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Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lectures ICTP Winter School on Optics 2016 Precision Spectroscopy of Molecular Hydrogen

and Physics Beyond the Standard Model Wim Ubachs LaserLaB, Vrije Universiteit Amsterdam

Topics: 1) Level structure and spectroscopy of the hydrogen molecule 2) Probe for a varying proton-electron mass ratio from H2 3) New forces and dimensions from precision studies of H2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lectures ICTP Winter School on Optics 2016

Wim Ubachs LaserLaB, Vrije Universiteit Amsterdam

Reading Material: Physics beyond the Standard Model from hydrogen spectroscopy

• W. Ubachs et al., J. Mol. Spectr. 320 (2016) 1-12

Search for a drifting proton-electron mass ratio from H2

• W. Ubachs et al., Rev. Mod. Phys. April (2016); ArXiv:1511.04476

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The Hydrogen Atom

Niels Bohr

M m mM

red

• Reduced mass: transformation from two one particle problem
• R

m n E

e red n

• 2

1

Rydberg constant

2 2 2

2 4

• e

m e R

• m

M

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The Proton-Electron Mass Ratio

From experiments: Fundamental Dimensionless Constant of Nature

Physical Review 82 (1951) 554

) 75 ( 15267245 . 1836

• e

p

m M

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

K sensitivity coefficients to -variation for Lyman- transition

• K

Definition of sensitivity coefficient: Calculation for Lyman-a transition

• e

red

m c R h E E

• 4

3

1 2

• 1

/ 1 / 1

e p e p e p e p e e red

m M m M m M m M m m

with So (note energy scale drops out !):

• K

E E E E 1 / 1 / 1 1

1 2 1 2 4

10 4 . 5 ~ 1 1

• K

Atoms are insensitive !

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Hamiltonian for a molecule

• r

R V M m H

A A A i i

• ,

2 2

2 2 2 2

• j

i ij B A B A B A i A Ai A

r e R R e Z Z r e Z r R V

2 2 , 2

4 4 4 ,

• i refers to electrons, A to nuclei;

Potential energy terms: Assume that the wave function of the system is separable and can be written as:

• R

R r R r

i A i

• nuc

el mol

; ,

• Assume that the electronic wave function

can be calculated for a particular R

• R

ri

• ;

el

• R

r R R R r

i i i i

• ;

;

el 2 nuc nuc el 2

• Then:
• el

2 nuc el nuc 2 el nuc el 2

2

• A

A A A A

• Born-Oppenheimer: the derivative
• f electronic wave function w.r.t

nuclear coordinates is small: Nuclei can be considered stationary. Then: Separation of variables is possible. Insert results in the Schrödinger equation:

el A nuc 2 el nuc el 2

• A

A

• nuc

el mol nuc el mol

• E

H

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

mol total nuc 2 2 2 el el , 2 2 2 2 nuc mol

2 4 4 4 2

• E

M R R e Z Z r e Z r e m H

B A A A A B A B A i A Ai A j i ij i i

• Separation of variables in the molecular Hamiltonian

The wave function for the electronic part can be written separately and “solved”; consider this as a problem of molecular binding.

• R

r E R r r e Z r e m

i i i A Ai A j i ij i i

• ;

; 4 4 2

el el el , 2 2 2 2

• Solve the electronic problem for each R and insert result Eel in wave function.

This yields a wave equation for the nuclear motion:

nuc total nuc 2 2 2

) ( 4 2

• E

R E R R e Z Z M

B A el B A B A A A A

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Schrodinger equation for the nuclear motion

The previous analysis yields:

nuc total nuc 2 2 2

) ( 4 2

• E

R E R R e Z Z M

B A el B A B A A A A

• This is a Schrödinger equation with a

potential energy:

R E R R e Z Z R V

B A B A B A

• el

2

4

• nuclear repulsion chemical binding

Typical potential energy curves in molecules Now try to find solutions to the Hamiltonian for the nuclear motion

R E R R V R M

A A A

• nuc

nuc nuc 2 2

) ( 2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Quantized motion in a diatomic molecule

Quantummechanical two-particle problem Transfer to centre-of-mass system

B A B A

M M M M

• Single-particle Schrödinger equation

R E R R V R

R

• nuc

nuc nuc 2

) ( 2

• Consider the similarity and differences

between this equation and that of the H-atom: Laplacian:

2 2 2 2 2 2

sin 1 sin sin 1 1

• R

R R R R R

R

• Angular part is the well-know equation

with solutions: Angular momentum operators Spherical harmonic wave functions !

