Neutrons, quantum bounds, extra interactions'

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Neutrons, quantum bounds, extra interactions.
Doesnt need a visa
Guillaume Pignol Valery Nesvizhevsky Konstantin
Protasov
Who did not manage to get a Visa in time
Quantum reflection workshop ITAMP Harvard
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Outline
1 Quantum reflection of Ultra Cold Neutrons 2
Slow neutrons and extra interactions in the range
between 1 pm and 5 nm 3 Gravitational quantum
states of neutrons in the Earth gravitational
field
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The institute Laue-Langevin in Grenoble, France
European Synchrotron
Mountain

• The ILL
• Nuclear core 53 MW
• The most intense neutron
• source in the world

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Outline
1 Quantum reflection of Ultra Cold Neutrons 2
Slow neutrons and extra interactions in the range
between 1 pm and 5 nm 3 Gravitational quantum
states of neutrons in the Earth gravitational
field
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Ultra Cold Neutrons (UCN)

• Optical neutrons
• wavelength gt2 Å
• interaction with bulk matter described by a mean
  potential (Fermi potential) 100 neV

10 MeV
production
Thermal neutrons
0.025 eV
Optical neutrons
100 neV
Ultra Cold Neutrons
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Quantum reflection of UCN
Measured reflectivity agrees with Q.M. simplest
calculation (Koester 1986 as an example)
Ultra Cold Neutrons

• velocity lt 7 m/s
• wavelength gt 50 nm
• Elastic reflection 99.99
• 10-4 inelastic reflection at phonons
• 10-5 inelastic reflection at
• surface nanoparticles
• 10-5 absorption

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Outline
1 Quantum reflection of Ultra Cold Neutrons 2
Slow neutrons and extra interactions in the range
between 1 pm and 5 nm 3 Gravitational quantum
states of neutrons in the Earth gravitational
field
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Slow neutrons and fundamental interactions

• Free neutrons feel all interactions very weakely
• Weak interaction
• ß decay 886 s
• Strong interaction
• Fermi potentials 100 neV
• Electromagnetism
• No electric charge
• B 1 T induce Zeeman split of 100 neV
• Gravity
• 1 m fall neutron increases its energy by 100
  neV

Neutrons can be very sensitive to new
interactions!
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Extra short range interaction
We assume a new interaction between neutron and
nucleus with A nucleons
Mediated by a new light boson of mass M
High Energy Physics
Modification of gravity
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Slow neutron scattering with extra interaction

• Coherent scattering length (Fermi)
• Isotropic
• Energy independant
• Scales as A1/3

• Not isotropic
• Energy dependant
• Scales as A

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1 Simple nuclear model
We aim to exclude a contribution A in the set of
measured scattering lengths
Random potential model
Peskhin, Ringo, Am. J. Phys. 39 (1971)

• Square well potential for
• nuclear interaction
• Radius R x A1/3
• Random depth.

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1 Simple nuclear model extra interaction
We repeated the analysis with an extra force
included
Additional parameter
Random potential model
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2 Comparing forward and backward scattering
Interference measurement
Bragg diffraction measurement

• Measurements using interference method
• sensitive to the forward scattering amplitude
• one actually measures
• Measurements using Bragg-diffraction method
• sensitive to q 10 nm-1 scattering amplitude
• one actually measures

The two methods for measuring the scattering
lengths do not bear the same sensitivity to extra
force
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2 Comparing forward and backward scattering
No difference is observed for the nuclei for
which both measures exist
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3 Comparing forward scattering and total X-section

• Measurements using optical method
• sensitive to the forward scattering amplitude
• one actually measures
• Measurements using transmission method
• sensitive to the total cross-section at 1 eV
• one actually measures

This idea first appeared in Leeb and
Schmiedmayer, PRL 68 (1992)
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3 Comparing forward scattering and total X-section
Very precise measurements exist for both methods,
on lead and bismuth nuclei. No deviation is
observed There is a hidden difficulty for
scattering at 1 eV, electromagnetic effects have
to be taken into account.
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Neutrons and extra interactions conclusions

• Neutron constraints on extra interactions are
  several orders of magnitude better than those
  usually cited in the range 1 pm 5 nm
• We provided several independant strategies
• neutron constraints are reliable

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Outline
1 Quantum reflection of Ultra Cold Neutrons 2
Slow neutrons and extra interactions in the range
between 1 pm and 5 nm 3 Gravitational quantum
states of neutrons in the Earth gravitational
field 1 Gravitational quantum states of
neutrons 2 The GRANIT experiment
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Gravitational quantum states of neutrons
Q.M. fact a particle bouncing above a perfect
mirror has discrete energy states.
Schrödinger equation

• The neutron is the best candidate
• it is electrically neutral and almost stable.
• This effect has indeed been discovered with the
  ILL UCN source.

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Universality of free fall violated
Newton equation
Classical free fall independent of mass
Schrödinger equation
Size of the wavefunctions does depend on mass
Watching a neutron falling, one can actually
measure its mass!
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Discovery of neutron quantum states in 1999
Nesvizhevsky et al, Nature 415 (2002)
CLASSICAL
QUANTUM
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Current situation

• Accuracy of position-like observables limited by
  absorber resolution
• Spectrometry of excited states
• difficult.

Nesvizhevsky et al, Eur. Phys. J. C 40 (2005)
Next step the GRANIT experiment

• GRAvity Neutrons Induced Transitions
• Precise measurement of energy-like observables
• First measurements start by the end of 2008.

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To excite resonant transitions
Initial neutron , we apply the perturbation
Probability to observe the neutron in excited
state after time t
Rabi frequency defines the strength of the
perturbation for transition N ? n
One measures differences of energies
One observes resonances
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To excite resonant transitions
Width of resonances

• Pulse time needed to resolve neighbouring
  states 10-2 s
• Flow through mode
• Ultimate accuracy due to neutron decay

• Step 1 to observe transitions in flow through
  mode
• Step 2 to trap quantum states
• in order to approach ultimate sensitivity

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Resonant transitions in flow through mode

• The transition is resonant for a single
  horizontal velocity, that we measure using free
  fall afterwards
• One can measure the transitions frequencies at
  1 level

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Trapping quantum states
Measurement sequence

• Fill the trap
• Oscillating magnetic gradient
• Extract neutrons from the trap

Storage time

• Goal T 1 s
• Accuracy 10-3 for the transition frequencies.

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The GRANIT experiment conclusions

• We observe quantum bounds violating the
  universality of free fall
• GRANIT will perform precise measurements of the
  spectrum of graviationally bound quantum states
  of neutrons
• Observing resonant transitions in flow through
  mode
• Increasing the precision using trapped quantum
  states
• The spectrometer is under construction,
• measurements will begin by the end of 2008