Lectures ICTP Winter School on Optics 2016 Precision Spectroscopy of - PowerPoint PPT Presentation

Vibrational motion - 2 � � 2 2 d 1 � � 2 � � � � � � k � Q ( ) E Q ( ) vib � 2 2 2 � � � d � � So the wave function of a vibrating molecule resembles the 1-dimensional harmonic oscillator, solutions: v / 2 1 / 4 � � � 2 � 1 � 2 � � �� � � Q ( ) exp H � � v v 1 / 4 � 2 � � v ! �� k e � e � � � with: and � � Energy eigenvalues: � � 1 � k � � 1 � � � � E � v � � v � � � vib e � � 2 � � 2 � 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 � � � � E BN ( N 1 ) DN ( N 1 ) rot Anharmonic vibrational motion 2 � � � � � � 1 1 � � � � � E � v � x � v � ... vib e e e � 2 � � 2 � Dunham expansion: k � � � 1 � � � � l 1 � E Y � v � N N 1 vN kl � 2 � k , l Vibrational energies in the H 2 -molecule Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Energy levels in a molecule: general structure v=2 � B v=1 Rovibrational structure J v=0 superimposed on electronic structure v=2 � A v=1 J v=0 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 � l � � s Very small coupling Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Electronic structure of the Hydrogen molecule; adiabatic “gerade” “ungerade” Inversion symmetry X 1 � g + 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: � � � � r , R r ; R R mol i A el i vib � � � � � � � � � � � � e r eZ R e N i A A Dipole transition between two states i A In a molecule, there may be a: � � � � � ' � � " d if - permanent or rotational dipole moment - vibrational dipole moment Two different types of transitions � � 2 � � � � d 1 d ' ' " " � � � � � � � � � � � � � � � � � � 2 d � � � � � � � � � � � if el vib e N el vib N 0 � � � � 2 � dR � 2 dR � � � R � � � ' " ' " e � � � � � � d r d R el e el vib vib � � In atoms only electronic transitions, ' " ' " � � � � � � � d r d R el el vib N vib in molecules transitions within electronic state Electronic transitions 2 � Note for transitions: e 2 � � B Einstein coefficient ij 2 � 3 � 0 Rovibrational transitions Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The Franck-Condon principle for electronic transitions in molecules Intensity of electronic transitions 1 st term: � � � 2 � 2 2 � � ' " ' " ' " � � � � � � � �� � � � � � � � I d R v ' v " d r d R if vib vib if el e el vib vib Only contributions if (parity selection rule) ' " � � � el el Franck-Condon approximation: The electronic dipole moment independent of internuclear separation: � ' " � � � � � M ( R ) d r e el e el Hence � ' " � � � � � M e ( R ) d R if vib vib Intensity proportional to the square of the wave function overlap Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Rovibronic spectra Vibrations � governed by the Franck-Condon principle v=2 Rotations � governed by angular momentum � B selection rules v=1 Transition frequencies J v=0 � � v T ' T " T B � � � T ' T G ' ( v ' ) F ' ( N ' ) B v � � � T " T G " ( v " ) F " ( N " ) A v R and P branches can be defined in the same way � � � � 2 � � � � � � � � 2 B 3 B B N B B N v=2 R 0 v ' v ' v " v ' v " � � � � 2 � � � � � � � B B N B B N � P 0 v ' v " v ' v " A v=1 J T A v=0 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Population distributions;Ϳ vibrations Probability of finding a molecule in a vibrational quantum state: P(v)/P(0) � E ( v ) / kT � � e P ( v ) � E ( v ) / kT e v � � � ( v 1 / 2 ) e 1 � kT e Z Boltzmann distribution H 2 : only v=0 populated at “any” T Note: not always thermodynamic equilibrium Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Population distributions; rotational states in a diatomic molecule HCl Probability of finding a molecule in a rotational quantum state: T=300 K � � � E / kT � 2 J 1 e rot � P ( J ) � � E / kT � ( 2 J ' 1 ) e rot J ' 1 2 2 � � � � BJ ( J 1 ) DJ ( J 1 ) � � ( 2 J 1 ) e Z rot Find optimum via dP ( J ) � 0 dJ Boltzmann-plot H 2 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 � � � � � M m m I= 0, 1 M S = -1, 0, 1 � � I I I ; I I I 1 2 1 2 � � � � � I 1 , M 1 , I � � A triplet of symmetric 1 � � � � � � � � I 1 , M 0 , , nuclear spin wave functions I 2 (symmetry related to interchange) � � � � � � I 1 , M 1 , I � � A singlet of an anti-symmetric 1 � � � � � � � � I 0 , M 0 , , Nuclear spin wave function I 2 Total wave function must be anti-symmetric for interchange of protons (Pauli principle): � � Ortho-hydrogen: triply degenerate A S Odd N -levels: N=1,3,5 … � rot nuc spin � � Para-hydrogen: singly degenerate S A Even N -levels: N=0,2 .. � rot nuc spin Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Isotope effects in molecules; sensitivity for � -variation Electronic Born-Oppenheimer: the derivative of electronic wave function w.r.t nuclear coordinates is small: � � el � 0 A Electronic wave functions and energies do not depend on nuclear masses (compare the case of the atom) 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 � � � k 1 � � � E v Vibrational energy: � vib � � 2 � K-coefficient for purely vibrational transition (overtone included): 1 1 � � � � � � � � � � � � � � � � � � � n 1 / 2 m 1 / 2 n 1 / 2 m 1 / 2 � � � � � � � � � � � � E E � � � � n m 1 � � � � � � 1 � � � � � � E E � � � n 1 / 2 m 1 / 2 n m � � � � � 1 � � � � 1 1 K � � � 2 1 � � For ALL vibrational transitions / vibrational energies K So: � 2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Isotope effects in molecules; sensitivity for � -variation � N ( N 1 ) C � � � � � � � � � � � Rotational energy: 2 E N ( N 1 ) N ( N 1 ) rot � 2 2 1 1 2 � 2 � 2 R 2 R e e K-coefficient for purely rotational transition (or rotational energy): � � � � � � � � d � � � � � � � � � � � 2 � � K C 1 � K � � � � � � d C � � � � � K 1 So: � Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Electronic spectra of H 2 H 2 2p �� H (Lyman- � ) ~ 121 nm 2p �� H 2 , 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 C B X 1 � g + - (2p � ) B 1 � u + X 1 � g + - (2p � ) C 1 � u X Doubly degenerate Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Franck-Condon Factors in H 2 absorption C B X B(v’) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Lyman and Werner band systems � � � component � � � component � � � component 2 (+) 2 (+) 2 (-) B 1 � u 1 (-) C 1 � u 1 (-) 1 (+) + 0 (+) R(1) R(1) Q(1) P(2) P(2) Q(2) R(0) R(0) P(1) 2 (+) 2 (+) 2 (+) X 1 � g X 1 � g + + 1 (-) 1 (-) 1 (-) 0 (+) 0 (+) 0 (+) N � � � � , � Parity N , M Y NM � -doubling lifts degeneracy � � ���� � � components Rotation-electronic coupling (beyond BO) R, P, Q lines Different parity Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

