Quantum Dynamics of Josephson Junction Based Circuits(III)

Quantum dynamics in
nano Josephson junctions
Permanent:
Wiebke Guichard
Olivier Buisson
Frank Hekking
Laurent Lévy
Bernard Pannetier
CNRS – Université Joseph Fourier
Institut Néel- LP2MC
GRENOBLE
Scientific collaborations: PTB Braunschweig ( Germany)
LTL Helsinki (Finland)
Rutgers (USA)
Projects: ANR QUNATJO
PhD:
Thomas Weissl
Etienne Dumur
Ioan Pop
Florent Lecocq
Aurélien Fay
Rapaël Léone
Nicolas Didier
Julien Claudon
Franck Balestro
Post-doc:
Alexey Feofanov
Iulian Matei
Zhihui Peng
Emile Hoskinson
Alex Zazunov

Introduction
Multi-level quantum
system
Two-degrees of
freedom
I
10µm
I b
Multi-degrees of
freedom
New physics…
10µm

Outline
Two-degrees of freedom artificial atom
- inductive dc SQUID
- spectroscopy measurements
- strong non-linear coupling
- coherent oscillations
Multi-degrees of freedom system
- Josephson junction chains
- quantum phase slip
- charging effects

Motivations : two degrees of freedom
Trapped ion NV centers in diamond
Leibfried, Rev.Mod.Phys (2003)
Blatt and Wineland, Nature (2008)
Superconducting artificial atom
with multiple degrees of freedom ?
Jelezko et al, PRL (2004)
High fidelity readout & Electromagnetically Induced Transparency

Modes of oscillations
where

L < L josephson
( b > 1 )
4
Parameter of dimensionality
where
4
L > L josephson
( b < 1 )
6

=3
Dynamics close to a minimum
Expansion in X and Y directions :
s
7

=3
Dynamics close to a minimum
Expansion in X and Y directions :
s
8

=3
Dynamics close to a minimum
Expansion in X and Y directions :
s
9

=3
Dynamics close to a minimum
Expansion in X and Y directions :
s
10

L < L josephson
Claudon, et al , PRL, 2004
Hoskinson and Lecocq , et al , PRL, 2009
Palomaki, et al , PRB, 2010
4
From a phase qubit …
Transverse mode high in energy
Considered in the ground state
1D dynamics
11 1

L > L josephson
4
…to a 2D oscillator
Transverse mode energy decreased
12

Outline
1 Introduction :
1D and 2D dynamics in a dcSQUID
2 Spectroscopic evidence of the transverse mode
and coherent manipulation
3 Using the non linear coupling :
coherent oscillations between internal modes
13

dcSQUID in aluminum
Fabricated by shadow evaporation
without suspended bridges
(Controlled Undercut Technique ) F.
Lecocq, et al , ArXiv 1101.4576v2
F. LECOCQ
Moriond 2011
Experimental Setup
14

Measurement technique :
Switching to the voltage state
Experimental Setup
Nanosecond
flux pulse
Escape = voltage = detection
15

Spectroscopy
Longitudinal mode
Transverse mode

Spectroscopy
Large anti-crossing at
the resonance
between and
Non linear coupling
Also discussed in quantum
optics and ion traps
Bertet et al, PRL (2002)
Vogel and Dematos, PRA (1995)
Strong coupling regime

Coherent oscillations of the two modes
T 1 = 75ns
T 1 = 200ns

Outline
1 Introduction :
1D and 2D dynamics in a dcSQUID
2 Spectroscopic evidence of the transverse mode
and coherent manipulation
3 Using the non linear coupling :
coherent oscillations between internal modes
19

Coherent oscillation between modes
(a)
(b)
Non linear coupling, strong ~700MHz

Coherent oscillation between modes
Coherent exchange of quanta
between the modes
Frequency conversion
back and forth
FFT

A dcSQUID with a large loop inductance
can be describe as two coupled oscillator
Non linear coupling
( exchange of 2 quanta in one mode, 1
quantum in the other)
Conclusion
Artificial atom with
two degrees of freedom…

Quantum dynamics in Josephson junction chains
Single Josephson (SQUID) junction chains
Wiebke Guichard
PhD: I. Pop
Fundamental research:
- collective behavior in multi-degrees of freedom system
- Quantum Phase-Slips
(Mateveev, Larkin, Glazman, PRL2002)
Possible applications: Current standard
New type of qubits topologically protected

