QIC 890/891, Module 4:

Microwave Parametric Amplification in

Superconducting Qubit Readout experiments

Instructor: Daryoush Shiri

Postdoctoral fellow, IQC

IQC, June 2015, WEEK-2

1

Parametric Amplifiers with Superconducting

Circuits Since 1979 people started to look at SQUIDS (Superconducting

QUantum Interference Device)

Based on Josephson Junctions (S-I-S sandwich) Provides

nonlinear/tunable Inductance

Ultra Low Noise Amplification is a must in Superconducting Qubit

Experiments

Qubit read out

Quantum feedback

Vacuum squeezing

Generating entanglement

Back-action evasion

2

3 Josephson Junction

REF: Quantum computing : from linear algebra to physical realizations, Nakahara, Mikio. Ohmi, Tetsuo, 1942-Boca Raton : CRC Press 2008.

4 DC-SQUID

Boundary Condition

Φext = external flux

Φ0 = h/2e =2.07x10-15 Weber

I. Siddiqi, UC-Berkeley

Josephson PA

5 T. Yamamoto, et al, Applied Physics Letters 93, 042510 (2008).

Recall “Negative Resistance Amplifier” (REFLECTIVE MODE)

fsignal = 10 GHz

fpump = 20 GHz

Gain = 17 dB, BW = 20 MHz

Noise temperature (TN)= 0.87 K

|Г|

90-90I. Siddiqi, UC-Berkeley

Josephson PA

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Recall this experiment

Recent Advances7 PUMPISTOR (Per Delsing, TU Chalmers)

Wideband PA (Martinis’ group, UCSB) using PUMPISTOR

8PUMPISTOR: Mixes flux and phase terms.

Pumpistor Sundqvist, et al, Appl. Phys. Lett. 103, 102603 (2013).

In addition to the standard nolinear inductance

(LJ), there is another TUNABLE component.

Tuable by pump-signal phase difference.

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IMPA (IMpedance transformed PA) Mutus, et al, Appl. Phys. Lett. 104, 263513 (2014)

Recall GAIN & BW trade off, how to circumvent this ?

Josephson-based Travelling Wave PA11

Implementation of Kerr nonlinearity. The group velocity depends on the amplitude of

the field because L depends on the phase (voltage) on each SQUID. As if the

refractive index(n) is intensity (Electric Field) dependent.

Amplification and squeezing of quantum noise with a tunable Josephson

metamaterial, M. A. CASTELLANOS-BELTRAN, et al, nature physics, 4, 928, Dec 2008

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S22

S21

Vacuum (thermal noise) squeezingRefer to the handwritten notes.

Applications:

generation of entangle photons

Phase measurement using homodyne detections

See Figure (a) where the in-phase (quadrature) component

of input noise is amplified (de-amplified) which results in

squeezing.

Quantum Feedback using PA

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R. Vijay, et al, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, NATURE, VOL 490, 4 OCTOBER 2012.

Rob Schoelkopf’s group, Yale University

Preserving the RABI oscillation by implementing

The classical Phase Locked Loop (PLL) idea.

See section (b): How PA amplifies one

quadrature of the QUBIT.

Amplitude of Q which is oscillating by Rabi

frequency is compared with 3MHz reference.

Refer to the handwritten notes for details.

Quantum Feedback …

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Refer to the handwritten notes for details.

D. SHIRI, DQMLab, IQC

15 PPLO: Parametric Phase Locked Oscillator (Parametron)

1- Proposed by John von Neumann, US patent No.2,815,488, IBM, 1957.

2- Eiichi Goto (University of Tokyo), “The parametron, a digital computing

element which utilizes parametric oscillation”. Proc. IRE. 47, 1304–1316 (1959).

3- The circuit has TWO states with 180 degree phase difference.4- Initial condition (e.g. noise) or input signal PHASE determines to which stable

state the oscillator should lock. It is ANALOG implementation of a DIGITAL

memory cell.

REF: Onyshkevych, L. S., Kosonocky, W. F. & Lo, A. W. Parametric phase-

locked oscillator–characteristics and applications to digital systems. Trans.

IRE. EC-8, 277–286 (1959).

VARACTOR type

Ferrite core type

16 Parametron

1- Assume that the tank inductor is being modulated by ωpump =2ω.

2- Then the output voltage has a sinωt component proportional to –ωГIsL03- As is a negative resistance is generate i.e. the sinusoidal part of the input signal gets amplified until it saturates by the nonlinearity of ferrite core (Self sustained sinωt

oscillation). See (B) and (C).

PPLO (parametron)

Lin, Z. R. et al. Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting

qubits. Nat. Commun. 5:4480 doi: 10.1038/ncomms5480 (2014).

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D. SHIRI, DQMLab, IQC

18 Steered oscillation by locking signal

Nr = 5.5 is large enough to avoid non-locking error,

Small enough to avoid readout back action.

Latching property:

Even after qubit has decayed (T1 = 690 nsec), during (td) the

mapped information (phase of PPLO) is still available.

Combined advantage of both linear and nonlinear

resonators.

Fast, latching type, single-shot readout.

D. SHIRI, DQMLab, IQC

19 Dispersive Reading

Dispersive Reading

D. SHIRI, DQMLab, IQC

20

D. SHIRI, DQMLab, IQC

21

D. SHIRI, DQMLab, IQC

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Reading microwave scattering (S) parameter (i.e. S21) to find the Qubit state

23 Reading Scattering (S) parameter (S21)

REF: Pozar, David M. Microwave engineering, 4th ed.

D. SHIRI, DQMLab, IQC

24

AC Stark EffectRefer to “Quantum feedback using PA” slides.

This is where the change of cavity

frequency with the number

of photons can be seen.