Measurements of the 1f noise in Josephson Junctions and the implications for qubits Jan Kycia, Chas

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Measurements of the 1/f noise in Josephson
Junctions and the implications for qubits Jan
Kycia, Chas Mugford- University of
WaterlooMichael Mueck- University of Giessen,
GermanyJohn Clarke- University of California,
Berkeley
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The Group
Chas Mugford 1/f noise
Shuchao Meng SQUID-sSET
Lauren Lettress TES sensors
Jeff Quilliam Ho YLiF4
Nat Persaud Liquifier
Jeff Mason SQUID NMR
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dc-SQUID

• The most sensitive magnetometer
• 1 µFo/ (Hz) 1/2

Ib
Io
Io
V
L
Lin
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Resistively and Capacitively Shunted Junction
Model
IS Ico sin (?), d?
2eV dt h

?h D(0) (2e)2 RN
EJ
Tilt ? I position ? ? velocity ? V One
period Fo
Tilted washboard model is the mechanical analog,
with a particle of mass C, moving along
an axis, ?, in a potential, U(?) -Icocos ? -
I?, with a viscous drag force, .
h d? 2eR dt
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J
The DC SQUID
I
J
I/2 J
I/2 -J
F
V
F/Fo
1
2
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A flux locked loop using a high frequency flux
modulation is used to provide a flux to voltage
converter with fixed gain and large dynamic
range.
V
dV
F/Fo
1
2
dF
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Magnified Image of DC SQUID
dc SQUID
2x2µm Junctions
Input coil
Shunts provide required dissipation but also
produce noise.
Palladium Shunt resistor
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SQUID as a near-quantum-limited amplifier at 0.5
GHz M. Mueck, J. B. Kycia, and John Clarke, APL
78, 967 (2001).
Find Self Heating at low temperatures
Loss of temperature dependence, at low
temperatures, is frequency independent
Wellstood et al found that self heating can be
reduced by adding a cooling pad to the shunt
resistor.
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The Hamiltonian, H -EJcos?1 -EJcos?2
Ec(Q/e)2
if EJ / EC gt 1, ? is a good quantum number, Q
fluctuates. if EJ / EC lt 1, ? fluctuates, Q
is a good quantum number.
Phase fluctuations allow the particle to diffuse
down the washboard d ? d t
? 0 ? V ? 0
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Transport Measurement Circuit with filters
Screened room
Lock-in reference input.
.
AC bias ? 0.1 nA
x100
.
.
x1000
Copper powder filters
LC? filters
300 K
RC? filters
4.2 K
Cu filters
Follow design of Martinis, Devoret,
Clarke, Phys. Rev. B, 35, 4682 (1987).
Cu filters
20 mK
Sample
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Temperature and dissipation dependence of sSET
RK Rg

• dissipation, g

g T2
G ohmic G transmission
line
(Ingold, Grabert PRL 1999)
g1/3 T5/3
(Wilhelm, Schön, and Zimanyi)
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New configuration Provides in situ control of EJ
, Ec , g and T.
H -EJ(f)cos?1 -EJ (f) cos?2 Ec(Q/e)2
H(R2deg)
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1 ?m
SEM image courtesy of Dan Grupp.
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Rimberg, Ho, Kurdak, Clarke PRL 1997
Wagenblast, Otterlo, Schon, Zimanyi PRL 1997
Good review Leggett, Chakravarty, Dorsey,
Fisher, Garg, Zwerger Rev Mod Phys (1987).
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Superconducting Qubits

• Charge based qubits Cooper pair box
• Demonstrated Rabi oscillation Nakamura et al,
  Nature 398, 786 (1999).
• Improved read out scheme, decoherence time 0.5
  ms (Q 25,000)
• Vion et al, Science 296, 886 (2002).
• Flux based qubits
• Demonstrated energy splitting dependence on
  applied magnetic flux
• Friedman et al, Nature 406 43 (2000), van der Wal
  et al, Science 290,
• 773 (2000).Coherent Oscillations observed with a
  dephasing time of
• 20 ns and a Relaxation time of 900 ns Chiorescu
  et al, Science 299,
• 1869 (2003).
• Phase based qubits
• Exhibited Rabi oscillations between ground state
  and 1st excited state of a current
• biased Josephson junction in its zero-voltage
  regime Yu et al,
• Science 296, 889 (2002), Martinis et al PRL 89,
  117901 (2002).