• interpretation of the wave function
• shape of the potential

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Angular momentum in a molecule

M N M M N N M N N N M N N

z

, , , ) 1 ( ,

2 2

• Solution:

with

N N N M N ,..., 1 , ... 3 , 2 , 1 ,

• And angular wave function
• ,

,

NM

Y M N

• Hence the wave function of the molecule:
• ,

, ,

nuc NM

Y R R

• Reduction of molecular Schrödinger equation

) ( ) ( ) ( 2 1 2

nuc rot vib, nuc 2 2 2 2 2

R E R R V N R R R R R

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Eigenenergies of a “Rigid Rotor”

Rigid rotor, so it is assumed that R = Re = constant Choose:

) (

• e

R V R V

All derivates yield zero

R

• )

( ) ( ) ( 2 1 2

nuc rot vib, nuc 2 2 2 2 2

R E R R V N R R R R R

• Insert in:

) ( ) ( 2 1

nuc rot vib, nuc 2 2

R E R N Re

• So quantized motion of rotation:

) 1 ( 2 ) 1 (

2 2 rot

• N

BN R N N E

e

• With B the rotational constant

Deduce Re from spectroscopy isotope effect

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Vibrational motion

) ( ) ( ) ( 2 1 2

nuc rot vib, nuc 2 2 2 2 2

R E R R V N R R R R R

• Non-rotation: N=0

Insert :

R R Q R ) (

• )

( ) ( ) ( 2

vib 2 2 2

R Q E R Q R V dR d

• Make a Taylor series expansion around r=R-Re

... 2 1 ) ( ) (

2 2 2

• e

e

R R e

dR V d dR dV R V R V ) (

• e

R V

by choice

• e

R

dR dV

at the bottom of the well Hence:

• 2

) (

e

R R k R V

• harmonic potential

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Vibrational motion - 2

) ( ) ( 2 1 2

vib 2 2 2 2

• Q

E Q k d d

• So the wave function of a vibrating molecule

resembles the 1-dimensional harmonic

• scillator, solutions:
• v

v v

H v Q

• 2

4 / 1 4 / 1 2 /

2 1 exp ! 2 ) (

with:

• e
• and
• k

e

Energy eigenvalues:

• 2

1 2 1

vib

v k v E

e

• isotope effect

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Finer details of the rovibrational motion

Centrifugal distortion:

2 2 rot

) 1 ( ) 1 (

• N

DN N BN E ... 2 1 2 1

2 vib

• v

x v E

e e e

• Anharmonic vibrational motion

Dunham expansion:

• 1

,

1 2 1

• N

N v Y E

l k l k kl vN

Vibrational energies in the H2-molecule

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Energy levels in a molecule: general structure

Rovibrational structure superimposed on electronic structure

J

v=0 v=1 v=2

J

v=0 v=1 v=2

A

• B

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Electronic structure of the Hydrogen molecule

Diabatic Potentials

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Singlet-Triplet structure in the Hydrogen molecule

singlets triplets Very small coupling

s l

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Electronic structure of the Hydrogen molecule; adiabatic

“gerade” “ungerade” Inversion symmetry X1g

+

is way below like H/He

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Radiative transitions in molecules

The dipole moment in a molecule:

A A A i i N e

R eZ r e

• In a molecule, there may be a:
• permanent or rotational

dipole moment

• vibrational dipole moment

2 2 2

2 1

• dR

d dR d

e

R N

In atoms only electronic transitions, in molecules transitions within electronic state

• R

R r R r

i A i

• vib

el mol

; ,

• Dipole transition between two states
• d

if

" '

• R

d r d R d r d d

N e N e if

• "

vib ' vib " el ' el " vib ' vib " el ' el " vib " el ' vib ' el

• Two different types of transitions

Electronic transitions Rovibrational transitions

2 2 2

3

ij

e B

• Note for transitions:

Einstein coefficient

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The Franck-Condon principle for electronic transitions in molecules

• R

d r d

e if

• "

vib ' vib " el ' el

• 1st term:

Only contributions if (parity selection rule)

" el ' el

• Franck-Condon approximation:

