Fast control of dissipation in a superconducting resonator

TL;DR

This paper demonstrates rapid, electrically-controlled tuning of a superconducting resonator's dissipation rate using a quantum-circuit refrigerator, enabling fast reset and potential qubit initialization.

Contribution

It introduces a method for fast, electrical control of resonator damping using a QCR, achieving significant tunability and rapid operation times.

Findings

Damping rate tunability up to nearly two orders of magnitude

Operation times as short as 10 nanoseconds

Potential application for fast qubit initialization

Abstract

We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently-developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active reset of a superconducting quantum circuit. In the future, a similar scheme can potentially be used to initialize superconducting quantum bits.

Tables

Table 1. Table 1: Parameters of the measured sample.

$R_T$	$14$ $k\Omega$	NIS tunneling resistance
$T_N$	0.17 K	electron temperature of the normal-metal island
${\gamma }_D$	$4\times {10}^{-4}$	Dynes parameter
$Z_r$	35 $\Omega$	resonator impedance
$C_c$	$840$ fF	capacitance between QCR and resonator
$C_m$	$5$ fF	NIS junction capacitance
$f_0$	8.683 GHz	resonator mode frequency
$\Delta$	215 $\mu$eV	energy gap parameter of the Al leads

Table 2. Table 2: Principle characteristic values of the obtained damping rates, see Fig.  2 (b), including maximal γ QCR max subscript superscript 𝛾 max QCR \gamma^{\mathrm{max}}_{\mathrm{QCR}} and minimal γ QCR min subscript superscript 𝛾 min QCR \gamma^{\mathrm{min}}_{\mathrm{QCR}} measured damping rate of the QCR, theoretical value of the QCR damping rate at zero bias voltage γ QCR off subscript superscript 𝛾 off QCR \gamma^{\mathrm{off}}_{\mathrm{QCR}} and measured damping rate of the transmission line γ tr subscript 𝛾 tr \gamma_{\mathrm{tr}} .

${\gamma }_{\mathrm{QCR}}^{\max }$	$6.7\pm 0.7\times {10}^8$ $s^{-1}$	measured
${\gamma }_{\mathrm{QCR}}^{\min }$	$1.6\pm 0.5\times {10}^7$ $s^{-1}$	measured
${\gamma }_{\mathrm{QCR}}^{\mathrm{off}}$	$1.1\times {10}^5$ $s^{-1}$	theory
${\gamma }_{\mathrm{tr}}$	$1.2\pm 0.1\times {10}^7$ $s^{-1}$	measured

Equations

$$A_{\mathrm{after}}=A_{\mathrm{before}}\exp \{-\frac{1}{2}[{\gamma }_{\mathrm{QCR}}(\tau -\Delta t_{\mathrm{rise}}-\Delta t_{\mathrm{fall}})$$

$$+({\gamma }_{\mathrm{tr}}+{\gamma }_{\mathrm{x}})(t_{\mathrm{a}}-t_{\mathrm{b}})+{\gamma }_{\mathrm{QCR}}^{rise/fall}(\Delta t_{\mathrm{rise}}+\Delta t_{\mathrm{fall}})$$

$$+{\gamma }_{\mathrm{QCR}}^{\mathrm{off}}(t_{\mathrm{a}}-t_{\mathrm{b}}-\tau )]\},$$

Full text

††preprint: AAPM/123-QED

Tunable dissipative environments for circuit quantum electrodynamics (cQED) are pursued intensively in experiments due to the unique opportunities to study non-Hermitian physics Leggett et al. (1987); Rastelli and Pop (2018), such as phase transitions related to parity-time symmetry Quijandría et al. (2018), decoherence and quantum noise Clerk et al. (2010). Interesting effects can be observed in experiments on exceptional points Partanen et al. (2018); Sweeney et al. (2019); Heiss (2012), which also gives possibilities to use such systems as models in nonlinear photonics, for example, for metamaterials Cui et al. (2013) and for photonic crystals Kim et al. (2016).

From the practical point of view, tunable environments are utilized to protect and process quantum information Mirrahimi et al. (2014); Kraus et al. (2008); Verstraete, Wolf, and Ignacio Cirac (2009) and to implement qubit reset Jones et al. (2013); Wendin (2017). The latter application calls for fast tunability of the environment due to the aim to increase the rate of the operations on a quantum computer. Recent advances in the field of cQED for quantum information processing Wendin (2017); DiVincenzo (2000); Devoret and Schoelkopf (2013); Reagor et al. (2016) render this topic highly interesting.