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Sources of Decoherence

• External flux noise
• Nyquist noise currents in nearby metal objects
• Noise in the measurement scheme
• Motion of trapped charge
• 1/f flicker noise in the critical current of
  the Josephson Junction

• The goal of our experiment is to measure the
  level of 1/f noise in the critical current of a
  resistively shunted Josephson Junction.
• Once the measurement is made, we can
• Measure the temperature, time, material, and
  fabrication parameter dependence of the 1/f noise
  level.
• Estimate the upper limit of the coherence time of
  superconducting qubits due to these noise
  sources.
• Make optimal qubits by selecting the device
  configuration to minimize the noise sources.

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Flux Qubit
Chiorescu et al, Science 299, 1869 (2003).
van der Wal et al, Science 290, 773 (2000).

• Small loop with three Josephson junctions
  produces the flux qubit.
• - Hysteretic DC SQUID is used to read the flux
  state.

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Ramsey Fringes in Flux Qubit
I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and
J.E. Mooij, Science 299, 1869 (2003).
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Quantronium
D. Vion, A. Aassime, A. Cottet, P. Joyez, H.
Pothier, C. Urbina, D. Esteve, M. H. Devoret,
Manipulating the Quantum State of an Electrical
Circuit, SCIENCE, 296, 886 (2002).
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Phase Qubit
Decoherence in Josephson Phase Qubits from
Junction Resonators Simmonds, Lang, Hite, Nam,
Pappas, and Martinis, Phys Rev Lett, 93,
077003-1, (2004).
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Resonances Observed -- likely due to defects
(fluctuators)
Decoherence in Josephson Phase Qubits from
Junction Resonators Simmonds, Lang, Hite, Nam,
Pappas, and Martinis, Phys Rev Lett, 93,
077003-1, (2004).
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1/f Noise Dutta-Horn Model Dutta and
Horn, Rev Mod Phys, 53, 497 (1981)Random
telegraph signal is produced by random
transitions between the states of a double
potential well. Define 1/t1 and 1/t2 as the
probability of a transition from state 1 to 2 and
2 to 1 respectively. If 1/t 1/t1 1/t2 then
the power spectrum is a Lorentzian of the
formS(f) ? t / 1(2pft)2If the transitions
are thermally activated then the characteristic
time is given by ti toexp(Ui/kBT), where 1/to
is an attempt frequency.S(f,T) is linear in T
because the kernel moves through the distribution
of RTSs as the temperature varies, selecting
only those processes that have characteristic
frequencies in the window of interest.
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Mechanism Behind 1/ Critical Current
Fluctuations in Josephson Junctions The currently
accepted picture of the mechanism behind critical
current fluctuations involves traps within a
Josephson junction. An electron is trapped in
the tunnel barrier and is subsequently
released. While trapped, the barrier height and
hence critical current is modified temporarily.
For a junction of area A the change in critical
current is modified by the change in area due to
an electron ?A. ?Ic(?A/A)Ic
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Dephasing due to current fluctuations and
critical current fluctuations Critical current
fluctuations with a l/f spectral density are
potentially a limiting source of intrinsic
decoherence in superconducting qubits..
W the frequency of oscillation between the
0.5Fo and 0.5Fo state.
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Dale Van Harlingen et al, PRB (2004).
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Methods of Measuring 1/ Noise of the Critical
Current of a Josephson Junction

• Critical current fluctuations have been measured
  in the non-zero voltage state.
• Is the 1/f noise the same when the junction is in
  the zero voltage state? We measured the critical
  current fluctuations using the same SQUID
  operated as an RF SQUID in the dispersive regime.
  

