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arXiv:cond-mat/0604198 · Physical Review B

Measurement scheme of the Berry phase in superconducting circuits

Mikko Möttönen, Jukka P Pekola, Juha J. Vartiainen, Valentina Brosco, F. W. J. Hekking

Published Jun 26, 2006• 76 citations
arXivHTMLPDF

Abstract

We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump---the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. To our knowledge the experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.

DOI
10.1103/physrevb.73.214523

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We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump---the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. To our knowledge the experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.
We have carried out first measurements on a novel type of a charge pump nicknamed the Cooper pair "sluice". The device is an adiabatic flux-assisted Cooper pair pump consisting of a mesoscopic superconducting island and of two SQUID loops. The operation is based on the periodic manipulation of a single voltage gate and two input coils controlling the magnetic flux through the SQUID loops. Based on theoretical estimates the device is capable of producing as high as 0.1 nA currents at better than 10-accuracy and looks thus like a promising candidate for the current source in completing the quantum measurement triangle. In spite of several nonidealities in our preliminary measurement setup, we have succeeded in verifying the pumping behavior of the sluice. The pumped currents were quite high, several hundred pA, but the accuracy needs to be increased. The results obtained so far suggest various ways of improving the measurement setup
We present the first measurements of the Berry phase in a superconducting Cooper pair pump. A fixed amount of Berry phase is accumulated to the quantum-mechanical ground state in each adiabatic pumping cycle, which is determined by measuring the charge passing through the device. The dynamic and geometric phases are identified and measured quantitatively from their different response when pumping in opposite directions. Our observations, in particular, the dependencies of the dynamic and geometric effects on the superconducting phase bias across the pump, agree with the basic theoretical model of coherent Cooper pair pumping.
Motivated by recent experiments on quantum mechanical charge pumping in a Cooper pair sluice, we present a measurement scheme for observing shifts of transition frequencies in two-level quantum systems induced by broadband environmental fluctuations. In contrast to quantum optical and related setups based on cavities, the impact of a thermal phase reservoir is considered. A thorough analysis of Lamb and Stark shifts within weak-coupling master equations is complemented by nonperturbative results for the model of an exactly solvable harmonic system. The experimental protocol to measure the Lamb shift in experimentally feasible superconducting circuits is analyzed in detail and supported by numerical simulations.
In this work four different mesoscopic superconducting devices have been experimentally studied: an ammeter based on a hysteretic Josephson junction switching from the superconducting state to the normal state, a conventional Cooper pair pump (CPP) based on two superconducting islands separated by tunnel junctions, a novel flux assisted Cooper pair pump and a thermometer based on a tunnel junction between a superconductor and a normal metal. These devices make use of phenomena related to superconductivity and are also benefiting from some properties of small structures, e.g., of quantum mechanical tunneling and of transport of single electrons. The present research focused on investigating performance limitations of these devices and the aim was to improve their performance. A hysteretic Josephson junction switching can be used as a sensitive current threshold detector. For many purposes, a smaller critical current Ic of the detecting junction would yield a higher current sensitivity. It was found in this Thesis that the main limitation of the ammeter is that with increasing sensitivity the negative effects due to dissipation start to dominate. In this Thesis the Josephson junction was also demonstrated as a shot-noise detector, and it was concluded that this kind of a device could probably be made into an absolute on-chip detector of Fano-factors and noise in general. A charge pump is a device which can periodically transfer a discrete amount of charge Q through an electrical circuit. The measured double island CPP introduced a frequency dependent current with a value close to the expected one at low pumping frequencies. The drawback in the measurements was that the direction of the pumped current was set by the bias voltage. The results of the measurement on flux assisted pumping were indeed very promising and the studied device was able to produce sufficiently high pumped currents of around 0.1 nA with reasonable accuracy. Thermometer based on NIS (Normal metal - Insulator - Superconductor) tunnel junctions is a very promising temperature sensor for bolometric radiation sensor applications. This work showed that it can be used as a sensitive thermometer up to MHz frequencies range and that its response time is limited by the electron-phonon scattering rate.
We present a detailed theoretical study of adiabatic Cooper-pair pumping in a one-dimensional array of Cooper-pair boxes and discuss its experimental feasibility. The Josephson tunneling and the gate voltage are two adiabatic couplings of our system. Using the concept of Berry phase and Abelian bosonization, we show that the evolution of the ground state follows a closed loop in the flux-voltage plane. Its adiabatic motion yields the Cooper-pair pumping in the system. We find the condition for blocking the Cooper-pair pumping even in the perfect pumping condition.
We introduce a model for a flux-assisted Cooper-pair pump, the sluice, which is used to study geometric charge transport. Our model allows for a nonvanishing loop inductance going beyond the usual treatment with an exact phase bias. We derive the device Hamiltonian and current operators for different elements of the system and calculate the pumped charge carried by the ground state in the adiabatic limit. We show that extending the model beyond the exact phase bias has a weak but potentially non-negligible effect on the charge transport. This effect is observed to depend on the external flux bias. The adiabatic energy level and eigenstate structures are studied and the unusual features are explained. Finally, we discuss the requirements of adiabaticity.