There are different ways for resetting superconducting qubits. Firstly, one may tune the qubit frequency to reduce its life time Reed et al. (2010). The disadvantages of this method include the broad frequency band reserved by the qubit and the required fast frequency sweep which may lead to an increased amount of initialization error Tuorila et al. (2019). Conventionally, it is beneficial to maintain the qubits at the optimal parameter points during all operations. Secondly, it is possible to use microwave pulses to actively drive the qubit to the ground state Geerlings et al. (2013); Egger et al. (2018); Magnard et al. (2018); Valenzuela et al. (2006). Such methods are popular because no additional components or new control steps are needed. However, to achieve high fidelity one usually needs to increase the reset time to the microsecond range. Thirdly, one can engineer a tunable environment for the qubits Jones et al. (2013); Basilewitsch et al. (2019); Tuorila et al. (2017); Wong et al. (2019). This approach demand changes in the chip design, but may lead to high fidelity for a fast reset without compromises on the other properties.

Here, we focus on a single-parameter-controlled tunable environment implemented by a quantum-circuit refrigerator (QCR) Partanen et al. (2018); Tan et al. (2017); Silveri et al. (2017); Masuda et al. (2018); Hyyppä et al. (2019); Silveri et al. (2019). The refrigerator is based on photon-assisted electron tunneling through two identical normal-metal–insulator–superconductor junctions (NIS). It has been used to cool down a photon mode of the resonator Tan et al. (2017), and to observe a Lamb shift in a cQED system Silveri et al. (2019). Furthermore, QCR can be used as a cryogenic photon source Masuda et al. (2018), which makes it applicable for a calibration of cryogenic amplification chains Hyyppä et al. (2019). Details of the QCR operation and theory are described in Ref. Silveri et al., 2017.

The QCR can potentially be incorporated in a quantum processor to significantly decrease the reset time. However, all previous related research has been based on the dc and low-frequency voltage control of the QCR-induced dissipation rates. In this paper, in contrast, we demonstrate nanosecond operation of the QCR, which serves to expand future application areas of the this device.

As shown in Fig. 1(a), the measured sample consists of a coplanar waveguide resonator, coupled to an rf transmission line at one end and to a normal-metal island of the QCR at the other end. The superconducting leads of the QCR are connected to two transmission lines with on-chip low-pass filters. The low-pass filters were introduced in this batch of samples for the first time in the context of the QCR and used to reduce the high-frequency noise. The filters are realized as lumped-element RC elements made of palladium fins capacitively shunted to ground through an aluminum oxide layer. All the measurements are carried out in a dilution refrigerator with the base temperature of 10 mK.

The fabrication of the sample is fully described in our previous publication Masuda et al. (2018). In brief, the sample is fabricated on a 500-µm-thick Si wafer. The resonator is defined in a 200-nm-thick sputtered niobium layer, and subsequently covered by a 50-nm-thick layer of $\mathrm{Al_{2}O_{3}}$. The NIS junctions are defined with electron beam lithography followed by two-angle evaporation (20 nm Al, 20 nm Cu).

We provide a summary of the relevant sample parameters in Tab. 1. The parameters are estimated from the fabrication process and previous measurements from similar samples Silveri et al. (2019). The SEM in Fig. 1 are obtained on a sample from the same fabrication batch as the sample, which is used in this work.

For the QCR characterization, we use homodyne detection to measure the amplitude of the resonator signal voltage from the connected transmission line. A schematic example of the measurement result together with the basic sequence of the applied pulses are shown in Fig. 1(b). First, we send an rf drive to the resonator to populate the fundamental mode. The power of the resonator rf drive is around –110 dBm at the sample input. Then we switch the drive off and observe the decay of the resonator signal. At this stage there are three main sources of decay: coupling to the transmission line, to the QCR in the off state, and to unknown excess sources. The value of the damping rate related to the unknown sources $\gamma_{\mathrm{x}}$ is estimated from the previous measurements Silveri et al. (2019) to be roughly 10% of the damping rate to the transmission line $\gamma_{\mathrm{tr}}$. The QCR-off damping rate $\gamma_{\mathrm{QCR}}^{\mathrm{off}}$ is negligible, in line with previous studies Silveri et al. (2019). At a chosen instant of time, we send a voltage pulse to the QCR, which changes the rate of the resonator signal decay. The QCR voltage pulse is formed by an arbitrary waveform generator.

To estimate the damping rate arising from the QCR during the voltage pulse (on state), we use a procedure, explained below. It is based on varying both the amplitude and the width of the QCR pulse in an effort to increase the precision of the measurements.

First, we choose two points in time, one before and one after the QCR pulse, see Fig. 1(b). These points are fixed for all subsequent measurements. We express the amplitude of the resonator signal after the QCR pulse as

[TABLE]

where $A_{\mathrm{after}}$ and $A_{\mathrm{before}}$ are the amplitudes of the resonator signal voltage after ($t_{\mathrm{a}}$) and before ($t_{\mathrm{b}}$) the QCR pulse, $\tau$ is the width of the pulse, $\gamma_{\mathrm{QCR}}$ is the damping rate arising from the QCR in the on state, excluding the times of the rise $\Delta t_{\mathrm{rise}}$ and fall $\Delta t_{\mathrm{fall}}$ of the QCR voltage, and $\gamma_{\mathrm{QCR}}^{\mathrm{rise/fall}}$ is the effective damping rate during the pulse rise and fall. In this work, we aim to extract $\gamma_{\mathrm{QCR}}$ which is is the most relevant parameter for fast circuit reset and can be connected to the theory, previous measurements, and future applications of the QCR.