“Isotope effects” in molecules; sensitivity for � -variation Add contributions to sensitivity: E rotational E vibrational - Electronic - Vibrational - Rotational E total In first order: E E E 1 E E � � � � � � K K K K 1 elec vib rot vib rot � elec vib rot E E E 2 E E tot tot tot tot tot E electronic E rotational E vibrational Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Dunham approach to sensitivity coefficients dE � � dE � � � g e � � � K � � Dunham coefficients C 1 � + i � � � � � u E E d d � � e g � � � � Dunham representation: � � k 2 l � � � � 1 � � � � � E v , J � Y v [ J J 1 ] kl 2 k , l With known mass dependence: � � � B � � � � � � � � kl l k / 2 Y A 1 � � kl kl � Dunham coefficients X 1 � + � � g � � dY Y k B � � � � � � kl kl kl l � � � � � d 2 � � Results in: � � � � k dE v , J dY 2 l 1 � � � kl � � � � � v [ J J 1 ] 2 � � d d k , l Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Local perturbations; beyond Born-Oppenheimer 2 � � � � � � 1 1 ' � � � H J L � B , v , J , p J L C , v , J ' , p ' Matrix elements: u B u C 2 � 2 R � � � E ( J ) H J ( J 1 ) � � C CB � � � H J ( J 1 ) E ( J ) � � CB B C 1 � u C(1) � B(10) C(2) � B(12) B 1 � u + C(3) � B(14) C(4) � B(17) X 1 � g + 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

Laser spectrum Hydrogen does not have a “molecular band spectrum” P. Hinnen, W. Ubachs et al. Can. J. Phys 72, 1032 (1994) 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

1 XUV + 1 UV REMPI spectroscopy Evaluation of uncertainties: Error budget Residual Doppler 40 MHz AC Stark 30 MHz Freq chirp (PDA) 100 MHz R(0) B-X I 2 calibration 10 MHz P(3) C-X (9,0) line Statistical 30 MHz (1,0) line Total (best lines): 0.005 cm -1 0.000005 nm 5 x 10 -8 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

