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### Sources of Decoherence:

### Outline

Measurements of the 1/f noise in Josephson Junctions and the implications for qubitsJan Kycia, Chas Mugford- University of WaterlooMichael Mueck- University of Giessen, GermanyJohn Clarke- University of California, Berkeley

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

Oxide barrier

Superconductor, 1

2

2

IC

The superconducting order parameters are:

The phase difference between the superconductors is = 2 - 1.

As the two superconductors are brought closer together, allowing electrons to tunnel, the phases start to interact.

Josephson (1962) predicted a phase dependent energy = -EJ cos,

where EJ = = . ,

1 = |1(x)| ei1 , 2 = |2| ei2

hIco h D(0)

2e (2e)2 RN

d2eV

dt h

=

IS = Ico sin (),

Resistively and Capacitively Shunted Junction Model

EJ

VdV

R dt

I = Icosin + + C

C

h d

2e dt

Use V = ,

R

hC d2 h d

2e dt2 2eR dt

+ + Ico sin = I

IS = Ico sin (),

d2eV

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

Ib

Io

Io

V

L

Lin

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

dc SQUID

2x2µm Junctions

Input coil

Shunts provide

required dissipation

but also produce noise.

Palladium Shunt resistor

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.

H = -EJcos1-EJcos2 + Ec(Q/e)2

if EJ / EC > 1, is a good quantum number,

Q fluctuates.

if EJ / EC < 1, fluctuates,

Q is a good quantum number.

Phase fluctuations allow

the particle to diffuse down

the washboard;

d

d t

0 V 0

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

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)

Provides in situ control of EJ , Ec ,g and T.

H = -EJ(f)cos1-EJ (f)cos2 + Ec(Q/e)2 + H(R2deg)

PRL 1997

Wagenblast, Otterlo, Schon, Zimanyi

PRL 1997

Good review: Leggett, Chakravarty, Dorsey, Fisher, Garg, Zwerger

Rev Mod Phys (1987).

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).

- 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.

- Small loop with three Josephson junctions produces the flux qubit.

- Hysteretic DC SQUID is used to read the flux state.

van der Wal et al, Science

290, 773 (2000).

Chiorescu et al, Science

299, 1869 (2003).

Ramsey Fringes in Flux Qubit

I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science 299, 1869 (2003).

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).

Decoherence in Josephson Phase Qubits from Junction Resonators

Simmonds, Lang, Hite, Nam, Pappas, and Martinis, Phys Rev Lett, 93, 077003-1, (2004).

e f

d

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).

1/f Noise: Dutta-Horn ModelDutta 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/t1and 1/t2as the probability of a transition from state 1 to 2 and 2 to 1 respectively. If 1/t = 1/t1 = 1/t2then the power spectrum is a Lorentzian of the formS(f) t / [1+(2pft)2]If the transitions are thermally activated then the characteristic time is given byti = toexp(Ui/kBT), where 1/tois an attempt frequency.S(f,T) is linear in T because the kernel moves through the distribution of RTS’s as the temperature varies, selecting only those processes that have characteristic frequencies in the window of interest.

barrier

I

trapped

s.c.1

height

no electron

barrier

trapped

s.c.2

trap

z

V

Mechanism Behind 1/ƒ 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

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 +0.5Foand –0.5Fostate.

Methods of Measuring 1/ƒ 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 Wellstood’s Thesis

Berkeley

Comparing different junctions:Invariant 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 Aand if the area blocked by a single trap isDA, then change in critical current for a single fluctuator isDIc = (DA /A)Ic

If nis 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 thatall values of n DA2 remarkably similar for all measured junctions. SI2scales as(Ic2 /A)

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

Measuring 1/ƒ Noise Due to Critical Current Fluctuations

in the Non-Zero Voltage State

Readout SQUID

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.

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

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.

due to a single fluctuator

Ic = 2.5uA

DIc = 0.65nA

This corresponds to a trap radius of ~ 5.6nm

Reading out an rf SQUID in the Dispersive Regime

Vrf

ƒmod

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.

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.

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.

New Device will allow the in situ control

of EJ, EC, and dissipation.

dependence of sSET

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.

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 γ → indirectly reduces screening

- The SQUID hysteresis parameter is defined as:
- If rf <1 the SQUID is dispersive. Ic is never exceeded
- If rf >1 the SQUID is hysteretic or dissipative.

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 <1

0

-1

0

1

rf >1

1

R

IS

0

F

F

L

-1

e

0

1

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.

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 it’s 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 rf<<1:

The flux qubit

φ

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).

Measuring 1/ƒ 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.

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

- 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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