order to avoid accumulation of errors due to nonideal control pulses. Thus our results demonstrate the effects of nonadiabatic quantum pumping and dissipation.

DOI
10.1103/physrevb.85.140504

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We demonstrate nonadiabatic charge pumping utilizing a sequence of coherent oscillations between a superconducting island and two reservoirs. The pumping rate for each elementary cycle is limited by the coupling between the island and the reservoirs given by the Josephson energy. Our experimental and theoretical studies show that relaxation can be employed to reset the pump in order to avoid accumulation of errors due to nonideal control pulses. Thus our results demonstrate the effects of nonadiabatic quantum pumping and dissipation.
In adiabatic Cooper pair pumps, which are operated by means of gate voltage modulation only, the quantization of the pumped charge during a cycle is limited due to the quantum coherence of the macroscopic superconducting wave function. In this work, we show that it is possible to obtain very accurate pumps in the nonadiabatic regime by a suitable choice of the shape of the gate voltage pulses. We determine the shape of these pulses by applying quantum optimal control theory to this problem. In the optimal case, the error, with respect to the quantized value, can be of the order of ${10}^{\ensuremath{-}6}e$, i.e., reduced by up to 5 orders of magnitude with respect to the adiabatic pumping. In order to test the experimental feasibility of this approach, we consider the effect of charge noise and the deformations of the optimal pulse shapes on the accuracy of the pump. Charge noise is assumed to be induced by random background charges in the substrate, which is responsible for the observed 1/f1/f1/f noise. Inaccuracies in the pulse shaping are described by assuming a finite bandwidth for the pulse generator. In realistic cases, the error increases to 1 order of magnitude at most as compared to that of the optimal case. Our results are promising for the realization of accurate and fast superconducting pumps.
We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
We theoretically study the pump-probe response of nonequilibrium BCS superconductors coupled to optical phonons. For ultrashort pump pulses a nonadiabatic regime emerges, which is characterized by oscillations of the superconducting order parameter as well as by the generation of coherent phonons. Using the density-matrix formalism, we compute the pump-probe response in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon system and determine the signatures of the order parameter and the phonon oscillations in the pump-probe conductivity. We find that the nonadiabatic dynamics of the BCS superconductor reflects itself in oscillations of the pump-probe response as functions of delay time $\ensuremath{\delta}t$ between pump and probe pulses. We argue that from the analysis of this oscillatory behavior both frequency and decay time of the algebraically decaying order-parameter oscillations can be inferred. Similarly, the coherent phonons are evidenced in the pump-probe conductivity by oscillations with the frequency of the phonons. Remarkably, we find that the oscillatory response in the pump-probe conductivity is resonantly enhanced when the frequency of the order-parameter oscillations is tuned to the phonon energy.
We introduce and discuss a scheme for Cooper-pair pumping. The scheme relies on the coherent transfer of a superposition of charge states across a superconducting island and is realized by adiabatic manipulation of magnetic fluxes. Differently from previous implementations, it does not require any modulation of electrostatic potentials. We find a peculiar dependence of the pumped charge on the superconducting phase bias across the pump and that an arbitrarily large amount of charge can be pumped in a single cycle when the phase bias is $\ensuremath{\pi}$. We explain these features and their relation to the adiabatic theorem.
By exciting a BCS superconductor with ultrashort pulses in the frequency range of the superconducting gap a nonadiabatic regime can be reached. In this regime the modulus of the order parameter oscillates in time. Although its average value can be identified with the gap in the absorption spectrum, the oscillation itself remains invisible in pump-probe spectra. In this Brief Report we demonstrate that by employing a coherent control-type scheme of excitation by two phase-locked pump pulses this oscillation can be unveiled in the probe spectrum. We find that the reaction of the superconductor to a second pump pulse depends strongly on its instantaneous state at the time of the impact of the second pulse. Based on numerical calculations performed on the mean-field level it is shown that by varying the delay time between the two pump pulses the transient oscillation of the order parameter can be transformed into an oscillation of its long-time value, which shows up in the absorption spectrum of a subsequent weak probe pulse as an oscillation of the gap when plotted as a function of the delay time.
Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. We investigate a complementary, stochastic approach to reducing errors: Instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. A 70% reduction in the quasiparticle density results in a threefold enhancement in qubit relaxation times and a comparable reduction in coherence variability.