Noise properties of a Josephson parametric oscillator Gopika Lakshmi Bhai1 2Hiroto Mukai1 2Tsuyoshi Yamamoto3 4and Jaw-Shen Tsai1 2 3y 1Graduate School of Science Tokyo University of Science

2025-05-02 0 0 4.37MB 7 页 10玖币

侵权投诉

Noise properties of a Josephson parametric oscillator

Gopika Lakshmi Bhai,1, 2, ∗Hiroto Mukai,1, 2 Tsuyoshi Yamamoto,3, 4 and Jaw-Shen Tsai1, 2, 3, †

1Graduate School of Science, Tokyo University of Science,

1–3 Kagurazaka, Shinjuku, Tokyo 162–0825, Japan

2RIKEN Center for Quantum Computing (RQC), 2–1 Hirosawa, Wako, Saitama 351–0198, Japan

3Research Institute for Science and Technology, Tokyo University of Science,

1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

4Secure System Platform Research Laboratories, NEC Corporation, Kawasaki, Kanagawa 211-0011, Japan

(Dated: January 19, 2023)

We perform the noise spectroscopy of a Josephson parametric oscillator (JPO) by implementing

a microwave homodyne interferometric measurement scheme. We observe the ﬂuctuations in the

self-oscillating output ﬁeld of the JPO for a long 10 s time interval in a single shot measurement and

characterize the phase and amplitude noise. Furthermore, we investigate the eﬀects of the pump

strength on the output noise power spectra of the JPO. We found strong ﬂuctuations in the phase

with a 1/f2characteristics in the phase noise power spectrum, which is suppressed by increasing

the pump strength.

I. INTRODUCTION

The study of noise in physical systems has a long his-

tory [1]. The measurement and performance aspects of

the physical systems have long been considered to be lim-

ited by the noise [2–5]. Various studies have been done

extensively to understand the noise sources and the pos-

sibility of evading the noise [6–11]. However, evading the

intrinsic noise of a physical system is highly challenging

and is a fundamental limitation [12–14]. Recently, sev-

eral advances have led to a renewed interest in the char-

acterization and mitigation of noise in the ﬁeld of circuit

quantum electrodynamics (c-QED) [11, 15–17] — one of

the most promising candidates in quantum computing

and quantum information processing [18–20]. The ongo-

ing quest to build a quantum computer has intensiﬁed

the eﬀorts to study the noise in qubits [11, 15, 16] — the

basic building block of a quantum computer. However,

the noise properties of other essential components used

for the readout of the qubit, such as Josephson paramet-

ric ampliﬁer (JPA) or JPO, are rarely explored.

A typical c-QED measurement network operates at fre-

quencies of a few GHz and a temperature of around 10

mK. Quantum devices such as qubits are commonly read

out at a few photon regimes to protect from measure-

ment backaction [11, 21, 22]. Low noise ampliﬁcation

of the signal is a practical need to detect weak photons

from the quantum devices operating in the microwave

regime. JPA, a typical parametric device consisting of

a superconducting resonator integrated with Josephson

elements [23–27] overcomes this obstacle by eﬀectively

amplifying the signal by adding a minimum noise allowed

by the fundamental law of quantum mechanics [14, 28].

These devices have become an essential component of

the readout chain since they attain the quantum-limited

∗gopika.lakshmibhai@gmail.com

†tsai@riken.jp

ampliﬁcation by high-frequency modulation of the induc-

tance of the nonlinear Josephson element [26, 29, 30].

When the modulation amplitude exceeds the instabil-

ity threshold, self-sustained oscillations start to build

up [31], and it works as an oscillator — Josephson para-

metric oscillator [32–34]. Due to the new accessible pa-

rameter regimes as a consequence of the strong nonlin-

ear properties of JPO, notable studies have been done

demonstrating the generation of squeezed states [35, 36],

two-mode entanglement [36], cat state engineering [37–

40], high-ﬁdelity qubit readout [32, 33, 41], etc. Nonethe-

less, the study of the noise properties of the JPO is left

unaddressed.

JPOs, like any other oscillators, have ubiquitous

noise properties, which gives rise to a ﬁnite oscillation

linewidth typically ranging from a few kHz to Hz de-

pending on the operating parameters [34, 42–45]. Sev-

eral unifying theories explain the noise characteristics of

an oscillator [46–48]. Over the last few decades, various

experimental and theoretical studies in the optical do-

main have investigated the noise properties of parametric

oscillators and lasers extensively [49–53]. Noise spectro-

scopic studies in the optics ﬁeld show the limiting factor

of the ﬁnite linewidth of lasers [13, 54] described by the

celebrated work of Schawlow-Townes [55]. These theories

and experimental observations shed light on investigat-

ing the noise properties of the JPO in superconducting

circuit systems, where a detailed study of the noise prop-

erties of the JPO is yet to be investigated.

In this work, we present the experimental study of

the noise characterization of a JPO pumped above its

parametric threshold, where the phase coherence of the

output photons from the oscillator is investigated. We

perform the spectral analysis of noise in the phase and

amplitude quadrature at low frequencies and explore the

possible noise sources in JPO.

arXiv:2210.15116v2 [quant-ph] 17 Jan 2023

II. EXPERIMENTAL SETUP

Our device consists of a λ/4 resonator made with

a segment of coplanar waveguide (CPW) terminated

by a dc superconducting quantum interference device

(SQUID) [26]. The CPW resonator is fabricated by etch-

ing out the sputtered niobium on a silicon wafer [56].

