Qubit Response to Optical Illumination

NIOBIUM BASED TRANSMON QUBITS ON SILICON SUBSTRATES FOR QUANTUM TRANSDUCTION

7.6 Qubit Response to Optical Illumination

Next we turn our attention to measurements with optical illumination. Since we will be inferring the qubit response by monitoring the readout resonator spectrum, we must first characterize the bare readout resonator response under optical illumination.

By sufficiently detuning the qubit from the readout resonator the qubit can be effectively decoupled from the readout resonator. This allows us to characterize the optical response of the readout resonator without the influence of the qubit. We perform spectroscopy on the readout resonator as we apply a 100 ns long, 85 𝜇𝑊 peak power laser pulse at a repetition rate of 10 kHz. The result of this measurement is shown in Fig ??. Clearly, there is no measurable change in the spectrum of the readout resonator after the laser pulse. This is as expected since the readout resonator is made entirely of Nb which has a very fast QP response.

Now we flux bias the qubit to be 320 MHz detuned from the readout resonator. We

Readout Amplitude(mV)

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7imH (μs) 7.46

7.47 7.48 7.49 7.50

9NA )rHquHnFy (GHz)

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 Laser

Laser pulse applied at t = 10µs

Figure 7.5: Readout resonator spectroscopy under optical illumination

probe the amplitude of the readout signal as an XY drive tone is swept around the qubit frequency. When the XY drive frequency is on resonance with the qubit fre- quency, the qubit is excited and the readout amplitude changes (in our measurement this appears as a dip in the readout amplitude). We use this technique to monitor the qubit frequency as we apply a 100 ns laser pulse at a 5 kHz repetition rate and peak power 240 𝜇𝑊. The result of this measurement is shown in Fig??.

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7imH (μs)

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−2000

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0W dHtuning (kHz)

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Readout Amplitude (mV)

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b.

Laser pulse applied (t=10µs)

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7ime (μV) 0.00

0.01 0.02 0.03 0.04 0.05 0.06

5eadRut Amplitude (mV)

Tr fit 15.74 s 0.10 μs

fit data

Figure 7.6: Spectroscopy of Nb qubit under optical illumination. a. Spectroscopy of Nb Qubit under optical illumination. b. Line-cut at 0 detuning showing recovery of the readout amplitude.

Fitting to an exponential yields a recovery timescale of 15.7𝜇 𝑠. Measurements performed with 100 ns laser pulse, 5 kHz repetition rate and 240𝜇𝑊 peak power.

We observe a sharp change in the qubit spectrum as the laser is pulsed. In particular, at t = 10𝜇 𝑠 when the laser is turned on, there is a downshift of the qubit frequency and a corresponding increase in the amplitude of the readout signal. As the delay from the laser pulse increases, the readout amplitude and qubit frequency relax back to their steady state value. A line cut at 0 microwave detuning shows the recovery of the readout signal. We find this recovery process fits well to an exponential with a relaxation time constant of 15.7𝜇 𝑠.

In the above measurement, we are probing the qubit by applying a continuous wave (CW) microwave signal to the XY drive line. We now utilize pulsed microwave signals on the XY line to measure the population, energy decay rate (𝛾

1 = ¹

2𝜋𝑇

1) and decoherence rate (𝛾^∗

2 = ¹

2𝜋𝑇^∗

2) of the qubit as a delay from the laser pulse. A set of these measurements performed at a 10 kHz repetition rate with a 100 ns laser pulse and a peak laser power of 85𝜇𝑊 is shown in Fig. 7.7.

Focusing on the population measurement, (Fig. 7.7a.), we observe the laser pulse initially inducing some excess population in the qubit which then relaxes to a steady state value on a timescale of∼30𝜇 𝑠. We also note that the steady state population (𝑃_{𝑒,𝑆 𝑆}) is higher than the thermal population in the laser off case (indicated by the gray line). Measurements of the energy decay rate (𝛾

1) and the decoherence rate (𝛾^∗

2) show a similar fast recovery timescale on the order of ∼10 𝜇 𝑠 and an excess decoherence rate in the steady state (𝛾^∗

2,𝑆 𝑆) due to a process slower than the repetition period (100𝜇 𝑠).

