Study of macroscopic quantum objects

Superconducting networks including Josephson tunnel junctions possess inherent coherence and allow engineering of quantum circuits having remarkable physical properties. In particular, like in an atom, the energy of these macroscopic circuits takes quantized values which can be controlled by external electromagnetic signals.

Josephson charge-phase qubit

As was recently demonstrated by several research groups (NEC, TU Delft, SUNY, Chalmers University, etc.), the superconducting circuits including Josephson junctions are very promising candidates for implementation of quantum computing in solid state chips [1]. There are several types of elementary quantum bits, or qubits, based on quantum coherence of the Josephson phase, magnetic flux or charge variables. These qubits have different design and the schemes of control and readout of the macroscopic quantum states. In our group a radio frequency charge-phase qubit was recently proposed [2], which combines advantage of the Cooper pair box [3] of loop configuration, enabling flux control of the Josephson coupling, and a radio frequency readout scheme of the Josephson junction impedance by Rifkin and Deaver, Jr. [4].

Simplified diagram of of the charge-phase qubit core element comprising two small Josephson junctions inserted in a superconducting loop. The junctions form a small island in between, which polarization is controlled by capacitively coupled gate, enabling the Cooper pair box operation [3]. In contrast to the rf-SQUID configuration having one Josephson junction in the loop, we insert in the loop the Bloch transistor [5], the element combining the Josephson feature of the transport current and the Coulomb blockade associated with its island.

The two lowest eigenenergies of the Bloch transistor inserted in the superconducting loop as a function of gate voltage and magnetic flux threading the loop. (This picture has the period of 2e with respect to the island charge which is proportional to the gate voltage and the period of flux quantum = h/2e with respect to the external flux; the given plot covers the range of single periods.) Either eigenstate of the system, |n=0> or |n=1>, presents a quantum superposition of states with a (small integer) number of extra Cooper pairs on the island. The weights and phases of particular contributions are different for n=0 and n=1 [6], so they form a convenient basis for realization and manipulation of the quantum state of type (see the review [7]). The manipulation can be made either by abrupt changes of the gate voltage or flux or/and by applying microwave pulses.

The idea of the readout of the charge-phase qubit is rather simple [4]; it is illustrated by the following diagram. Our qubits of SQUID-configuration include the Bloch transistor inserted into a loop and on-chip inductor of the tank circuit. Our design allows a dispersive read-out by an inductively coupled tank-circuit with a resonant frequency of about 77 MHz. Since the loop inductance L is sufficiently small, the circulating supercurrent and the overall Josephson phase are substantially less subject to thermal noise than in the case of the conventional current-biased configuration.

Our Qubit of SQUID-configuration qubit is strongly inductively coupled to a high-Q tank circuit whose resonance frequency depends on the value of the Josephson inductance LJ of the Bloch transistor. The value LJ of the inductance of the Bloch transistor is probed by small rf-oscillations induced by the strongly-couped tank circuit; LJ refelects the inverse curvature of the energy surface [2], which is determined by the qubit bias (dc gate voltage and flux) and the qubit quantum state A0 or A1. Thus, the resonance detuning allows to discriminate the qubit state.

At PTB the experiment on the charge-phase qubit is in progress. The complete samples are fabricated on one 9 x 9 mm²-chip. They consist of a Nb tank circuit and an Nb- or Al-washer (the loop) including the Bloch transistor with Nb- or Al-Josephson junctions.

(a) Photo of a sample in gradiometer layout with the Bloch transistor in the center. (b) SEM-micrograph of the Bloch transistors with Nb/AlOx/Nb Josephson junctions.

The measurements are performed in a dilution refrigerator Kelvinox 400. The signal from the tank circuit is amplified by a cold preamplifier.

Experimental setup for the investigation of qubits at PTB - on the left the electrical circuit diagram and on the right the dilution refrigerator.

In our recent experiments we investigated charge-phase qubits with Al/AlOx/Al and Nb/AlOx/Nb Josephson junctions. The sub-µm Nb junctions fabricated at PTB show in dc-measurements low sub-gap leakage currents [8] and the critical currents determined from the phase modulation characteristics are of the order of the Ambegaokar-Baratoff values.

