Low temperature dissipative behavior in uncoated fused

silica slabs

Flavio Travasso

Dip. Fisica – Università di Perugia and INFN Perugia

Virgo - Perugia

Cryogenic Activity in Perugia1. Cryogenic Coating Measurements:

– Changes in the coating Фcoat(T): to find a change in the coating changing the temperature

– Different coatings: to measure the different loss angles of different coatings

• Measured Slabs (3 samples – provided and coated by LMA-Virgo Lion):– Uncoated Slab– Titania doped tantala coated slab (slab A)– Cobalt doped tantala coated slab (slab B)

• Dimension: – A & B: 41mm x 5 mm x 104 μm– Uncoated: 45mm x 5 mm x 104 μmDifferent frequencies

• Coatings:– A: 520 nm TiO2 doped Ta2O5 mono-layer coating– B: 500 nm Co doped Ta2O5 mono-layer coating

2. Fused silica Substrate cryogenic behavior

– Experimental activity: • about 20 modes studied for 3 uncoated slabs

– Theoretical activity: For the amorphous material the classical laws used for the crystalline materials are

not so easy to use or to support that’s why is usefull and hard find a:• theory to explain the Ф frequency trend of the modes at each temperature above

140K• theory to explain the Ф temperature peak around 20K

Sample holds

Labview Interface

Ni

He

Ni

He

He

Cu

Laser

HV Amplifier

Clamp tightened using a spring

Cooling down rate: 1-2 K/h

…to avoid particular thermal/mechanical stress

Measurement Apparatus

Summury on coating activity

Work in progress:

• To improve the measurements of coating at low temperature we plan on testing the same coating on new substrates • To design a new clamping system and/or new geometry for the samples• New materials for the coating

Coating Results:

• The coating ФCoat is almost costant in the temperature range of 300K-90K

• The Cobalt doped tantala coating shows a ФCoat better than the titania doped tantala coating:

ФCoat Mean Value = 3.4E-3 ± 1E-3

ФCoat Mean Value = 7E-4 ± 2E-4

• The measurements are limited by the substrates losses… (see Work in progress)

0 50 100 150 200 250 300

10-5

10-4

10-3

10-2

Lamina B Uncoated Lamina Phi Coating

Temperature [K]

0 50 100 150 200 250 300

10-5

10-4

10-3

10-2

Temperature [K]

Fused Silica Substrates dataIn the following we focus our attention on the low temperature properties of the fused silica material

Introduction

1. Φ vs temp: choosing a mode of the slab, how change the loss angle of this mode changing the temperature

• We found 2 peaks

2. Φ vs freq: selecting a temperature, what is the loss angle of the first 20 modes of the slabs (or rather how the loss angle changes with the frequency)

• We found 3 different scenarious in 3 temperature ranges => 3 different dissipative processes

0 2000 4000 6000 8000 10000 12000 14000

2.0x10-5

4.0x10-5

6.0x10-5

8.0x10-5

1.0x10-4

1.2x10-4

1.4x10-4

1.6x10-4

Frequency [Hz]

T = 90K

What we are going to see:

Ф vs. Temp(for a fixed mode)

0 50 100 150 200 250 300

10-5

10-4

10-3

Temperature [K]

@ 3800Hz

0 50 100 150 200 250 300

10-5

10-4

10-3

Temperature [K]

@ 47Hz

0 50 100 150 200 250 300

10-5

10-4

10-3

Temperature [K]

@ 290Hz

Ф vs. Temp

Quite costant loss angle

A new dissipative mechanism comes into play: Frequency dependent trend (see next slides)

A different process… (see next slides)

All the modes have the same behavior

Ф vs. Freq (for a fixed temperature)

Losses vs freq3 Scenarios

1. 290K-140K: The samples show a quite costante loss angle

3. 70K- 4K: the slabs still have a frequency dependent trend but with a different slope...see next slide

2. 140K-70K: There’s a frequency depended loss angle

-2000 0 2000 4000 6000 8000 10000 12000 14000

0.0

2.0x10-5

4.0x10-5

6.0x10-5

8.0x10-5

1.0x10-4

Temperature [K]

T = 200K

0 2000 4000 6000 80003.0x10-4

4.0x10-4

5.0x10-4

6.0x10-4

7.0x10-4

8.0x10-4

Temperature [K]