The electronic dipole moment independent

• f internuclear separation:
• r

d R M

e e

• "

el ' el

) (

• R

d R Me

if

• "

vib ' vib

) (

• Hence

Intensity of electronic transitions

2 2 " vib ' vib 2

" ' v v R d I

if

• Intensity proportional to the square
• f the wave function overlap

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Rovibronic spectra

J

v=0 v=1 v=2

J

v=0 v=1 v=2

A

• B
• Vibrations governed by the

Franck-Condon principle Rotations governed by angular momentum selection rules Transition frequencies TB TA

) ' ( ' ) ' ( ' ' N F v G T T

v B

• )

" ( " ) " ( " " N F v G T T

v A

• "

' T T v

• R and P branches can be defined

in the same way

• 2

" ' " ' '

3 2 N B B N B B B

v v v v v R

• 2

" ' " '

N B B N B B

v v v v P

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Population distributions;Ϳ vibrations

kT v v kT v E kT v E

e

e Z e e v P

) 2 / 1 ( / ) ( / ) (

1 ) (

• Probability of finding a molecule

in a vibrational quantum state: Note: not always thermodynamic equilibrium P(v)/P(0) Boltzmann distribution H2: only v=0 populated at “any” T

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Population distributions; rotational states in a diatomic molecule

• 2

2

) 1 ( ) 1 ( ' / /

) 1 2 ( 1 ) 1 ' 2 ( 1 2 ) (

• J

DJ J BJ rot J kT E kT E

e J Z e J e J J P

rot rot

Probability of finding a molecule in a rotational quantum state: Find optimum via

) (

• dJ

J dP

HCl T=300 K Boltzmann-plot H2 in Q1232+082 Quasar

(Ivanchik MNRAS 2010)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Para and Ortho Hydrogen; nuclear spin

2 1

I I I

• 2

1

I I I

m m M

• ;

I= 0, 1 MS = -1, 0, 1

• ,

1 , 1

I

M I

• ,

, 2 1 , 1

I

M I

• ,

1 , 1

I

M I

• ,

, 2 1 ,

I

M I

A triplet of symmetric nuclear spin wave functions (symmetry related to interchange) A singlet of an anti-symmetric Nuclear spin wave function Total wave function must be anti-symmetric for interchange of protons (Pauli principle): Ortho-hydrogen: triply degenerate

S spin nuc A rot

• Para-hydrogen: singly degenerate

A spin nuc S rot

• Odd N-levels: N=1,3,5 …

Even N-levels: N=0,2 ..

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Isotope effects in molecules; sensitivity for -variation

Born-Oppenheimer: the derivative of electronic wave function w.r.t nuclear coordinates is small:

el A

Electronic wave functions and energies do not depend on nuclear masses (compare the case of the atom) Electronic Mass dependences In the above mass dependences expressed as “reduced mass”; Note that we assume:

red

• Proportionality with “baryonic mass” (neutrons and protons)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Isotope effects in molecules; sensitivity for -variation

• 2

1

vib

v k E

• Vibrational energy:

K-coefficient for purely vibrational transition (overtone included):

• K

m n m n m n E E E E

m n m n

1 2 1 1 1 2 / 1 2 / 1 1 2 / 1 2 / 1 1 2 / 1 2 / 1 1

So:

2 1

• K

For ALL vibrational transitions / vibrational energies

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Isotope effects in molecules; sensitivity for -variation

Rotational energy:

K-coefficient for purely rotational transition (or rotational energy):

• K

1

• K

2 2 rot

2 ) 1 (

e

R N N E

• So:
• 1

2

• C

C d d K

• C

N N N N Re

• )

1 ( ) 1 ( 2

1 1 2 2 2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Electronic spectra of H2 H2

H (Lyman-) ~ 121 nm

2p 2p

H2, Lyman en Werner BANDS ~90 - 110 nm Extreme Ultraviolet Wavelengths

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lyman and Werner band systems

(1s)2- (1s)(2p) Threefold 2p orbitals X1g

+ - (2p) B1u +

X1g

+ - (2p) C1u

Doubly degenerate B C X

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Franck-Condon Factors in H2 absorption

B C X B(v’)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lyman and Werner band systems

B1u

+

X1g

+

0 (+) 1 (-) 2 (+) 0 (+) 1 (-) 2 (+) R(0) R(1) P(1) P(2) C1u X1g

+

0 (+) 1 (-) 2 (+) 1 (-) 2 (+) R(0) R(1) P(2) component 0 (+) 1 (-) 2 (+) 1 (+) 2 (-) Q(1) Q(2) component component

