Institute Laue-Langevin, Grenoble - IN2P3moriond.in2p3.fr/EW/2006/Transparencies/V.V.Nesvizhevsky.pdf"Let us consider another possibility, an atom held together by gravity alone. For

INSTITUT MAX VON LAUE - PAUL LANGEVIN17.03.0617.03.06 V.V.Nesvizhevsky

Institute Laue-Langevin, Grenoble

INSTITUT MAX VON LAUE - PAUL LANGEVIN17.03.0617.03.06

1. Short Introduction: Ultra Cold Neutrons - UCN. First experiment in 1968 in JINR, Dubna: V.I.Luschikov et al (1969). JETP Letters 9: 40-45.

2. Quantum states of neutrons in the Earth’s gravitational field above a mirror. Textbooks on quantum mechanics + V.I.Luschikov at al (1978), JETP Letters 28(9): 559-561.

3. Observation and study. V.V.Nesvizhevsky et al : Nature 415: 297-299 (2002); Physical Review D 87: 102002 (2003); Europ.Phys.Journ. C 40(4):479-491 (2005). Collaboration: ILL, LPSC (France), PNPI, Lebedev Inst., Khlopin Inst., JINR (Russia), Mainz Univ., Heidelberg Univ., DESY (Germany).

4. Multi-disciplinary: Search for spin-independent and spin-dependent short-range forces in the range of 1nm - 10µm; limit for the neutron electric charge; verification of extensions of the quantum mechanics; the loss of quantum phase coherence; a rare opportunity to measure distribution of hydrogen above/below surface; solution for the problem of neutron-tight valve for UCN traps; convenient tool to observe Andersen-type neutron localization, or to study interaction of waves with rough surfaces; advanced UCN guides.

5. Project GRANIT. Resonance transitions between the gravitationally bound quantum states of neutrons. ANR project 2005-2008: Collaboration: ILL-LPSC-LMA (France) +

V.V.Nesvizhevsky

Plan of this presentation

INSTITUT MAX VON LAUE - PAUL LANGEVIN17.03.0617.03.06

UCNNeutron

Nuclei in matter Usually:

~99.99 % - elastic reflection

~10-4 - inelastic reflection at phonons to the thermal energy range

~10-5 - inelastic reflection at surface nanoparticles to the UCN energy range

~10-5 - absorption

mKTmH

eVE

smV

fieldsEarth

UCN

UCN

UCN

1~1~

10~

/)61(~

'

7−

÷

1. Effective Fermi-potential and storage of UCN in traps

V.V.Nesvizhevsky

INSTITUT MAX VON LAUE - PAUL LANGEVIN17.03.06 V.V.Nesvizhevsky

2. How to observe any quantum states of matter in a gravitational field ?

"Let us consider another possibility, an atom held together by gravityalone. For example, we might have two neutrons in a bound state.When we calculate the Bohr radius of such an atom, we find that it would be 108 light years, and that the atomic binding energy would be 10-70 Rydbergs. There is then little hope of ever observing gravitational effects on systems which are simple enough to be calculable in quantum mechanics."

Brian Hatfield, in "Feynman Lectures on Gravitation" ;R.P. Feynman, F.B. Morinigo, W.G. Wagner, Ed. Brian Hatfield

Addison-Wesley Publishing Company, 1995, p. 11


Neutron above a mirror in the Earth’s gravitational field

1) Electric neutrality (usually any gravitational interaction in laboratory conditions is much weaker that other interactions)

2) Long lifetime

3) Small mass

4) Energy (temperature) of UCN is extremely small and not equal to the installation temperature

⎟⎠⎞

⎜⎝⎛

∆≈∆

τhE

⎟⎠⎞

⎜⎝⎛ ≈∆⋅∆

mx hv

3

2

41

89

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −⋅⋅⋅⋅⎟

⎠⎞

⎜⎝⎛ ⋅

≈ ngmE nn hπ

2. How to observe any quantum states of matter in a gravitational field ?

Quantum state energy in the Bohr-Sommerfeld approximation :


2. Probability to observe a neutron above a mirror

The precise solution of the corresponding Schrödinger

equation

Height above a mirror in microns



How the experiment with neutrons is related to the falling down of an apple in the gravitational field ?

