Experiments with superconducting flux qubits
Evgenii Glushkov1,2, Gleb Fedorov1,2 and Kirill Shulga1,2,3
1 Moscow Institute of Physics and Technology, 141700 Dolgoprudnii, Russia
2 National University of Science and Technology "MISIS", 119049 Moscow, Russia
3 Russian Quantum Center, 143025 Skolkovo, Russia
Abstract
Sample Design
Landau-Zener Interference
Development of superconducting quantum bits (qubits) has made a significant progress
in the areas of quantum computation and quantum metamaterials. We have made a
series of measurements of the spectral characteristics of superconducting flux qubits
using Frequency Division Multiplexing (FDM) technique. The flux qubits were coupled to
λ/4 resonators and the readout was done in the dispersive regime using quantum
non-demolition measurements. As a result we received an avoided-level crossing picture
and a spectrum of the flux qubit. Using that data we obtained the values of the qubit level
splitting, dispersive shift of the resonator and coupling strength between them. Also we
observed multi-photon effects, such as Landau-Zener-Stuckelberg interferometry.
The samples were manufactured in the 7-qubit architechture, shown on the picture
below, in collaboration with IPHT, Jena, Germany3. This design allows performing the
readout of all seven qubits simultaneously through seven resonators with slightly
different frequencies.
An interesting effect was observed while irradiating a qubit-resonator system with
microwaves of different magnitudes and, at the same time, sweeping over the range of
magnetic flux penetrating the qubit.
Flux Qubit
Flux qubit1 is an artificial implementation of a quantum system that has two
distinguishable states. Originally it consisted of a superconducting metallic ring
interrupted by one Josephson junction (JJ), later two more Josephson junctions were
added to make the flux qubit less coupled to the environment. The use of Josephson
junctions for creating superconducting qubits was evident as one could get two isolated
energy levels only in an anharmonic potential, thus using a non-linear element. The only
known non-dissipative and non-linear circuit element is the Josephson junction, which is
(1) and
(2),
governed by the two Josephson equations2:
where φ is the phase difference across the junction and I0 is the critical current.
Fig. 2 Sample overview:
a) The experimental sample with seven λ/4
resonators, capacitevely coupled to the
common feedline.
b) Upper end of one of the resonators with
pins to catch Abrikosov vortices.
c) Flux qubit placed near the end of the
resonator to maximize the mutual
inductance between the qubit and
resonator.
d) Capacitor coupling the resonator to the
common feedline.
This design also implements the idea of quantum
non-demolition measurements using ths so-called
“dispersive shift” of the readout resonator. When the
qubit changes its state it also slightly changes the
frequency of the corresponding resonator due to their
inductive coupling, which can be observed as a shift of
the transition coefficient minimum.
Fig. 6 Landau-Zener-Stuckelberg Interference4
Fig. 3 Resonator dispersive shift.
Results
Fig. 1 a) Detailed micrograph of an aluminum flux qubit with 3 JJ. b) Schematic view of a 3JJ
flux qubit, also called persistent-current qubit as the two basis states are the clockwise and
counterclockwise directions of the current, circulating in the loop. c) Enlarged micrograph
showing two JJ’s, manufactured using shadow evaporation technique.
In the sequence of several experiments we managed to measure the anti-crossing and
the energy spectrum of superconducting flux qubits. The measurements were made in
the period of several months, with the constant tuning of the experimental setup . The
best data we measured is shown below.
Conclusion
To spectroscopically characterize the flux qubit one needs to measure the transition
frequency between the two levels in dependance to the external magnetic flux.
We have measured spectral characteristics of several superconducting flux qubits using
quantum non-demolition measurements in a new laboratory, which has been built in
NUST MISIS, Moscow over the last two years. This is the fisrt step towards performing
more sophisticated experiments with, for example, chains of qubits (so-called, “quantum
metamaterials”) or more complex qubit structures (quantum optics with microwave
photons). We also aim at fabricating qubits from various types of materials, including
those with high kinetic inductance (NbN, TiN), at the cleanroom facility at Moscow
Institute of Physics and Technology.
Experimental Setup
Fig. 4 Schematic view of the
experimental setup.
All measurements were performed in a newly built
laboratory in NUST MISIS, Moscow. The main parts of the
setup were Oxford Instruments dilution refrigerator,
Agilent PNA-X network analyzer, Agilent microwave
source and Keitheley current source. The input signal
was attenuated by 60-70 dB of attenuators to reach
single-photon regime, the output signal was amplified
using cryogenic and room-temperature amplifiers. A
small external coil was used to excite the qubit by
applying a microwave tone to it. The excitation of the
qubit was also possible as a second tone with a
directional coupler.
Magnetic flux effectively controls qubit energy splitting, so when it matches the energy
of k photons in the resonator, we observe the change in transmission S21 at the resonator
frequency. Interaction between the qubit and the resonator lifts the degeneracy,
permitting us to see two resonances, ω r ± Ω, and a peak of S21 at ωr. That lift is dependent
on both n and Φ: it increases with n and decreases with Φ, so the resonances with greater
k’s can only be seen with larger n’s, that means, with larger MW magnitudes. That explains
why every pair of side-peaks on the Fig. 6 appears later with power. A quasi-periodic
dependence of S21 on the excitation power (Stuckelberg oscillations) can be noted.
Fig. 5 Experimental data. a) Anti-crossing picture: the energy level of the resonator is
crossed by the energy spectrum of the qubit at two points. This happens due to the
hyperbolic shape of the spectrum. b) The energy spectrum of the qubit, i.e. the
dependance of the transition frequency on the magnetic flux governed by Eq. (3).
The hyperbolic shape of the spectrum is due to the dependance
, where
and
and ∆ is the distance between two qubit levels at zero flux (so-called
“degeneracy point”). One can estimate the value of ∆ from the Fig. 5b which is 1.8 GHz.
The value of coupling strength can be estimated from the Fig. 5a and is around 20 MHz
while the dispersive shift is about 0.8 MHz.
On the Fig. 5b one can also see the two-photon process, when the trasition from ground
to the first excited state happens with the absorbtion of two photons, resulting in an
inverse hyperbola with the maximum at the degeneracy point. In the next section we
disscuss one more multi-photon phenomenon.
References
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5430-P. 1036-1039
2. Josephson B. D. Possible new effects in superconductive tunnelling // Physics Letters.
-1962.- Vol. 1, no. 7. -P. 251-253
3.Jerger Markus. Experiments on Superconducting Qubits Coupled to Resonators. //
KITBibliothek. - 2013.
4. W. D. Oliver and S.O. Valenzuela. Large-amplitude driving of a superconducting
artificial atom. Quantum Information Processing 8, 2-3 (June 2009), 261-281