To gain further insight into this slow process, we measure the steady state population (𝑃_{𝑒,𝑆 𝑆}) and decoherence rate (𝛾^∗

2,𝑆 𝑆) of the qubit at a delay of 81 𝜇 𝑠 from the laser pulse while sweeping the peak power of the laser pulse. The results are shown in Fig. 7.8.

We fit the steady state population at each laser power to a Boltzmann distribution 𝑛_{𝑡 ℎ}(𝑇_{𝑒 𝑓 𝑓}) with an effective temperature 𝑇_{𝑒 𝑓 𝑓}. We find that this effective qubit temperature scales linearly with peak laser power in the low power regime𝑇_{𝑒 𝑓 𝑓}(𝑃)= 𝑇_{𝑜 𝑓 𝑓} + 𝛽 𝑃, with𝑇_{𝑜 𝑓 𝑓} =126 mK and 𝛽 =1.6±0.097 mK/𝜇𝑊. We find a similar linear scaling of the decoherence rate of the qubit as a function of laser power (P), 𝛾^∗

2,𝑆 𝑆(𝑃)=𝛾

2,𝑜 𝑓 𝑓 +𝛽 𝑃^𝑛, with𝑛=1.03±0.17 and 𝛽=0.53±0.41 kHz/𝜇𝑊^𝑛. We further probe the dependence of the steady state population 𝑃_{𝑒,𝑆 𝑆} as a function of repetition rate and laser pulse duration Fig. 7.9. We find that the population fits well to a Boltzmann distribution with an effective temperature that scales linearly in

0 10 20 30 40 50 60 70 80 DelDy froP lDser pulse, Td (μs) 0.0

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3opulDtion

T_r fit 30 s 2 μs lDser off reference fit

dDtD

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DHlDy from lDsHr pulsH, Td (us) 0.05

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γ1 (0Hz)

T_r fit 21 s 5 μs ^fitlDsHr off rHfHrHncH rDngH dDtD

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DHlDy from lDsHr pulsH, Td (us) 0.15

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γ* 2 (0Hz)

Tr fit 12 ± 1 μs

fit

lDsHr off rHfHrHncH rDngH dDtD

a.

b.

c.

𝑇_!

Readout Laser

Qubit XY _𝜏

𝜋/2 𝜋/2

Readout Laser

𝑇!

𝑇!

Readout Laser

Qubit XY _𝜏

𝜋

Pe,SS

𝛾!∗

##

Figure 7.7:Recovery of niobium qubit after laser illumination. a.Qubit excited state population, b. energy decay rate (𝛾

1), andc. decoherence rate (𝛾^∗

2) versus delay,𝑇_𝑑 from a 100 ns long laser pulse (peak power: 85𝜇W, repetition rate: 10 kHz). Gray line indicates a reference measurement with the laser off. Dashed line is an exponential fit indicating a recovery time,𝑇_𝑟. With the laser on, the steady state population (𝑃_{𝑒, 𝑆 𝑆}) and decoherence (𝛾^∗

2, 𝑆 𝑆) is higher than the laser off value (gray line). The right column shows the corresponding pulse sequences used for each measurement.

both repetition rate and laser pulse duration. Our results indicate a trade-off between power, repetition rate, and pulse duration. For a given pulse duration, we can use higher peak laser powers by operating at lower repetition rates.

So far we have been focusing on the qubit population and decoherence at long delays (81𝜇s) from the laser pulse. We also investigate the effect on the qubit decoherence rate when the laser pulse is appliedduringa Ramsey pulse sequence on the qubit.

