In the "flux-qubit" team, we study mesoscopic superconducting circuits containing tunnel junctions in order to use them as building blocks for a quantum computer.
We acknowledge support from the following institutions
Mesoscopic quantum systems
Our group studies mesoscopic circuits (typical size : 1 µm) in which a few superconducting islands are connected by tunnel junctions (see figure 1 as an example). A number of experiments have shown recently that the electrical variables of such a circuit - the charge on each island and the current flowing through the junctions - exhibit a quantum mechanical behavior when the sample is cooled at a sufficiently low temperature (about 30 mK). The charge and flux variables (the currents through the junctions are directly related to the magnetic flux threading the circuit) are conjugate : a Heisenberg-type uncertainty relationship was indeed experimentally demonstrated . Incoherent tunneling of the flux variable through an energy barrier was also observed . Microwave spectroscopy experiments performed on such structures show quantized energy levels , and it has even been possible to demonstrate coherent superpositions of these levels .
Fig. 1 : SEM picture of a "persistent-current qubit" sample . The inner loop which contains three Josephson junctions is the qubit. The outer loop, containing two junctions, is a SQUID which measures the qubit's state.
Thus, in many regards, mesoscopic superconducting circuits are really like artificial atoms. An important distinction has to be made, still, since the number of particles involved here is very large (for example, in the circuit shown at figure 1, millions of Cooper pairs contribute to current), which makes them a unique tool to investigate quantum-mechanical concepts like entanglement and decoherence in macroscopic systems.
It was suggested that such circuits could be used as basic building blocks for a quantum computer, the "qubits". Compared with other quantum microscopic systems like neutral atoms or photons, this system has a big advantage in terms of scalability. To be of any practical use, a quantum computer should indeed contain a large number of qubits. Mesoscopic circuits with many qubits would not be much more difficult to fabricate than with a single one. In this respect, superconducting qubits are very promising systems. But one important problem has to be solved to make possible many-operation quantum computing : the coupling of the qubit’s degrees of freedom to the environment, in particular through the measurement leads, randomizes the phase of its wavefunction after a certain time called the dephasing time τφ. Any quantum computing task should be realized in a shorter timescale than τφ.
THE "PERSISTENT-CURRENT" QUBIT
We designed a circuit made of one loop containing three junctions, the "persistent-current flux qubit" , in order to minimize the effects of environment (see figure 2A). When biased at a flux Φ around Φ0/2, the qubit has two low-energy levels. If Φext is far from Φ0/2, the two energy eigenstates carry a mesoscopicsupercurrent (typically 300nA) which flows either clockwise or anticlockwise. If Φ=Φ0/2, the energy eigenstates are coherent superpositions of the two current-carrying states (see figure 2B). One can induce a transition between those two levels by applying microwave radiation at the resonance frequency. We use a DC SQUID coupled to the qubit to measure the flux generated by the persistent currents flowing through it, and thus to detect its state after all coherent operations are done (figure 2C).
Fig. 2 : A) The persistent-current qubit is a three-junction loop biased by an external flux. B) Low-energy diagram of the persistent-current qubit C) Detection (in gray) and manipulation (in purple) of the qubit.
Spectroscopy of the qubit
Spectroscopic measurements fully confirmed the energy diagram of figure 2B . An SEM picture of the sample is shown at figure 1. We measured the average switching current of the SQUID as a function of the external flux while applying CW microwave. Figure 3A shows the data for different microwave frequencies. The peaks and dips result from transition between the two energy levels of the qubit. On the figure 3B was plotted the microwave frequency as a function of the external bias flux. As predicted on figure 2B, the transition frequency varies linearly at large bias fields, and exhibits an anti-crossing around Φ0/2. This is an indirect proof that a coherent superposition of current states was achieved .
Coherent dynamics of a qubit
We observed the coherent dynamics of a persistent-current qubit. In this
sample, the three-junction loop and the detection Squid share a common branch as
can be seen on the SEM-picture of figure4. We used microwave pulses of variable
length and amplitude to coherently manipulate the quantum stateof the loop. The
readout by the Squid was also pulsed and revealed quantum-state oscillations
with high fideity (see figure 4).Under strong microwave driving, it was possible
to induce hundreds of coherent oscillations. We could performRabi, Ramsey and
echo-type sequences. We measured a relaxation time of 900 nanoseconds and a
free-induction dephasing time of 20 ns.  To learn more about this
Inductive measurement of a qubit Switching of the measuring DC-SQUID to the finite voltage state strongly perturbs
the measurement circuit and the qubit. We investigate a method for the readout of a flux
qubit based on a direct measurement of the Josephson inductance of the DC-SQUID. The
DC-SQUID is shunted by a capacitor, such that the plasma frequency is in the range
0.5-1 GHz (see fig. 5A). Close to the resonance frequency of this circuit the output voltage is very
sensitive to the flux produced by the qubit. We have characterized this method and
measured the state of a persistent current qubit, obtaining a relaxation time of the
order of 80 ms (see figure 5B). The fidelity of the measurement is 70%, being limited at this stage by
the amplifier added noise.
Inductive measurement of a qubit
Switching of the measuring DC-SQUID to the finite voltage state strongly perturbs the measurement circuit and the qubit. We investigate a method for the readout of a flux qubit based on a direct measurement of the Josephson inductance of the DC-SQUID. The DC-SQUID is shunted by a capacitor, such that the plasma frequency is in the range 0.5-1 GHz (see fig. 5A). Close to the resonance frequency of this circuit the output voltage is very sensitive to the flux produced by the qubit. We have characterized this method and measured the state of a persistent current qubit, obtaining a relaxation time of the order of 80 ms (see figure 5B). The fidelity of the measurement is 70%, being limited at this stage by the amplifier added noise.
PROJECTS AND PERSPECTIVES
Epitaxial Josephson junctions
Up to now, the Josephson junctions in the superconducting circuits were fabricated with two-angle shadow evaporation. This technique is easy to use and standard practice for making sub-micron structures. However, the reproducibility of the junctions is limited, as the junction region is non-planar and the area is therefore poorly defined. As the sample is covered with resist during evaporation, cleaning the surface by heating is not possible and resist outgassing might also limit the junction quality. In particular, fluctuations in the critical current density make it difficult to achieve more complex qubit circuits. Critical current noise due to impurities in the barrier may lead to additional decoherence. Therefore we try to establish a fabrication scheme based on epitxially grown Al/Oxide/Al trilayers. Single-crystalline aluminum films and trilayers have been grown already. The TEM picture (figure 6A) shows the lattice planes of the aluminum films. The oxide layer in between is also very uniform. Presently, we are setting up a fabrication procedure for making sub-micron Josephson junctions out of these trilayers (see figure 6B).
 W. J. Elion et al., Nature 371, 594 (1994)
 J. M. Martinis et al. , PRB 35, 4682 (1987)
 Y. Nakamura, Y. Pashkin, J. Tsai, Nature 398, 786 (1999)
 J. E. Mooij et al., Science 285, 1036 (1999)
 C. H. van der Wal et al., Science 290, 773 (2000)
 I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, J. E. Mooij, published online in Science : 13 February 2003 10.1126/science.1081045
The flux-qubit team:Hans Mooij, Kees Harmans (faculty members)