Higher probability to observe neutrons (an apple) at some heights and zero probability –for a pure quantum state – to observe them somewhere in between


Neutrons spend longer time at the top of its “trajectory” and the spacing between the maxima is bigger at the top as well



Vhorizont~4-15 m/sVvertic~2 cm/s

τ∆≈∆hE

Selection of vertical and horizontal velocity components

2. General scheme of the experiment

-Effective temperature of neutrons is ~20 nK

-Background suppression is a factor of ~108-109

-Absolute horizontal leveling precision is ~10-6 rad

-Parallelism of the bottom mirror and the absorber/scatterer is ~10-6


mxv h≈∆⋅∆

2. Measurement


2. Measurement


2. Measurement


2. Measurement


2. Measurement


2. Measurement


2. Measurement


2. Theoretical descriptionThe model of tunneling through gravitational barrier

1>>ξ],

34[)( 2

3

ξξ ⋅−≈ ExpD )()( ξωξ Dnn ⋅=Γ h/)( 1 nnn EE −≈ +ω

⎪⎩

⎪⎨⎧

>⋅−⋅

<=

0],34[

0,1)(

23

ξξ

ξξ

ExpAD

n

))(()( τξξ ⋅Γ−= nn ExpP

))(()(hor

nn VLExpP ⋅Γ−= ξξ

∑⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ −∆⋅−⋅⋅⋅−⋅=∆

n

nn

hornhor z

zzExpC

VLExpVzF

23

0

2

34),( αβ


3. ResultsNarrow spectrum; soft fraction; comparison to the theoretical model

Experiment 1999


µmµm

mz statsyst µ,7.02.23.21exp2 ±±=

mz statsyst µ,7.08.12.12exp1 ±±=

mz

mzclassquasi

classquasi

µ

µ

0.24

7.13.

2

.1

=

=

3. ResultsNarrow spectrum; soft fraction; comparison to the theoretical model


3. Measurements with such a position-sensitive detector

1

43

2


4. Applications in fundamental physicsAdditional short-range forces

( )λ/)( 0 zExpVzV −⋅−=

20 2 λραπ ⋅⋅⋅⋅⋅⋅= mG mGV

( ))/exp(1)( 1212

2112 λα r

rmmGrV G −⋅+⋅⋅⋅

−=

Why additional forces?

-Light particles

-Additional spatial dimensions


Frequency of perturbation, Hz

Probability of transition

eVE 18min 10−≈δ

6

12

min 10−≈− EE

Eδ

ijji wEE ⋅=− h

Hz14021 ≈ν

Quantum trap

Resonance transition

5. Resonance transitions between quantum states

- Oscillations of a bottom mirror – due to nuclear forces;

- Oscillations of a mass – due to gravitational forces;

- Oscillations of electro-magnetic forces …

How to excite such a resonance transition :



Transitions due to electromagnetic forces – “easy” cmGs /10~β

2 20 0

max 2 2 21 0

4( )( ) 4

n n

n n n

P Ω Ω= =Ω − + Ω

ωω ω

Transitions due to gravitational forces – the probability could be of ~0.01 for ~100 kg oscillating test mass – could be measured

Transitions due to oscillating mirror – “easy” – oscillation amplitude of <1µm



But parameters of this spectrometer are very challenging!

It will not be easy to suppress many false effects, for instance:

-Vibrations (have to be not too much higher than the seismic noise (extremely difficult inside a reactor building!);

-Waviness of mirrors (have to be as small as a few times 10nm for a mirror of ~30cm size);

-Adjustments and accuracy of production of optics elements at a typical level of 10-6-10-5;

-Expected neutron count rate is ~50 events/day at the best available today UCN source … etc



Also !

-Surface roughness (low life-tome in a quantum state);

-Impurities on surface (produce “roughness” for even ideally flat mirror);

-Dust on surface (huge coherent scattering);

-“Complete” control of magnetic fields/ gradients of magnetic fields;

-Low-background neutron detectors (remember the value for expected count rate);

-Etc … etc…


Idea of this experiment

1. To populatea low quantum state

2. To populate an excited state using a

resonant transition

3. To study mixing betweenneighbouring states

4. To detect neutrons (for instance, using again a resonance transition)

End 2008 (ANR)

30-50 cm

100-

1000

µm

StorageStorage timetime ~ 1 s~ 1 s




In order to review theoretical aspects of this project and to discuss physics, which could be done with this installation, we organize a

MINI-WORKSOP on Resonance transitions between gravitationally bound quantum states of neutrons in Grenoble, 6-7 April 2006

Registration is still open at:

http://lpsc.in2p3.congres/granit06/informations-pratiques.php

INSTITUT MAX VON LAUE - PAUL LANGEVIN17.03.06

5. Scales of temperature and energy in neutron physics

V.V.Nesvizhevsky

10-12 10-7 10-1 107 Neutron energy, eV

Reactor moderators

Cold moderators

Ultra cold nanoparticles

?

Quantum states of neutrons in the Earth’s gravitational field

VUCN

10-3

Temperature, K 101 10310-320 nK

Fission

Documents

Institute Laue-Langevin, Grenoble - IN2P3moriond.in2p3.fr/EW/2006/Transparencies/V.V.Nesvizhevsky.pdf"Let us consider another possibility, an atom held together by gravity alone. For