ˆ ˆ 2
H E ( Q / e)
d
C
2
d
( / 2)
2
Quantum phase-slip in a single junction
Q, 2ie
Schrödinger equation:
E E
J
cos
EC
EC
Exponentially small
overlap of
E
J
E J slightly larger
than E C
cos
ˆ
0
V=E J cos
8EJ EC
Phase-slip
3 1/
4
rate E J EC
exp 8EJ
/ EC
Gaussian tails
p
/
Gaussian
wave function

E Pot=-E Jcos()
Phase biased Josephson junction chain
N Josephson junctions in series
1 j
N Phase-slip
i
N
i
Phase slip rate in a chain:
j
2
N N
N
N
i1
i
N

E
pot
i
i
NE
N
E
J
“Classical regime”: E J large and E C =0
1 2 N
N J
[ 1cos(
)]
[ 1cos(
/ N)]
i
i1
i
NE J
E()
2N

E
2
i
2
N N
2
j
N N
pot
i
NE
NE
E
J
J
J
“quasi-classical regime ”: E J >>E C
1 2 N
N [ 1cos(
)]
[ 1cos(
/ N)]
[ 1cos((
-2 ) / N)]
i
Phase-slip
i1
NE J
i
E()
2N

1 2 N
N Low energy levels
of the chain:
E
m
EJ
( 2m
)
2N
Critical current of chain:
I
chain
c
“quasi-classical regime ”: E J >>E C
I
N
c
2
Phase-slip
i1
NE J
i
E()
2N

E()
m-1
“Quantum regime”: E J >E C
i1
1 2 N ~/N
q 1
chain
m
q 2
m+1
H
N
/2
i
EJ
2N
m
2mˆ
chain
q N-1
1/
4
E E exp
8E
E
3
N /
J
C
J
(
C
2
m 1
m
m
m 1
)
Matveev et al (2002)

C
Experimental verification of the quantum-phase slip model
in a 6 Josephson junctions chain
Idea:
tune strength of quantum
fluctuations with flux
SQ
J
E E f
J ( f ) cos( )
E E
I
I
Readout
c
SQUID
c
E
SQUID
J
E
c
3
C
330nA
83nA
6 SQUID chain
Read-out junction
Nanofab-facility

I chain ()
I b
Measurement circuit
I c
Statistic of N=10 000 events
Switching event:
I I ( )
b
2 C / 0 /
50%
chain
I SW
I
C
2

R
R
E
E
Measurement of the ground state of the chain
as a function of bias phase
Switching current at 50%
escape probability
SQUID
Readout
J
C
2 K
968
0.
66
3.
87
K
k
I. Pop, et al., Nature Physics (2010)
Good agreement with quantum phase-slip model

Strong quantum fluctuations
Chain with phase-slip amplitude ~0
I. Pop, et al., Nature Physics (2010)
Measuremen
Theory

Conclusion
- Evidence of quantum phase slips
in a short Josephson junction chains
- Current-phase relation: I=I c chain sin(d)
- Ground state well understood
What about excited states?
- Current standard in a chain?
With microwave irradiation
W. Guichard and F. Hekking,
Phys. Rev B (2010)

Conclusion
Superconducting quantum circuits:
- controllable artificial atoms
- model system for quantum experiments
- adjustable circuits parameters to reach:
- qubits
- multilevel system
- 2D properties
- multi-degrees of freedom system
In the future:
- reproduction of well known atomic or quantum optics experiments
- realization of new quantum experiments and phenomena

Projects:
ANR QUNATJO
THANK YOU TO!
Wiebke Guichard, Bernard, Pannetier,
Frank Hekking, Laurent Lévy, Cécile Naud,Ioan Pop,
Iulian Matei, Florent Lecocq, Zihui Peng
and Quantum Coherence group
Cryogénie:
Pierre Chantib, Guillaume Donnier-Valentin,
Christian Gianese, André-Julien Vialle, Anne Gerardin,
Henri Godfrin…
SERAS:
Cyril Bruyère, Olivier Tissot…
Service électronique:
Olivier Exshaw, Maurice Grollier, Jean-Luc Mocellin,
Christophe Gutin, Julien Minet…
Nanofab:
Thierry Fournier, Thierry Crozes, Christophe Lemonias….
Administration:
Nathalie Bourgeat-Lami, Caroline Bartoli, Assya Achour,
Véronique Fauvel, Louise Infuso, Sabine Gadal, Marielle
Lardato, Christine Martinelli,
Martine Lemoine, Jessica Fernandez
and all others I forgot…
Service informatique
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