Next, we vary $\tau$ such that it is still smaller than $t_{\mathrm{a}}-t_{\mathrm{b}}$. Only two components in the exponential function are changing with this variation, namely, those related to $\gamma_{\mathrm{QCR}}$ and $\gamma_{\mathrm{QCR}}^{\mathrm{off}}$. The latter, as mentioned above, is negligibly small. Thus ln($A_{\mathrm{after}}$/$A_{\mathrm{before}}$) is a linearly decreasing function of $\tau$ with a slope $\gamma_{\mathrm{QCR}}/2$, see Fig. 2(a). In this figure, we observe a flat region at short pulses, which is related to the rise and fall of the QCR voltage. The flat region extends to approximately 8 ns, which is significantly longer than $\Delta t_{\mathrm{rise}}+\Delta t_{\mathrm{fall}}=2.50$ ns. This effect can be explained by the distortions of the voltage pulse due to the imperfection of the QCR control line. The width of the flat region is varying depending on the height of the voltage pulses and the sum of the rise and fall times (data not shown). Importantly, a clear linearly decreasing part of the graph yields the damping rate of the QCR during the pulse.

Figure 2(b) shows the extracted damping rate of the QCR, $\gamma_{\mathrm{QCR}}$, as a function of the height of the applied QCR voltage pulse $V^{\mathrm{pulse}}_{\mathrm{QCR}}$. There are four different data sets, corresponding to the different $\Delta t_{\mathrm{rise/fall}}$, which are varied in an effort to reduce the switching time of the QCR. The shortest measured sum of the rise and fall times is 6 ns, which was obtained with nominal $\Delta t_{\mathrm{rise}}+\Delta t_{\mathrm{fall}}=0.34$ ns and $V^{\mathrm{pulse}}_{\mathrm{QCR}}=345$ $\mathrm{\mu}{}V$ ($0.8\times 2\Delta$). The results in Fig. 2(b) follow well the theoretical prediction. There are no experimental data points lower than $1.6\times{}10^{7}$ $\mathrm{s}^{-1}$. The difficulty to measure in this range is explained by the fact that the damping rate of the transmission line $\gamma_{\mathrm{tr}}$ is around this value, and hence dominates the decay at the voltages lower than 0.6$\times 2\Delta$. This decreases the signal-to-noise ratio in the extraction procedure for $\gamma_{\mathrm{QCR}}$. The damping rate of the transmission line $\gamma_{\mathrm{tr}}$ is calculated from the measured decay of the resonator signal prior to the QCR voltage pulse. Short list of the specific characteristic values of the extracted damping rates are shown in Tab. 2.

In our experiment the total damping rate of the resonator can be tuned up to factor of $56\pm 8$, which is calculated from the ratio $\gamma^{\mathrm{max}}_{\mathrm{QCR}}/\gamma_{\mathrm{tr}}$. Based on the theory Silveri et al. (2017), however, we estimate that the damping rate of the QCR changes by almost four orders of magnitude. Thus in our experiment the efficiency of the QCR is limited by the strong coupling of the resonator to the transmission line. However, our observations support the abovementioned scenario of resetting superconducting qubits. The measurement results on $\gamma_{\mathrm{QCR}}$ in Fig. 2(b) suggest that the QCR is giving very small changes of the damping rate in the off state and an optimized QCR voltage pulse can reduce the number of the resonator photons to less than 1% of the original number in a few tens of nanoseconds.

In conclusion, we experimentally demonstrated that a QCR can be turned on and off in a nanosecond time scale. This renders it as a potentially useful device in resetting a multitude of quantum electric circuits. In the future, we aim to couple the QCR with transmon qubits which allows a more accurate measurement of the on/off ratio and the resulting temperature of the refrigerated system.

ACKNOWLEDGMENTS

This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant No. 795159 and under the European Research Council Consolidator Grant No. 681311 (QUESS), from the Academy of Finland Centre of Excellence in Quantum Technology Grant No. 312300, No. 316619. and No. 305237, from JST ERATO Grant No. JPMJER1601, from JSPS KAKENHI Grant No. 18K03486, from the EU Flagship project QMiCS, from the Emil Aaltonen Foundation, from the Alfred Kordelin Foundation, and from the Vilho, Yrjö and Kalle Väisälä Foundation. We acknowledge the provision of facilities and technical support by Aalto University at OtaNano - Micronova Nanofabrication Centre.