• doubling lifts degeneracy components

Rotation-electronic coupling (beyond BO) Different parity

N

• ,

,

NM

Y M N

• Parity

R, P, Q lines

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

“Isotope effects” in molecules; sensitivity for -variation

Eelectronic Evibrational Erotational Etotal Evibrational Erotational Add contributions to sensitivity:

• Electronic
• Vibrational
• Rotational

In first order:

tot rot tot vib tot rot rot tot vib vib tot elec elec

E E E E E E K E E K E E K K 1 2 1

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Dunham approach to sensitivity coefficients

• 2

/

1

k l

kl kl kl

B A Y

• l

J J k v l k kl Y J v E ] 2 1 [ 2 1 , ,

• d

g dE d e dE g E e E i K

With known mass dependence:

• kl

kl kl

B k l Y d dY 2

Dunham representation:

• l

J J k v l k dY d J v dE

d

kl

] 2 1 [ 2 1 , ,

• Results in:

Dunham coefficients C1+

u

Dunham coefficients X1+

g

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

X1g

+

B1u

+

C1u C(3) B(14) C(2) B(12) C(1) B(10) C(4) B(17)

• )

( ) 1 ( ) 1 ( ) ( J E J J H J J H J E

B CB CB C

• L

J H

• '

Local perturbations; beyond Born-Oppenheimer

' , ' , , 2 , , ,

1 2 2 1

p J v C L J R p J v B

C u B u

• Matrix elements:

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lyman and Werner Bands; sensitivity for -variation

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Hydrogen does not have a “molecular band spectrum”

• P. Hinnen, W. Ubachs et al.
• Can. J. Phys 72, 1032 (1994)

Laser spectrum

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Precision measurements with tunable XUV laser

Pulsed Dye Amplifier

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Evaluation of uncertainties: Error budget Residual Doppler 40 MHz AC Stark 30 MHz Freq chirp (PDA) 100 MHz I2 calibration 10 MHz Statistical 30 MHz Total (best lines): 0.005 cm-1 0.000005 nm 5 x 10-8 P(3) C-X (1,0) line R(0) B-X (9,0) line

1 XUV + 1 UV REMPI spectroscopy

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

162 lines measured at ~ 5 x 10-8

L15 R(2)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Conclusion : H2 dipole-allowed absorption spectrum

i – set of accurate wavelengths Ki – set of sensitivity coefficients fi – set of line oscillator strengths (from ab initio theory) i – set of damping coefficients (from ab initio theory) Lyman (B-X) and Werner bands (C-X) are the strong absorptions (1s – 2p) Molecular database is available To be used in astrophysical applications

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lectures ICTP Winter School on Optics 2016 Precision Spectroscopy of Molecular Hydrogen

and Physics Beyond the Standard Model Wim Ubachs LaserLaB, Vrije Universiteit Amsterdam

Part 2 Probe for a varying proton-electron mass ratio from H2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

QSO

12 Gyr ago

Lab

today 90-112 nm ~275-350 nm

Empirical search for a change in

Compare H2 in different epochs Cosmological redshift

i i z i

z

• 1
• Practical: atmospheric transmission only for z>2
• 2

/ 3

1 1 1

abs

z T T

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

anchor blue shifter red shifter

Sensitivity of H2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

VLT – UVES Paranal, Chili Keck – HIRES Hawaii

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Quasars: Ultrazwakke objecten

Q2348-011 z = 2.42 Magnitude 18.4 ESO-VLT 2007

1 arcsecond

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

UVES: Ultraviolet – Visual Echelle Spectrograph

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Blue chip: 300-500 nm Red chips: 420-1100 nm

Calibration with UVES

Photon management Standard calibration: Comparison QSO exposure vs ThAr lamp exposure (Attached / Non-attached) Problems: 1. Different light path in spectrograph 2. Uniform illumination of slit 3. Red and blue parts of spectrum recorded on different CCDs Systematic effects may mimic a 0 !

