MEASUREMENT
Application note

Dynamically modulated Autler-Townes effect in atransmon qubit
Jiazheng Pan and Guozhu Sun, Research Institute of Superconductor Electronics,
School of Electronic Science and Engineering, Nanjing University, China

Introduction
By applying a coupling microwave field gated by random-telegraph-noise (RTN), we report the experimental
demonstration of dynamically modulated Autler-Townes effect (ATE) in an artificial atom – a superconducting
transmon qubit – and obtain the distinguished characteristics when a system is affected by RTN. Numericalcalculations agree well with the experimental data.
A superconducting qubit based on Josephson junctions can behave like an artificial atom and exhibit macroscopic
quantum coherence. Such an artificial atom has been employed as a testing ground for atomic-physics andquantum optics experiments in a nearly macroscopic system. Numerous phenomena including those, which cannot
even occur in natural atoms, have been explored in the superconducting qubit, one of which is the well-known
Autler-Townes effect (ATE).
Generally speaking, in ATE a three-level (|a>,|b>,|c>) atom is irradiatedby a sufficiently strong resonant (between |a>and |b>) external field;
the uncoupled and degenerate states |a,N+1> and |b,N> (N represents
the number of photons) will repel each other and are transformed
into dressed states. This means the original energy levels split andmanifest themselves as doublets around the transition frequencyof the uncoupled system. Such doublets in the atom’s absorption
spectrum (between |b>and |c>) can be probed by another weak tone.
The spacing of the doublet is equal to the coupler strength, i.e., Rabi
frequency, of the resonant field.
In order to further explore the characteristics and possible applicationin quantum information processing and quantum simulation ofother systems, here we focus on the dynamically modulated ATE ina superconducting transmon qubit. The coupling field is modulated
by a random-telegraph noise (RTN) process. RTN is a stationary anddichotomous Markovian process characterized by an average jumpingrate. The number of the jumps is a Poisson process.

Experimental set-up with Triton 500
Cryofree dilution refrigerator

MEASUREMENT
Application note

Experiment
Our device is a transmon qubit in an aluminum three dimensional cavity with its fundamental resonant
frequency ωcav/2π = 10.678 GHz. The sample is made via electron beam lithography and double-angle
evaporation on a high resistance Si substrate, in which a single Al/AlOx/Al Josephson junction is capacitively
shunted by two Al pads as shown in Figure 1(a). The device is located in Oxford Triton 400 dilution
refrigerator with careful electromagnetic shielding and filtering. The states of the transmon are measured
using Jaynes-Cummings readout. From the spectrum we can get ω01/2π = 8.865 GHz, ω12/2π = 8.637GHz. Due to the anharmonic characteristics of a transmon, only the ground (|0>), first (|1>), and second
excited states (|2>) of the transmon qubit are considered in our experiment when the system is driven
by fields resonant or nearly resonant with ω01 and ω12. Thus the qubit can be regarded as a laddertype three-level artificial atom as shown in Fig. 1(b). The coupler (probe) fields are near resonant with thetransition frequency between |1> and |2> (|0> and |1>).
We use a monochromatic field with RTN-process modulation to drive the transmon qubit. An arbitrary
waveform generator is programed to generate a continuous pseudorandom rectangular waveform with twovoltage levels 0 and 1.2 V to switch off/on the coupler field. The jumps of voltage levels during time t areconsistent with the Poisson process with the probability of the number of jumping , Pn(Xt) = (Xt)ne-Xt/n, in
which X is an average jumping rate. Then another weak probe field is applied to characterize the spectrumof the qubit.

Figure 1. (a) Optical micrograph of transmon.
(b) Energy level diagram indicating the energy levels, probe,and couplers. The coupler is modulated by RTN process.

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Application note

Experimental results
Figure 2 shows the result of ATE with RTN-process modulation. Here the strength of the coupler wave is Ωc/2π = 16MHz. The spectrum versus the average jumping rate X of RTN process is obtained by sweeping the probe wave. As one
can see, the spectrum is quite different from that without RTN process. In the regular ATE, there are only two peaks
resulting from the dressed states |±> with spacing which is equal to the coupler strength Ωc/2π = 16 MHz. Here whenthe jumping rate is low, the spectrum shows three peaks. The middle peak located at Δp = 0 is the resonant peak at
ω01, which disappears in the regular ATE for a strong coupler strength. The other two peaks locate symmetricallyat Δp/2π = ±8 MHz. These are the dressed states |±> in the regular ATE. Such effect comes from the RTN process.
The switching on/off of the coupler wave means the coupler wave is applied or not randomly, which results in theappearance or disappearance of the spectral lines corresponding to |±> and |1> in the spectrum. When the jumping
rate is not so high, the states |±> and |1> can switch swiftly back and forth, thus three peaks emerge. As the jumping
rate increases, there is no time for the states |±> and |1> to drift into the direction of the noise. Therefore when thejumping rate is larger than a threshold, which we define as ξ, the population measured in the steady state is anaverage of that in the states |±> and |1>. So the previous three peaks merge pairwise into two new peaks located atΔp/2π = ±4 MHz. Because the numbers and position of the peaks in the measured spectrum depend on the RTN, one
may use the modulated ATE to detect RTN process.

Figure 3. (a) Experimental and (c) numerical calculated spectra of the ATEwith RTN-process modulation as a function of average jumping rate X
with Ωc/2π = 16 MHz. (b) Horizontal cuts of the spectrum at X/2π = 6.633
MHz, 16.432 MHz, 30 MHz in (a), respectively.

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Application note

Conclusion
In summary, we have observed RTN-modulated ATE in a superconducting transmon qubit. The measuredspectra are drastically different from those in the regular ATE of a three-level atom. In the modulated
ATE with RTN process, the dressed states in the regular ATE and the bare state will be averaged when
the noise jumping rate in RTN process is larger than the coupler strength. The result may help us todetect RTN with modulated ATE and explore the robustness of quantum switches and quantum routersagainst RTN. Also it is promising in quantum simulation such as simulating the motional averaging inother systems.

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July 2018, Issue 1