F.C.Wellstood, PhD thesis, University of
California, Berkeley 1988. B.Savo,
F.C.Wellstood,, and J.Clarke, APL 49, 593
(1986). V.Foglietti et al., APL, 49, 1393
(1986) R.H.Koch, D.J. van Harlingen, and
J.Clarke, APL, 41, 197 (1982). F.C. Wellstood, C.
Urbina, John Clarke, APL, 5296, 85 (2004).
Fred Wellstoods Thesis Berkeley
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Comparing different junctionsInvariant noise
parameter
Normalize current noise spectrum to the critical
current Choose T 4.2K and 1Hz.
But this does not take into account junction
area. For a junction of area A and if the area
blocked by a single trap is DA, then change in
critical current for a single fluctuator is DIc
(DA /A)Ic If n is the number of traps per area,
then the critical current spectrum should scale
as SI2 n A (DA /A)2Ic2 n DA2 (Ic2
/A) Van Harlingen et al found that all values of
n DA2 remarkably similar for all measured
junctions. SI2 scales as (Ic2 /A)
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Scaled quantity invariant quantity (van Harlingen
et al. PRB 2004)
Wellstood et al. average value of 6
junctions 26
Lukens et al. IEEE 2005 Also see slower than
linear T dependence
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Measuring 1/ Noise Due to Critical Current
Fluctuations in the Non-Zero Voltage State
DC SQUID and read-out SQUID circuit

• The sample SQUID is voltage biases.
• The readout SQUID measured the current running
  though the 2W resistor.
• Fluctuation in the critical current leads to a
  redistribution of the currents
• flowing through the junction and the resistor.

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rf tight - low field -superconducting sample
container
rf tight SMA connectors
Readout SQUID
Sample SQUID
Superconducting lead shield
rf tight copper sample container
Coaxial µ-metal shields
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1/f noise in DC biased junction
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Applying Current Bias Reversal DC current bias
method
Current bias reversal eliminates 1/f noise,
therefore this 1/f noise is not due to flux
noise.
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Critical current fluctuations due to a single
fluctuator
Ic 2.5uA
DIc 0.65nA
This corresponds to a trap radius of 5.6nm
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Reading out an rf SQUID in the Dispersive Regime
rf SQUID and FET amplifier circuit

• A tank circuit is driven off-resonance with a
  360-MHz current of fixed amplitude.
• - The tank circuit voltage is read out with a low
  noise amplifier cooled to 4.2K.
• Fluctuations in the critical currents of the two
  junctions modulate the SQUID
• inductance and thus the resonant frequency of
  the tank circuit.

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Comparing the zero-voltage noise measurement
method to the non-zero voltage noise measurement
method

• No difference between the measurements.
• The 1/f noise is temperature dependent.

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Annealing Study
Annealing lowers critical current and lowers
noise
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Comparison of Noise Parameter
Best Sample
Van Harlingen et al. 12 Wellstood et al.
26 Lukens et al. 1.5
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Conclusion We have demonstrated that the l/f
noise in a dc SQUID due to critical current
fluctuations has the same magnitude in the zero
voltage and non-zero voltage regime. Thus, the
levels of critical current l/f noise measured by
others in the nonzero voltage state should
pertain to qubits operated at zero voltage.
Measured noise of different junctions, reduce
1/f noise. Future Experiments Temperature
dependence of 1/f noise down to dilution
refrigerator temperatures. The dispersive method
has no dissipation - best for low temperatures.
We can cut away the shunt resistors to see if
they are somehow responsible for noise. Continue
varying processing parameters. Study dissipation
is submicron Josephson junction.
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New Device will allow the in situ control of EJ,
EC, and dissipation.
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Temperature and dissipation dependence of sSET
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Outline

• Describe how Josephson Junctions and SQUIDS
  work.
• Describe how superconducting qubits work.
• Explain why 1/f noise is relevant to
  superconducting
• qubits.
• - Present results on 1/f noise measurements.