The pulse sequence for this measurement is shown in the inset of Fig. 7.10. We time the laser pulse to arrive just after the first ^𝜋₂ pulse of the Ramsey sequence and probe the effect of the laser pulse on the decoherence rate of the qubit as a function of peak laser power (Fig.7.10a.) and repetition rate (Fig.7.10b.). Even at a high repetition rate of 50 kHz, we find a range of powers upto a few 𝜇𝑊 where the qubit is able to

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Toff 126 P.

3opulaWion in |e⟩ aW T_d 81 μs fiW

laser off reference range daWa

a.

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PHak powHr (μW) 0.12

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γ* 2,SS (0Hz)

(xcHss dHcohHrHncH aW Td 81 μs fiW

lasHr off rHfHrHncH rangH daWa

b.

Figure 7.8:Dependence of qubit population and decoherence on peak optical power.Dependence of a. steady state excited state population, 𝑃_{𝑒, 𝑆 𝑆} andb. decoherence rate, 𝛾^∗

2, 𝑆 𝑆 of Nb qubit as a function of peak laser power (P). Experimental sequence is repeated at 10 kHz repetition rate.

Horizontal gray regions indicate laser off values up to one standard deviation. Dashed line ina.

is a fit to𝑛_{𝑡 ℎ}(𝛽 𝑃), where𝑛_{𝑡 ℎ}(𝑇) is the Boltzmann distribution assuming a two level system with temperature T. Dashed line inb.is a fit to the expression𝛾_{2, 𝑜 𝑓𝑓} +𝛽 𝑃^𝑛.

10¹ 10²

3ulse duration (ns) 0.00

0.05 0.10 0.15 0.20 0.25 0.30

Pe,SS

Toff 127 P.

fit

laser off reference range data

a. b.

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5HpHtitiRn ratH (kHz) 0.00

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Pe,SS

Toff 127 m.

fit

lasHr Rff rHfHrHncH rangH data

Figure 7.9: Dependence of qubit population on repetition rate and optical pulse duration.

Steady state excited population𝑃_{𝑒, 𝑆 𝑆}as a function ofa. Repetition rate (R) (Peak power = 89𝜇𝑊; pulse duration = 100 ns) andb. Laser pulse duration (D) (Peak power = 9.5 𝜇𝑊; Repetition rate

= 10 kHz). Horizontal gray regions indicate laser off values up to one standard deviation. Dashed line in a. is a fit to a Boltzmann distribution 𝑛_{𝑡 ℎ}(𝑇_{𝑒 𝑓 𝑓}), where 𝑇_{𝑒 𝑓𝑓} (𝑅) = 𝑇_{𝑜 𝑓 𝑓} + 𝛽 𝑅, with 𝛽=16.9±0.34 mK/kHz. Dashed line inb. is a fit to a Boltzmann distribution𝑛_{𝑡 ℎ}(𝑇_{𝑒 𝑓 𝑓}), where 𝑇_{𝑒 𝑓 𝑓} (𝐷)=𝑇_{𝑜 𝑓𝑓} +𝛽 𝐷, with𝛽=0.36±0.0017 mK/ns.

maintain coherence after the laser pulse. There is a trade-off between repetition rate and peak laser power to maintain qubit coherence.

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lasHr Rff 12μW 31μW

10⁰ 10¹ 10²

3Hak powHr (μW) 0.10

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γ* 2 (0Hz)

fiW lasHr off daWa

a. b.

𝜏 𝜋/2 𝜋/2

Readout Laser Qubit XY

Figure 7.10:Ramsey measurement interrupted by a laser pulse.Decoherence rate extracted using a Ramsey sequence interrupted by a laser pulse as a function ofa. Peak laser power (Repetition rate = 50 kHz) andb. Repetition rate. Horizontal gray regions indicate laser off values up to one standard deviation. Inset ofa. shows the pulse sequence used in both measurements. Pulse duration was 100 ns for both measurements. Dashed line ina. is a fit to𝛾^∗

2(𝑃)=𝛾_{2, 𝑜 𝑓𝑓} +𝛽 𝑃^𝑛, where P is peak power. 𝛽=1.42±0.32 kHz/𝜇𝑊^𝑛and𝑛=1.2±0.1.