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Th-Ar calibration

+ asteroids + “solar twins”

Dispersion of Echelle Orders on to CCDs

Blue chip Two red chips

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Supercalibrations

Asteroids and ‘Solar Twins’ targets ThAr calibrated spectrum vs FTS spectrum Linear slope correction Long-range wavelength distortions

Rahmani et al. MNRAS 435 (2013) 861 Whitmore & Murphy MNRAS 447 (2015) 446

Solar twin Convoluted FTS

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

H2

Resolution 110000 ; zabs=2.0593

J2123-005 from HIRES-Keck at Hawaii

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Various systems

• bserved

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Analysis method: “comprehensive fitting”

i – set of accurate wavelengths Ki – set of sensitivity coefficients fi – set of line oscillator strengths (from ab initio theory) i – set of damping coefficients (from ab initio theory) Produce molecular fingerprint

• i

abs i i z i

K z z 1 1 1

Astrophysical conditions b– Doppler width parameter z – red shift NJ – column densities Fit equation onto spectrum “Treat” HI and metal lines Multiple velocity components (?)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

= (5.6 ± 5.5stat ± 2.9syst) x 10-6 = (8.5 ± 3.6stat ± 2.2syst) x 10-6 Keck: VLT:

Unique spectrum from Keck;Ϳ Resolution 110000 ;Ϳ seeing 0.3” Spectrum from VLT;Ϳ R=54000;Ϳ seeing 0.8”;Ϳ better SNR

The best system: J2123-005 at zabs=2.05

37 panels, 3071 – 3421 Å ~100 H2 + 7 HD lines

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Q1441+272 ; the most distant

zabs = 4.22 ; 1.5 Gyrs after the Big Bang

Systematic analysis

• Phys. Rev. Lett. 114, 071301 (2015)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Limited H2 absorbers at high redshift

(+ CO) Rahmani Done Done Done Done Done Done Done Done

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Varying constants and the ratio m,

Status of cosmological -variation

= (3.1 1.6) x 10-6

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Varying Constants ?

Bekenstein-Barrow –Sandvik – Mageijo – Light scalar fields 1) Coupling to cosmology Variation on cosmological time scales “matter dominated” “dark energy dominated”

• d

l c e F F A c j L S

mat

• 2

2

2 4

• Coupling constants are free parameters in Standard Model

2) Coupling to matter density -> “chameleons” Coupling to gravity

Jacob Bekenstein

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Hydrogen nearby; white dwarf stars in our galaxy

Cosmic Origins Spectrograph Hubble Space Telescope

Spectrum of GD-133 and GD29-38 White Dwarf stars H2 in VUV In search for the Chameleon scenario WD=(GM/Rc2)=104Earth

Dependence of on gravitational field

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

~ 130-140 nm

Contributions of many lines in the B-X Lyman system

• max

max

) (

exp ) 1 2 )( ( exp ) 1 2 )( ( ) (

v v v J J vJ I vJ I vJ

kT E J J g kT E J J g T P High temperatures High v populated Franck-Condon factors

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Dependence of on gravitational field

GD133: = (-2.7 +/- 4.7) x 10-5 GD29-38: = (-5.9 +/-3.8) x 10-5

• max

max

) (

exp ) 1 2 )( ( exp ) 1 2 )( ( ) (

v v v J J vJ I vJ I vJ

kT E J J g kT E J J g T P Invoke partition function: Invoke intensities (1500 lines):

) (

" " " ' " '

T P f N I

J v J J v v col i

Fit T and

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Outlook: More sensitive molecules

K = -4.2

Quantum tunneling

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Calculations Extreme shifters

Quantum tunneling: hindered rotation

Outlook: More sensitive molecules

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

48372.4558 MHz; K=-1 48376.892 MHz; K=-1 12178.597 MHz; K=-33 60531.1489 MHz; K=-7 Extreme shifters; towards radio astronomy

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Effelsberg Radio Telescope

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Effelsberg Radio Telescope

K=-33 K=-1 K=-7

PKS-1830-211

at z=0.88582 (7 Gyrs look-back)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Result from three telescopes

Chajnantor, Chile 5 km altitude IRAM-30m 261 GHz 160 GHz

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lectures ICTP Winter School on Optics 2016 Precision Spectroscopy of Molecular Hydrogen

and Physics Beyond the Standard Model Wim Ubachs LaserLaB, Vrije Universiteit Amsterdam

Part 3 3) New forces and dimensions from precision studies of H2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The Standard Model of Physics What do we know ? What do we not know ?