A systematic analysis of the ground state of the charge-phase qubit for different ratios of the Josephson coupling energy and the Coulomb charging energy allows the determination of the complete set of sample parameters including the critical current, whose value is of the order of some nA [9].

3D-plot of the phase shift of the tank circuit measured as a function of the applied dc-flux (proportional to I_dc) and the gate voltage V_G. This peak and valley plot corresponds to the ground state of the Bloch-transistor.

Another main point of our current research is the analysis of Al based qubit structures, showing the so called quasiparticle poisoning effect. This is the stochastic tunneling of single electrons, which changes the working point of the qubit and is an additional source of decoherence. Our recent measurements have demonstrated the transfer of energy of non-equilibrium quasiparticles to our charge-phase qubits and they allow drawing conclusions about the dynamics of quasiparticle excitations leading to a selection rule of such quasi-particle-induced transitions [10].

At PTB the Josephson charge-phase qubit is investigated in the frame of the EU-projects and EuroSQIP and QUROPE. The goal is the development of superconducting qubits based on quantum coherence of the Josephson phase, magnetic flux or charge variables. This project is funded by the Future and Emerging Technologies arm of the IST-FET-QUIPC proactive initiative.

The partners involved are Chalmers University of Technology, Delft University of Technology, University of Karlsruhe (exp), University of Karlsruhe (theor.), CEA-Saclay, Scuola Normale (Pisa), Institut Néel, CNRS (Grenoble), Institute of Photonic Technology (Jena), National Institute of Nuclear Physics (Bari), Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences (Innsbruck), Ludwig-Maximilians-Universität (München), Landau Institute for theoretical physics (Moscow), and Swiss Federal Institute of Technology (Zürich).

Phase-Qubits and dc-SQUID Quantum Systems

In collaboration with external partners we are exploring additional quantum systems based on Josephson junctions. So called phase-qubits are investigated in cooperation with the University of Karlsruhe (Prof. Ustinov).These phase-qubits including a read-out SQUID are fabricated at PTB in niobium technology. The use of a sub-µm Josephson junctions together with a low loss capacitor in parallel should result in long coherence times [11]. A possible ways of reducing the losses in the on-chip capacitor is the utilization of an appropriate dielectric material, for example, SiN_x instead of SiO_x.

Phase-qubit in Nb-technology with sub-µm Josephson junction and parallel SiO_x-based capacitor.

A quantum systems based on a dc-SQUID is investigated in cooperation with the Institut Néel, CNRS (group of Olivier Buisson) in Grenoble. Preliminary measurements of first Nb samples have shown coherence times of the order of 100 ns, comparable to results achieved by other groups with Al phase qubits. Recently our working group has fabricated a new generation of dc-SQUIDs with integrated high frequency structures and filters in Nb-technology. The detailed analysis of the samples at the Institut Néel in a dilution refrigerator at mK temperatures demonstrated, that the DC-SQUID can be operated as a qubit, i.e. as a two level quantum system [12].

(a) Photo of a DC-SQUID qubit in Nb-technology, (b) Rabi-oscillations of the SQUID operated as a phase-qubit.

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The staff of working group "Macroscopic quantum objects".

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References

[1] See, e.g., J. Clarke, Science 299, 1850 (2003) and references therein.

[2] A.B. Zorin, Physica C 368, 284 (2002); cond-mat/0312225.

[3] V. Bouchiat, D. Vion, P. Joyez, D. Esteve, and M. Devoret, Phys. Scripta T76, 165 (1998).

[4] R. Rifkin and B.S. Deaver, Jr., Phys. Rev. B 13, 3894 (1976).

[5] D.V. Averin and K.K. Likharev, Single-electronics: correlated transfer of single electrons and Cooper pairs in small tunnel junctions. In: Mesoscopic Phenomena in Solids, edited by B.L. Altshuler, et al. (Amsterdam, North-Holland: Elsevier, 1991) pp. 173-271.

[6] K.K. Likharev and A.B. Zorin, J. Low Temp. Phys. 59, 347 (1985).

[7] Yu. Makhlin, G. Schön, and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001).

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Contact

Head of Working Group		Dr. Ralf Dolata Phone: ++ 49-531-592-2247 E-Mail: Ralf Dolata
Address		Physikalisch-Technische Bundesanstalt AG 2.45 Bundesallee 100 38116 Braunschweig GERMANY