MEASUREMENT
Application note

Absorption spectra of superconducting qubits driven
by bichromatic microwave fields
Jiazheng Pan and Guozhu Sun, Research Institute of Superconductor Electronics, School ofElectronic Science and Engineering, Nanjing University

Introduction
An experimental observation was reported of two distinct
quantum interference patterns in the absorption spectra
when a superconducting transmon qubit is subjected to abichromatic microwave field with the same Rabi frequencies.
The results show good agreement between the numericalsimulation and experimental data. Such multiphoton
interference may be used in manipulating the quantum
states and/or generate nonclassical microwave photons.
Superconducting qubits are one of the most promising
candidates for the implementation of circuit quantum
electrodynamics (QED) platforms. The coupling of the systemwith driving fields has proven to have a high potential for
scalability. Superconducting qubit architectures, whichinteract with the external field couplings, have beenextensively studied.
In this work, we reveal the nonlinear dynamical level
splitting of superconducting circuits driven by a bichromatic
microwave field. The external field possesses two equal
amplitude components with frequencies scanned fromlarge detuning to resonance frequencies. We focus on thenear-resonance frequencies where subharmonic resonances
generate fringe patterns in the transition probability spectra.
We also demonstrate these results theoretically.
can be used as a measure of the quality of this interface.
At low temperatures the superconducting electrodes
induce superconductivity in the topological insulator by theproximity effect, with a finite Josephson current observed
across a sufficiently narrow gap.

Experimental set-up with Triton 500
Cryofree dilution refrigerator

MEASUREMENT
Application note

Experiment
Our device consists of a superconducting transmon qubit coupled to a three-dimensional aluminum cavity. Thelength, width, and depth of the cavity are 15.5, 4.2, and 18.6 mm, respectively. The transmon is made via electron
beam lithography and double-angle evaporation, in which a single Al/AlOx/Al Josephson junction is capacitively
shunted by two Al pads on a high-resistance Si substrate. The schematic of the experimental setup is shown in
Figure 1. The device is located in an Oxford Triton 400 dilution refrigerator below 20 mK with magnetic shielding.
The microwave lines to the cavity are heavily attenuated at each stage of the dilution refrigerator and sent to thecavity through low-pass filters with a cutoff frequency of 12 GHz. The output signal from the cavity is passed
through cryogenic circulators and a high-electron-mobility transistor (HEMT) amplifier located in the dilution
refrigerator and further amplified at room temperature. It is then mixed down and digitized by a data acquisition
card.
Three microwave drives are used in the experiment. Qubit control waves (denoted as probe and coupler) arecontinuous while the readout wave (denoted as cavity) is triggered. Cavity, probe, and coupler waves are combinedby two power splitters at room temperature before being sent to the dilution refrigerator. In a sampling period, thecavity wave is turned on at time t = 70 ns for 2100 ns and the data acquisition card starts to record at time t = 270
ns. The repetition rate is 10 kHz so the whole sequence is repeated every 100 μs.
The states of the transmon are measured by using a Jaynes-Cummings readout. The cavity wave is applied at thebare cavity frequency ωcav/2π = 10.678 GHz. We obtain the transition resonance frequency ωge/2π = 8.865 GHzand ωef /2π = 8.637 GHz from the spectrum, from which we get the Josephson energy EJ/h = 45.33 GHz and thecharging energy Ec/h = 228 MHz. Using the pump-probe method we obtain the energy relaxation time T1 = 0.53
μs. The spin-echo measurement shows the dephasing time T2 = 0.51 μs.

Figure 1. Energy level and microwave
drive diagrams represent one-photontransition (left) and two-photontransition (right), respectively.

Figure 1. Circuit diagram of set-up. Attenuators, filters, and circulators
are used to reduce the external noise. The output signal is thenamplified and down-converted with a local oscillator and digitized.

MEASUREMENT
Application note

Experimental results
To demonstrate the effect of two near-resonance microwave fields driving, the probe and coupler waves are turnedon continuously, so the system stays at a steady state during the measurement. By sweeping both Δp = ωp − ωgeand Δc = ωc − ωge (which are the detunings of the probe and coupler, respectively) around zero, we measure thespectrum of the qubit. As illustrated in Figure 2, in the one-photon transition experiment, the coupler frequency ωcand the probe frequency ωp are both near the transition resonance frequency ωge, and the coupling strengths areΩc/2π = Ωp/2π = 4.16 MHz. In the two-photon transition experiment, ω′c and ω′p are near ωge/2 and Ω′
c/2π =Ω′p/2π = 0.973 MHz.
The experimental and theoretical transition probabilities are presented in Figure 3, when a transmon superconducting
qubit is subject to two near-resonance to resonance microwave fields. Figure 3(a) and 3(b) correspond to the casewhen the single-photon transition condition is satisfied. In this case, absorption spectrum near the single-photon
resonance can be produced by transverse and/or longitudinal coupling between a two-level system. Figure 3(c) and3(d) present the experimental and theoretical results for the observation of the two-photon transitions. In this caseabsorption spectrum near the two-photon resonance can only be produced by a longitudinal coupling between thequbit and the bichromatic microwave field. The results show good agreement between the numerical simulation andexperimental data.

Figure 3(a) Experimental measurement (b) theoretical result of the singlephoton transitions in a superconducting transmon qubit. (c) Experimental
measurement (d) theoretical result of the double-photon transitions in asuperconducting transmon qubit.

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Application note

Conclusion
In summary, we report experimental observation of two distinct quantum interference patterns in the absorption
spectra when a superconducting transmon qubit is subject to a bichromatic microwave field.
The results show good agreement between the numerical simulation and experimental data. These observations
and interpretation may be used not only to generate multilevel tunable energy structures, but also to explore
nonclassical microwave photons, which are the fundamental elements in quantum information processing,
especially in microwave quantum photonics.

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July 2018, Issue 1