L15 R(2) 162 lines measured at ~ 5 x 10 -8 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Conclusion : H 2 dipole-allowed absorption spectrum Lyman (B-X) and Werner bands (C-X) are the strong absorptions (1s – 2p) Molecular database is available � i – set of accurate wavelengths K i – set of sensitivity coefficients f i – set of line oscillator strengths (from ab initio theory) � i – set of damping coefficients (from ab initio theory) 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 H 2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Empirical search for a change in �� Compare H 2 in different epochs Lab QSO � z � 1 � i z � i 0 today 12 Gyr ago i 90-112 nm ~275-350 nm � � 1 � � T T 1 � � Cosmological redshift � � 0 � 3 / 2 1 z � � abs Practical: atmospheric transmission only for z>2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Sensitivity of H 2 red shifter anchor blue shifter 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 1 arcsecond ESO-VLT 2007 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

Calibration with UVES Blue chip: 300-500 nm Red chips: 420-1100 nm 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

Dispersion of Echelle Orders on to CCDs Th-Ar calibration + asteroids + “solar twins” Blue chip Two red chips Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Supercalibrations Solar twin Long-range wavelength distortions Rahmani et al. MNRAS 435 (2013) 861 Whitmore & Murphy MNRAS 447 (2015) 446 Asteroids and ‘Solar Twins’ targets ThAr calibrated spectrum vs FTS spectrum Linear slope correction 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

J2123-005 from HIRES-Keck at Hawaii Resolution 110000 ; z abs =2.0593 H 2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

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

Analysis method: “comprehensive fitting” Produce molecular fingerprint � i – set of accurate wavelengths f i – set of line oscillator strengths (from ab initio theory) � i – set of damping coefficients (from ab initio theory) Astrophysical conditions b � – Doppler width parameter z – red shift N J – column densities � � � � � z � � Fit equation onto spectrum � � � � � � � 1 z 1 z 1 K i � � “Treat” HI and metal lines i abs i � � 0 � � Multiple velocity components (?) i K i – set of sensitivity coefficients Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

The best system: J2123-005 at z abs =2.05 Unique spectrum from Keck;Ϳ Resolution 110000 ;Ϳ seeing 0.3” Spectrum from VLT;Ϳ R=54000;Ϳ seeing 0.8”;Ϳ better SNR 37 panels, 3071 – 3421 Å ~100 H 2 + 7 HD lines Keck: ���� = (5.6 ± 5.5 stat ± 2.9 syst ) x 10 -6 VLT: ���� = (8.5 ± 3.6 stat ± 2.2 syst ) x 10 -6 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Q1441+272 ; the most distant z abs = 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 H 2 absorbers at high redshift Done Done Done Done Rahmani Done Done (+ CO) Done Done Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Status of cosmological � -variation Varying constants and the ratio � m , � �� ������ = (3.1 � 1.6) x 10 -6 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Varying Constants ? Coupling constants are free parameters in Standard Model Bekenstein-Barrow –Sandvik – Mageijo – Light scalar fields � � j � � c � � � � � � � � � � � � � � �� � � � � 2 S L A F F e d 0 � � �� � mat 2 c 4 2 l � � Jacob Bekenstein 1) Coupling to cosmology Variation on cosmological ����� time scales “dark energy dominated” 2) Coupling to matter density -> “chameleons” Coupling to gravity “matter dominated” Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Hydrogen nearby; white dwarf stars in our galaxy Dependence of ���� on gravitational field Cosmic Origins Spectrograph Spectrum of GD-133 and GD29-38 White Dwarf stars H 2 in VUV In search for the Chameleon scenario � WD =(GM/Rc 2 )=10 4 � Earth Hubble Space Telescope 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

Contributions of many lines in the B-X Lyman system � ~ 130-140 nm � � � E � g ( J )( 2 J 1 ) exp � � vJ High temperatures I � kT � � P ( T ) High v populated � � vJ v J ( v ) E � max max � � Franck-Condon factors � g ( J )( 2 J 1 ) exp � � vJ I kT � � � � v 0 J 0 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Dependence of ���� on gravitational field Invoke partition function: � � E � � g ( J )( 2 J 1 ) exp � � vJ I � kT � � P ( T ) � � vJ v J ( v ) E � max max � � � g ( J )( 2 J 1 ) exp � � vJ I kT � � � � v 0 J 0 Invoke intensities (1500 lines): i � I N f P ( T ) col v ' v " J ' J " v " J " Fit T and ����� GD133: ���� = (-2.7 +/- 4.7) x 10 -5 GD29-38: ���� = (-5.9 +/-3.8) x 10 -5 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Outlook: More sensitive molecules Quantum tunneling K = -4.2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Outlook: More sensitive molecules Quantum tunneling: hindered rotation Calculations Extreme shifters Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