T = 50K

0 1000 2000 3000 4000 5000 6000 70003.0x10-4

4.0x10-4

5.0x10-4

6.0x10-4

7.0x10-4

8.0x10-4

Temperature [K]

T = 4.6K

This plot is not in the same scale of the other ones because there’s a factor 100 of difference

Frequency [Hz]

Frequency [Hz]

Frequency [Hz]

0 2000 4000 6000 8000 10000 12000 14000

0.0

2.0x10-4

4.0x10-4

6.0x10-4

8.0x10-4

1.0x10-3

1.2x10-3

80K 77K 64K 50K 40K 30K

140K 120K 110K 100K 90K 85K

Frequency [Hz]

0 2000 4000 6000 8000 10000 12000 14000

0.0

2.0x10-4

4.0x10-4

6.0x10-4

8.0x10-4

1.0x10-3

1.2x10-3

Frequency [Hz]

25K 20k 15k 10K 6.7K 4.6K

Φ for T < 140K (Freq. dep. process)

The frequency dependent trend is clear…

…but it’s also clear that the data for T<30K have a slope smaller than the data between 140K-40K.

Power law

KT

TB

fBC B

0

0

with

)*2(**

We used the following 2 power laws:

BfA*

0 2000 4000 6000 8000 10000 12000 14000

2.0x10-5

4.0x10-5

6.0x10-5

8.0x10-5

1.0x10-4

1.2x10-4

1.4x10-4

1.6x10-4

Frequency [Hz]

T = 90K

What we can do?

We can use the first simpler law to fit the data and to check the second law in order to understand where the double well potential model is valid

…that comes from a double well potential model

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

Exp

on

ent

po

wer

law

: B

Temperature [K]

Exponent of power law: B

KT

TB

0

Above 140K the loss angle appears to be NOT frequency dependent

The freq. Dependent process is becoming more active

These results are interesting because

1. In literature the explored frequency range is 500Hz-MHz (there are no infos on our frequency range)

2. In literature K = 0 …we have to consider another process to improve the actual physical models

A different dissipative mechanism comes into play: dissipative quantum tunnelling , that is quantum tunnelling assisted by thermal fluctuations

Sharp transition? System instability? Work in progress…

0 20 40 60 80 100 1200.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35 B = (0.00346 ± 7E-5)*T - (0.044 ± 0.004) => T0 = 289K

Exp

on

ent

po

wer

law

: B

Temperature [K]

Linear Fit of B: 110K-40K

KT

TB

0

…as you remind the BWP forseen a liner law for B(T)

Amplitude of power law: A

0 50 100 150 200 250 300-1.0x10-4

0.0

1.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

5.0x10-4

6.0x10-4

7.0x10-4

8.0x10-4

Am

plit

ud

e o

f p

ow

er la

w:

A

Temperature [K]

The trend is very similar to the Ф(T) one… infact A α Ф(T)

0 20 40 60 80 100 120

0.0

1.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

5.0x10-4

6.0x10-4

7.0x10-4

8.0x10-4

9.0x10-4

1.0x10-3 Temp range: 110K-40K

Chi^2/DoF = 1.0167E-10R^2 = 0.99616 C 0.06028 ±0.00464tau 3.2202E-13 ±2.2426E-13T0 289 ±0k -0.044 ±0

Am

plit

ud

e o

f p

ow

er la

w:

A

Temperature [K]

Fit A

BBCA )2(** 0Using for B the value evaluated in the previous slide

The losses are higher than what forseen by the double well potential model: 2 competive dissipative processes

Comments

SiO2 Results: 

The measurements show a clear behaviour with temperature: -  an almost constant loss angle above 140K  - between 140K and 30K the loss angle has a significant increase that can be interpreted by calling for thermally activated relaxation dynamics (in multi-stable potentials)  - below 30K the loss angle starts to decrease: the thermally activated dissipation is less effective and a different dissipative mechanism starts to drive the dynamics (quantum tunnelling effects become active at very low temperature… that is quantum tunnelling assisted by thermal fluctuations )

Work in progress:A new refined dynamical model for the interpretation of the losses in the low frequency region is in preparation (See F. Marchesoni)