QIC 890/891, Module 4: Microwave Parametric Amplification in Superconducting Qubit Readout experiments

Transcription

1 QIC 890/891, Module 4: Microwave Parametric Amplification in Superconducting Qubit Readout experiments 1 Instructor: Daryoush Shiri Postdoctoral fellow, IQC IQC, June 2015, WEEK-2

2 2 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

3 3 Josephson Junction REF: Quantum computing : from linear algebra to physical realizations, Nakahara, Mikio. Ohmi, Tetsuo, Boca Raton : CRC Press 2008.

4 4 DC-SQUID I. Siddiqi, UC-Berkeley Boundary Condition Φ ext = external flux Φ 0 = h/2e =2.07x10-15 Weber

5 Josephson PA 5 T. Yamamoto, et al, Applied Physics Letters 93, (2008). Recall Negative Resistance Amplifier (REFLECTIVE MODE) Г f signal = 10 GHz f pump = 20 GHz Gain = 17 db, BW = 20 MHz Noise temperature (T N )= 0.87 K

6 Josephson PA I. Siddiqi, UC-Berkeley Recall this experiment

7 Recent Advances 7 PUMPISTOR (Per Delsing, TU Chalmers) Wideband PA (Martinis group, UCSB) using PUMPISTOR

8 8 PUMPISTOR: Mixes flux and phase terms.

9 9 Pumpistor Sundqvist, et al, Appl. Phys. Lett. 103, (2013). In addition to the standard nolinear inductance (LJ), there is another TUNABLE component. Tuable by pump-signal phase difference.

10 10 IMPA (IMpedance transformed PA) Mutus, et al, Appl. Phys. Lett. 104, (2014) Recall GAIN & BW trade off, how to circumvent this?

11 11 Josephson-based Travelling Wave PA 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

12 12 Vacuum (thermal noise) squeezing Refer 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. S 22 S 21

13 Quantum Feedback using PA 13 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. Rob Schoelkopf s group, Yale University R. Vijay, et al, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, NATURE, VOL 490, 4 OCTOBER 2012.

14 Quantum Feedback 14 Refer to the handwritten notes for details.

15 15 PPLO: Parametric Phase Locked Oscillator (Parametron) 1- Proposed by John von Neumann, US patent No.2,815,488, IBM, Eiichi Goto (University of Tokyo), The parametron, a digital computing element which utilizes parametric oscillation. Proc. IRE. 47, (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. Ferrite core type VARACTOR type D. SHIRI, DQMLab, IQC REF: Onyshkevych, L. S., Kosonocky, W. F. & Lo, A. W. Parametric phaselocked oscillator characteristics and applications to digital systems. Trans. IRE. EC-8, (1959).

16 16 Parametron 1- Assume that the tank inductor is being modulated by ω pump =2ω. 2- Then the output voltage has a sinωt component proportional to ωгi s L 0 3- 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).

17 17 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: /ncomms5480 (2014).

18 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 (T 1 = 690 nsec), during (t d ) 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 19 Dispersive Reading D. SHIRI, DQMLab, IQC

20 20 Dispersive Reading D. SHIRI, DQMLab, IQC

21 21 D. SHIRI, DQMLab, IQC

22 22 Reading microwave scattering (S) parameter (i.e. S 21 ) to find the Qubit state D. SHIRI, DQMLab, IQC

23 23 Reading Scattering (S) parameter (S 21 ) REF: Pozar, David M. Microwave engineering, 4th ed.

24 24 AC Stark Effect Refer to Quantum feedback using PA slides. This is where the change of cavity frequency with the number of photons can be seen. D. SHIRI, DQMLab, IQC