The Josephson junctions are then made by standard

double-angle shadow evaporation of aluminum [Fig. 1(b,

c)]. The presence of the SQUID makes the reso-

nance frequency of the resonator tunable by a vari-

able Josephson inductance LJwhich follows a relation

LJ= Φ0/(4πIc|cos (πΦdc/Φ0)|). Here, Icis the criti-

cal current through the junction, Φdc is the dc magnetic

ﬂux through the SQUID, and Φ0is the ﬂux quantum.

By changing the ﬂux through the dc-SQUID Φdc, the

Josephson inductance can be varied.

An input signal and a pump signal are applied to the

device through the attenuated lines with ﬁlters to the

respective ports on the chip. On-chip dc bias is applied

through the same pump line using a bias-tee. The mea-

surements of the device are carried out in a cryogenic

environment using a dilution refrigerator at the base tem-

perature of 10 mK [Fig. 1(a)]. The output signal from

the device is routed through a microwave ﬁlter, circula-

tor, and isolator, which is ampliﬁed using a high-electron-

mobility transistor (HEMT) at 4K. The output signal is

then further ampliﬁed at room temperature using R.T

ampliﬁers.

At ﬁrst, we characterize the system dynamics by scan-

ning the resonator frequency dependence on the applied

magnetic ﬂux using a dc source. A weak probe signal is

coupled to the cavity through a circulator in the mix-

ing chamber, and the output from the device is ana-

lyzed using a vector network analyzer (VNA) by mea-

suring the complex reﬂection coeﬃcient S11. The bare

resonator frequency in the absence of ﬂux was found to

be ωr0/2π= 6.239 GHz. The estimated critical current

for each Josephson junction is 1.89 µA which is obtained

from ﬁtting the resonator spectrum. The external and

internal cavity loss are found to be κext/2π= 11 MHz

and κint/2π= 0.3 MHz at a ﬂux bias of Φdc/Φ0= 0.35

with a resonance frequency of ωr/2π= 5.94 GHz. To fur-

ther characterize the operational properties of the JPA,

we apply a pump signal with a frequency ωp≈2ωrwhere

ωris the resonator frequency at a speciﬁc ﬂux point. The

pump photons interact with the incoming signal photons

and generate an ampliﬁed signal with an approximate

gain of 20 dB at pump power, Pp=−63.4 dBm.

To investigate the photon generation, we apply the

pump signal at twice the resonance frequency in the ab-

sence of the input signal and examine the output from

the JPA by increasing the pump power Pp. As the

pump power increases beyond the parametric instabil-

ity threshold, self-sustained oscillations build up expo-

nentially in time inside the cavity. This can be under-

stood as a second-order phase transition from a ground

state below the threshold to an excited state above the

HEMT/ R.T.amps

Isolator

Circulator

LPF

BiasTee

Attenuator

100 mK

800 mK

4 K

50 K

Output InputDC biasPump

JPO chip

300 K

20 dB

10 dB

10 dB 0 dB

6 dB

10 dB

0 dB

20 dB

10 dB 6 dB

10 dB 20 dB

20 dB

(a)

10 mK

(b) (c)

ωs

x 2

JPO

att

HPF

BPF

ADC

I(t)

Q(t)

(d)

doubler phase

shifter

Cryostat

pump line

dc-SQUID

50 μm500 nm

2ωsωs

~1.6 GHz

~12 GHz

(8.4 -13

GHz)

(4.9 - 6.2

GHz)

FIG. 1. (a) Schematic illustration of the cryogenic microwave

measurement setup. (b) Scanning electron microscope (SEM)

image showing SQUID consisting of two parallelly connected

Josephson junctions. The SQUID made of aluminum is gal-

vanically coupled to the central conductor of the CPW pat-

terned on a niobium ﬁlm which is deposited on a silicon sub-

strate through sputtering. There are ground plane holes to

pin the trapped ﬂux on the chip. (c) SEM image showing

Josephson junction made of Al/AlOx/Al. (d) Microwave in-

terferometric setup to measure the phase noise of the JPO:

input lines are color-coded with the cryogenic circuit lines in

Fig. 1(a), which describes the signal ﬂow.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

NoisepropertiesofaJosephsonparametricoscillatorGopikaLakshmiBhai,1,2,HirotoMukai,1,2TsuyoshiYamamoto,3,4andJaw-ShenTsai1,2,3,y1GraduateSchoolofScience,TokyoUniversityofScience,1{3Kagurazaka,Shinjuku,Tokyo162{0825,Japan2RIKENCenterforQuantumComputing(RQC),2{1Hirosawa,Wako,Saitama351{0198,Japan3Resea...

展开>> 收起<<

Noise properties of a Josephson parametric oscillator Gopika Lakshmi Bhai1 2Hiroto Mukai1 2Tsuyoshi Yamamoto3 4and Jaw-Shen Tsai1 2 3y 1Graduate School of Science Tokyo University of Science.pdf

共7页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Noise properties of a Josephson parametric oscillator Gopika Lakshmi Bhai1 2Hiroto Mukai1 2Tsuyoshi Yamamoto3 4and Jaw-Shen Tsai1 2 3y 1Graduate School of Science Tokyo University of Science

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: