超伝導量子回路における開放量子系の制御

中村 泰信東京大学先端科学技術研究センター （2012年4月～）

東京大学大学院工学系研究科物理工学専攻（2012年1月～）

東京大学ナノ量子情報エレクトロニクス研究機構

理化学研究所基幹研究所

新研究室＠先端研（東大駒場Ⅱキャンパス）

http://www.qc.rcast.u-tokyo.ac.jp

Acknowledgements

NEC/RIKENOleg AstafievFarruh Abdumalikov

(→ETH Zurich)Yuri Pashkin (→Lancaster Univ.)Fumiki YoshiharaKunihiro InomataToshiyuki MiyazakiTsuyoshi YamamotoPierre BillangeonZhirong LinJawShen Tsai

Collaborators:Kazuki Koshino (Tokyo Medical&Dental Univ.)Satoshi Ishizaka (NEC→Hiroshima Univ.)Hirotaka Terai (NICT)Wei Qiu (NICT)Zhen Wang (NICT)Will Oliver (MIT)Jonas Bylander (MIT)Simon Gustavsson (MIT)Fei Yan (MIT)

Quantum mechanical

system

Environment(bath)

Control(drive)

General picture as non-equilibrium system

Outline

• Superconducting qubits as an artificial atom

• Decoherence and environment

• Qubit as quantum spectrum analyzer

• Microwave quantum optics

• Atoms in cavity

• Atoms in 1D waveguide

Macroscopic quantum coherence

A.J. Leggett, Prog. Theor. Phys. Suppl. 69, 80 (1980); Phys. Scr. T102, 69 (2002).

0

Does quantum mechanics hold in macroscopic systems?

Schrödinger 1935

Superconducting qubits

Artificial two-level system in electric circuits

Coherent control of quantum states in macroscopic systems

Y. Nakamura et al. Nature (1999)

Chiorescu, Nakamura, Harmans, Mooij, Science (2003)

Charge qubit Flux qubit

Superconducting qubit – nonlinear resonator

LC resonator

inductive energy = confinement potentialcharging energy = kinetic energy quantized states

ener

gyJosephson junction resonator

Josephson junction = nonlinear inductor

anharmonicity effective two-level system

Josephson effect

Cooper-pairtunneling

-2e Eel

n=-2 -1 0 1 2 3-1 0 1

E

/

2EJ

Tight-binding model in 1d lattice Bloch band

n

number n phase difference

B. D. Josephson 1962

Superconducting qubits – artificial atoms in electric circuit

small large

Josephson energy EJ = confinement potentialcharging energy EC = kinetic energy quantized states

typical qubit energy

typical experimental temperature

Flux qubitCharge qubit Phase qubit

ener

gy

Superconducting qubits – macroscopic artificial atom in circuits

2 m

charge qubit/NEC flux qubit/Delft

“quantronium”/Saclay phase qubit/NIST/UCSB

~100 m

“transmon”/Yale

“ｆluxonium”/Yale

Decoherence

environment

interaction

qubit

Loss of coherence due to coupling with uncontrolled environment• dissipation• dephasing

tunable tunable

Qubit as a tool for characterization of environment

Possible decoherence sources

phonons?

photons?

magnetic-field noise?

charge fluctuations?

paramagnetic/nuclear spins?

trapped vortices?

charge/Josephson-energy fluctuations?

quasiparticletunneling?

environment circuit modes?

Energy relaxation

relaxation and excitation

for weak perturbation: Fermi’s golden rule

ex. Johnson noise in Ohmic resistor R

spontaneous emissionabsorption

zero-point fluctuation of environment

• qubit energy E01 variable• relaxation S(+E01 ) and excitation S(-E01 ) quantum spectrum analyzer

Dephasing

free evolution of the qubit phase

dephasing

sensitivity of qubit energy to the fluctuations of external parameter

tunable

information of S() at low frequencies

tunablefor Gaussian fluctuations

A long-lived flux qubit

Aluminum 4JJ flux qubit on SiO2/Si

Rabi oscillations

In collaboration with Jonas Bylander, Simon Gustavsson, Fei Yan, Will Oliver (MIT)

Dynamical decoupling pulse sequences

Carr and Purcell, PR 94, 630 (1954); Meiboom and Gill, RSI 29, 688 (1958); Uhrig et al., NJP 10, 083024 (2008)

Recovery of dephasing time

CPMG

Noise spectrum

J. Bylander et al. Nature Phys. 7, 565 (2011)

Decoherence time of superconducting qubits

0.001

0.01

0.1

1

10

100

Dec

oher

ence

tim

e (

s)

2012200820042000

year

T1 T2

~103 ×(gate time)

Atoms

1 m

(a stereotype of) atom Our artificial atom

Circuit quantum electrodymanics (circuit QED)

A. Blais et al. PRA 69, 062320 (2004); A. Wallraff et al. Nature 431, 162 (2004) Yale

Jaynes-Cummings Hamiltonian:

Strong coupling:

g/2~10 MHz (,)/2~1 MHz

…

…

…

|qubit, photon

vacuum Rabi splitting

Single artificial-atom maser

/2 coplanar waveguide resonator

~

• Population inversion generated by current injection

• Capacitive coupling with cavity mode

-2e

Cooper-pair box + voltage biased tunnel junction

-e-e

O. Astafiev et al. Nature 449, 588 (2007)

Photons in transmission line

J. L. O’Brien et al. Nature Photonics 3, 687 (2009) Bristol

Frequency 100-1000 THzWavelength 3 m – 300 nm

Optical fiber, low loss ~0.2 dB/kmPhotonic on-chip circuits, ~0.1 dB/cm

Weak nonlinearity

Frequency 1-10 GHzWavelength 30 cm – 3 cm

Microwave on-chip circuits, ~0.3 dB/km(?)

Strong nonlinearity available

Optics Microwave

coplanar waveguide

Superconducting transmission line

• small dissipation for• 1D transmission mode• Photon life time ~ 100 s, 10 km (?)

microstrip line slot linecoplanar waveguide

distributed element

lumped element

Variety of transmission lines:

Confined photon and flying photon

• in resonator (confined “0D” photon; single-mode)

• through transmission line (flying photon; multi-mode; continuum)

Atom-photon strong coupling

Strong coupling in cavity QED

“Strong coupling” in 1D waveguide

Superconducting qubits coupled to a transmission line

•Superconducting qubits as artificial atoms•Fixed on chip•Strong coupling•Multi levels, selection rules

•Beauty of 1D•Microwave transmission line as 1D channel•Perfect spatial mode matching

•Use of interference•Importance of temporal modes•Limitation with bandwidth

•Spontaneous emission – coherent process

Resonant scattering in 3D space

• Small scattering cross section • Spatial mode mismatch between incident and radiated waves

Resonant scattering in 1D waveguide

Destructive interference of transmitted wave Extinction of transmittance Perfect reflection

Shen and Fan, PRL 95, 213001 (2005) Stanford; Chang et al. PRL 97, 053002 (2006) Harvard

Artificial atom in 1D open space

• Flux qubit coupled to transmission line via kinetic inductance• Strong coupling to 1D mode• Large magnetic dipole moment• Confined transmission/radiation mode Input-output mode matching

• Broadband

~

transmissionreflection

Au

Al

20 m

sourceIsc

1 m

I0

At degeneracy point

Transmission spectroscopy elastic scattering

Strong extinction of transmitted wave

O. Astafiev et al. Science 327, 840 (2010)

Transmission spectroscopy elastic scattering

/2 (MHz)-50 500

|t|2

O. Astafiev et al. Science 327, 840 (2010)

Perfect reflection

0.00.20.40.60.8

-80 -40 0 40 80-0.4-0.20.00.20.4

Re(

r)

Im(r

)

/2 (MHz)

Power dependence saturation of atom

largerprobepower

inputreflection

transmission

Inherent nonlinearity of the two-level atom

Resonance fluorescence: inelastic scatteringdressed state

pump fluorescence

Mollow triplet:

O. Astafiev et al. Science 327, 840 (2010)

Pin (dBm)

Flux qubit as a three-level artificial atom

• Josephson junction qubits = effective two-level system• presence of auxiliary states• large anharmonicity/nonlinearity• selection rule due to symmetry when flux bias =0

|2

|1|0

Spectroscopy of a three-level atom

/0(10-3)

01

/2

(GH

z)

|t|

t/tmin

02 /2

(GH

z)

suppressed excitation due to selection rule

Ladder system at degeneracy point: induced transparency

ladder-typepump

probe

Biased at degeneracy pointTransition 0 2 not allowed

“Electromagnetically-induced transparency”

increasing pump power

A. A. Abdumalikov et al. PRL 104, 193601 (2010)

Ladder system at degeneracy point: induced transparency

Autler-Townes doublet

Transmission of probe signal

dressed statepump

probe

01

/2

(MH

z)

A. A. Abdumalikov et al. PRL 104, 193601 (2010)See also, I.-C. Hoi et al. PRL 107, 073601 (2011) (Chalmers)

R/2 (MHz)

|t|2

R/2 (MHz)

|t|

R/2 (MHz)

01

/2

(MH

z)

Stimulated emission and amplification

pump

stimulated emission

relaxation population inversion

input

amplification

increasing pump power

O. Astafiev et al. PRL 104, 183603 (2010)

Summary

•Superconducting qubits as artificial atoms•Electrical circuits fixed on chip•Gigantic dipole, strong coupling with EM modes•Multiple levels, selection rules•Qubit as quantum spectrum analyzer

•Coupling to 1D channel•Microwave transmission line as 1D channel•Perfect spatial mode matching•Interference between transmitted and scattered fields•Design and control of modes

•Future: quantum-optics tools in microwave domain•Single photon source/detectors•Squeezed state generators•Parametric amplifiers