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Tunable coupling via curent
B.L.T. Plourde, J. Zhang, K.B. Whaley, F.K.W.,
T.L. Robertson, T. Hime, S. Linzen, P.A.
Reichardt, C.E. Wu, and J. Clarke PRB 70,
140501(R) (2004).
Bias current
Screening current

• Extra flux at constant bias
• directly increases screening
• increases ? ? indirectly reduces screening

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rf SQUID
Two kinds of behaviour are observed in rf SQUID
loops depending of the SQUID hysteresis
parameter ?rf. The difference is seen in the
applied flux ?e vs the flux threading the loop ?.
1
?rf lt1
0
-1
0
1
?rf gt1
1
R
IS
0
F
L
-1
F
e
0
1
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Critical current fluctuations may be a major
source of intrinsic decoherence of qubits made
from Josephson junctions. We have measured the
1/f noise due to critical current fluctuations in
macroscopic ( area ? 2 ? 2 ?m2 ) Josephson
junctions. We have exploited two ways for
measuring critical current fluctuations, one way
where we directly measure changes in the critical
current of a voltage biased junction, and a
second way in which we measure 1/f flux noise in
an rf SQUID running in the dispersive mode. With
both methods, we find the magnitude of the
critical current fluctuations, at a temperature
of 4.2K, to be ?Ic/Ic ? 10-5 at a frequency of 1
Hz.
Abstract
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The Bloch sphere
Convenient representation of the two-state
Hamiltonian and state
Beff
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Tank Circuit Coupled to Josephson Inductance
Using the Josephson relations
A Josephson element can be described as a
nonlinear inductor by deriving the relationship
Where
When a junction is inserted into a
superconducting loop its behaviour affects the
total inductance of the loop.
The effective inductance of a SQUID can be
approximated by
The flux threading the loop is
and the circulating supercurrent
Combining these three it follows that
Coupling a SQUID loop to a inductor of a tank
circuit yields an effective tank circuit
resonance modified by the SQUID loop for ?rfltlt1
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The flux qubit
?
f
Evidence for superposition of macroscopic
states
C.H. van der Wal, A.C.J. ter Haar, F.K.W., R.N.
Schouten, C.J.P.M. Harmans, T.P. Orlando, J.E.
Mooij, Science 290, 773 (2000).
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Measuring 1/ Noise Due to Critical Current
Fluctuations in the Zero Voltage StateUsing an
rf SQUID in Dispersive Mode
Applying an external flux gives rise to a
circulating current which in turn modifies the
inductance of the junctions. Fluctuations in the
critical current Ic appear as equivalent to flux
noise. Operating the SQUID in the dispersive
regime means that the screening current imposed
by an applied flux is always smaller than the
critical current Ic of a junction.
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Critical Current Noise Specific Measurement
Techniques The spectral density components of low
frequency SQUID noise are represented by.
S?(f) flux noise due to motion of flux
vortices. SI(f) critical current noise
in-phase fluctuations are represented by the
second term and the out-of-phase component is
represented by the third. AC flux modulation with
lock-in detection rejects only the in-phase
component of the critical current noise,
furthermore it does not affect noise due to flux
motion. Reverse bias scheme will eliminate
out-of-phase fluctuations in the critical current
but does not affect out-of-phase fluctuations due
to flux motion. Thus ac modulation with reverse
bias will eliminate in-phase and out-of-phase
fluctuation due to critical current fluctuations.
Therefore if excess noise due to motion of flux
vortices exists, the out-of-phase component will
still be observed
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• Lab at Waterloo
• Dilution refrigerator (Base temperature 12 mK)
• e-beam lithography (for fabrications of
  sub-micron devices)
• Optical lithography (for fabrications of large
  number
• of micron
  scale multi-layered devices)
• Measurement electronics (low noise environment,
  low 1/f noise)

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Conclusion of sSET work