• Dark Matter
• Dark Energy
• How does Gravity fit to SM ?
• Why is Gravity so weak ?
• Constants are constant ?

Are there only 3+1 dimensions ? Are there only 4 forces ? In atomic/molecular systems:

• Gravity can be ignored
• QCD can be ignored (except nuclear spin)
• Weak force can be ignored (in light systems)

Test of QED = Test of Standard model

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Historical Note: Lamb shift

Willis E Lamb

Breakdown of the Dirac theory of the electron The advent of Quantum Electro Dynamics Measurement of the tiny 2S1/2 – 2P1/2 splitting in H-atom

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Precision measurements on quantum levels:

• n weak and strong lines

E2 E1

• h

E E

• 1

2

• Cu

E2 E1

• h

E E

• 1

2

• Cu

A

• Bu

B C

3 3

8 c h B A

• A

1

• Einstein coefficients

2 2 2

3

ij

e B

• Dipole strength

Lifetime Heisenberg uncertainty

• 2

1

• Strong lines broadened

Weak lines narrow

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

1000 cm-1 = 0.1239 eV

QED in the H2 ground state

Black and Dalgarno, Astroph. J. 203 (1976) 132

Long-lived quantum states H2 has no dipole moment Possibility for precision spectroscopy

• Very weak transitions
• Use excited states ?

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Decomposition of dissociation energy in H2

For v=0, J=0

Ab initio theory:

• K. Pachucki et al., JCTC 5, 3039 (2009)

and many papers

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Frequency metrology of the EF-X two photon transition in H2

EF, v=0, J=0 = 150 ns Fourier-transform limited pulses, 20-40 ns

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Amplifier and conversion to deep-UV

0.2 mJ/pulse at 202 nm

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

• S. Hannemann et al. Phys. Rev. A74, 062514 (2006)

Frequency measurement via Frequency-comb laser

Measure fcw via beat-note comb, via RF filter Fix at 22 MHz

100 m Master

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Transition Energies Q0 99164.78691(11) Q1 99109.73139(18) Q2 99000.18301(11) HD Q0 99301.34662(20) Q1 99259.91793(20) Q0 99461.44908(11) Q1 99433.71638(11) Q2 99378.39352(11) H2 D2

= 1 x 10-9

H2 EF-X (0,0) Q(1) line

Result

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

• High Precision measurements on rotation less X 1+

g-EF 1+ g (0,1) band

• Bypassing the direct quadrupole measurement
• Accuracy of 2x10-4 cm-1
• Good agreement with ab initio provides a stringent test of QED in molecules

1 uncertainty with ab initio calculations

Dickenson et.al, Phys. Rev. Lett., 110, 193601 (2013)

Fundamental vibration in H2

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

EF1g

+, v=0, N=0,1

t~150 ns X1g

+,

v=0, N=0,1 H2

+ : X2g +,

v+=0, N+=0,1 54p

Measurement of IP in H2 : 3 step approach

1. 2. 3. Ei (ortho) = 124 357.237 97 (36) cm-1 Ei (para) = 124 417.491 13 (37) cm-1

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Benchmark: Dissociation energy H2

Do(H2) = EIP(H2 ) + Do(H2

+) - EIP(H)

Do(H2

+) = 21379.350232(50) cm-1

EIP(H) = 109678.7717426(10) cm-1

EIP(H2) Do(H2)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

QED D0: Comparison Theory/Experiment

Theory: Pachucki et al.

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Jmax (v=0) = 8 T

equiv = 12,000 K

• Phys. Rev. Lett. 107, 043005 (2011)

Rotational effects on QED: hot hydrogen

Photolysis chemical production of hot H2 Two-photon spectroscopy/ compare QED

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Q(1)

Precision study of H2 X1g

+ v=12 Now; Three independent lasers Production of H2, v=12 Photolysis of H2S Steadman & Baer (1989)

JCP Comm 142 (2015) 081102

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

• W. Ubachs et al., J. Mol. Spectrosc. 320, 1 (2016)

Experiment – QED Calculation comparisons

MHz Various precision experiments: full agreement with QED theory

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Interpretation: Molecules as a metrology test system

Search for physics beyond the Standard Model from molecular spectroscopy experiment

Test of theory (QED) New Physics: Theory is needed – only for “calculable” systems this is possible Hydrogen has become a calculable system

theory

E E E

• exp

2 2 exp theory

E E E

• E

E

• E

E

• E

E Vnew

• Discover new physics

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Is there a fifth force ?

Yukawa potential (Phenomenological)

Hideki Yukawa

Assume: Extra hadron-hadron interaction Parametrize (quantum field theory) as:

• c

r r N N r V

• /

exp

5 2 1 5

Strength: Range: Mass of force carrying particle: Hadron numbers: N1, N2

5

• c

m5 /

• 5

m

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Calculate the expectation value of the energy operator

5 1 5 1

;

• V

V

• r ~ 0.75 A

N2 N1

v=1

v=0

Level shifts: Transition shift: Differential effect larger for very high v’s (D0 limit)

5 1 5 1

• V

V

• )

( / exp ) ( ) ( / exp ) (

' ' ' ' ' ' ' ' ' ' ' ' 2 1 5 , 5

r r r r r r r r c N N V

J v J v J v J v

• Calculable from the known wave functions for H2; parameters 5 and

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Impose constraints on 5th force from spectroscopy H2

E V

• 5
• c

N N E

• 2

1 5

hence

For HD+ see : Nature Comm. 7, 10385 (2016)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Molecules

Salumbides, Ubachs, Korobov

• J. Mol. Spectr. 300, 65 (2014)

Search for 5th forces; the grand picture

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Physics of extra spatial dimensions

Immanuel Kant:

Number of dimensions consequence

• f Newton's Universal law of gravitation

Flux Law:

Immanuel Kant

3-dim: N-dim: Gravitational attraction depends on dimensionality

encl V

kQ A d F

• 2

2

1 r F r A

V

• 1

1

1

• N

N V

r F r A

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

“Compactification”

Oscar Klein

Theory of consistent EM + Gravity in 5 dimensions (Kaluza) Extra dimensions are not observed in the macroscopic world They may be compactified: rolled up (Klein 1926) String theory: “M-Theory” (Witten) is consistent in 11 dimensions

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

ADD and Large Extra Dimensions

Arkani–Hamed, Dimopoulos, Dvali theory

Electromagnetism, Weak and Strong forces confined in normal (3+1)-dim space Gravity leaks out to extra n-dim diluting its strength Gauss law dictates deviation from (1/r)-form of potential for r<<Rn

Hierarchy problem: Why is gravity so much weaker? Or: Why is the Planck mass Mpl so much bigger?

• Phys. Lett. B 429, 263–272 (1998)

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Gravity in Extra Dimensions with compactification r R m m G r V

n comp n ADD

1 ) (

2 1 ) 3 (

• for

r m m G r VNewton 1 ) (

2 1 3

• n

R r

1 2 1 ) 3 (

1 ) (

• n

n ADD

r m m G r V

for

n

R r

Gravity outside Klein radius Gravity inside Klein radius

• 3

) 3 (

G R G

n comp n

• n

comp ADD

r R r m m G r V

• 2

1 3

) (

derive Enhancement factor for gravity in n extra dimensions

Newton ADD

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

A Cavendish torsion balance at 1 Å distance

2 protons in H2 behave quantum mechanically

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

R

Angstrom-scale Cavendish experiment

Two protons act as Cavendish gravitating balls Better to have large differences between quantum states

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

ADD in Molecules

• 1

1 1 2 1

1 1

n n G ADD

r r N N V

• n

n

R R n n n G ADD

dr r r r r dr r r r r R N N r V

2 * 2 1 * 2 1

) ( 1 ) ( ) ( 1 ) ( ) (

• Expectation value for the ADD-compactification in a molecule:

Difference between two quantum states: Test for:

E VADD

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Constraints from H2 D0

M-theory (10 dim): Compactification on m scale !! Rc < 0.6 m

• E. J. Salumbides, A. N. Schellekens, B. Gato-Rivera, W. Ubachs, New J. Phys. 17 (2015) 033015

Forbidden region n extra dimensions

• )

1 ( 2 1

• n

G n comp

r N cN E R

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

OUTLOOK: A future molecular test system for physics

Lifetimes 106 seconds (!) Quadrupole transitions ~ 1014 Hz Possible precision 20-digit

There is room at the bottom guys

Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Thanks & Acknowledgement

Edcel Salumbides Kjeld Eikema Michael Murphy Frederic Merkt Krzysztof Pachucki Julija Bagdonaite MingLi Niu