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

PKS-1830-211 Effelsberg Radio Telescope at z=0.88582 (7 Gyrs look-back) K=-33 K=-1 K=-7 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Result from three telescopes IRAM-30m Chajnantor , Chile 5 km altitude 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 H 2 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 Measurement of the tiny 2S 1/2 – 2P 1/2 splitting in H-atom Breakdown of the Dirac theory of the electron The advent of Quantum Electro Dynamics Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Precision measurements on quantum levels: on weak and strong lines E 2 E 2 � � � � � � A E E E E h h Cu Cu Bu � � � 2 2 1 1 E 1 E 1 Heisenberg uncertainty Lifetime Einstein coefficients Dipole strength C � B 2 1 1 � e 2 � � � � � � B 3 ij � � 2 �� A 8 h � A 2 3 � � 0 3 B c Strong lines � broadened Weak lines � narrow Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

QED in the H 2 ground state Long-lived quantum states H 2 has no dipole moment Black and Dalgarno, Astroph. J. 203 (1976) 132 Possibility for precision spectroscopy - Very weak transitions - Use excited states ? 1000 cm -1 = 0.1239 eV Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Decomposition of dissociation energy in H 2 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 EF, v=0, J=0 in H 2 � = 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

Frequency measurement via Frequency-comb laser Measure f cw via beat-note comb, via RF filter 100 m Master Fix at 22 MHz S. Hannemann et al. Phys. Rev. A74, 062514 (2006) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Result H 2 EF-X (0,0) Q(1) line Transition Energies H 2 Q0 99164.78691(11) Q1 99109.73139(18) Q2 99000.18301(11) HD Q0 99301.34662(20) Q1 99259.91793(20) D 2 Q0 99461.44908(11) Q1 99433.71638(11) Q2 99378.39352(11) ���� = 1 x 10 -9 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Fundamental vibration in H 2 • 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) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Measurement of IP in H 2 : 3 step approach + : X 2 � g + , H 2 v + =0, N + =0,1 3. 54p 2. EF 1 � g + , v=0, N=0,1 t~150 ns 1. X 1 � g + , v=0, N=0,1 E i (ortho) = 124 357.237 97 (36) cm -1 E i (para) = 124 417.491 13 (37) cm -1 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Benchmark: Dissociation energy H 2 D o (H 2 ) = E IP (H 2 ) + D o (H 2 + ) - E IP (H) D o (H 2 + ) = 21379.350232(50) cm -1 E IP (H) = 109678.7717426(10) cm -1 E IP (H 2 ) � D o (H 2 ) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

D 0 : Comparison Theory/Experiment Theory: Pachucki et al. QED Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Rotational effects on QED: hot hydrogen Photolysis chemical production of hot H 2 Two-photon spectroscopy/ compare QED J max (v=0) = 8 T equiv = 12,000 K Phys. Rev. Lett. 107, 043005 (2011) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Precision study of H 2 X 1 � g + v=12 Q(1) Production of H 2 , v=12 Photolysis of H 2 S Steadman & Baer (1989) Now; Three independent lasers JCP Comm 142 (2015) 081102 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Experiment – QED Calculation comparisons MHz Various precision experiments: full agreement with QED theory W. Ubachs et al. , J. Mol. Spectrosc. 320 , 1 (2016) 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 � � � E E E � � � Test of theory (QED) E E exp theory � � � E E New Physics: � � � � � 2 2 E E E exp theory Theory is needed – only for “calculable” systems this is possible � Hydrogen has become a calculable system � � � � � V new E E Discover new physics Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Is there a fifth force ? Assume: Extra hadron-hadron interaction Parametrize (quantum field theory) as: Yukawa potential (Phenomenological) � � � � � � exp r / � � � � V r N N c � � � 5 1 2 5 � r � Hideki Yukawa � Strength: 5 � � / m 5 c � Range: m Mass of force carrying particle: 5 Hadron numbers: N 1 , N 2 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Calculate the expectation value of the energy operator Level shifts: v =1 � � � � V ; V 1 5 1 0 5 0 Transition shift: v =0 � � � � � V V 1 5 1 0 5 0 N 1 N 2 Differential effect larger for very high v’s (D 0 limit) • r ~ 0.75 A � � � � � � � � � � exp r / exp r / � � � � � � � � V N N c ( r ) ( r ) ( r ) ( r ) � � � � 5 , 5 1 2 v ' J ' v ' J ' v ' ' J ' ' v ' ' J ' ' r r � � Calculable from the known wave functions for H 2 ; parameters � 5 and �� Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Impose constraints on 5 th force from spectroscopy H 2 � E � � � � � � � � V E hence 5 �� N N c � 5 1 2 For HD+ see : Nature Comm. 7, 10385 (2016) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Search for 5 th forces; the grand picture Salumbides, Ubachs, Korobov Molecules J. Mol. Spectr. 300, 65 (2014) Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Physics of extra spatial dimensions Immanuel Kant: Immanuel Kant Number of dimensions consequence of Newton's Universal law of gravitation Flux Law: � � � � � F d A kQ encl V 1 � � � 2 A r F 3-dim: V 2 r 1 � � � � N 1 A r F N -dim: V � N 1 r Gravitational attraction depends on dimensionality Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

“Compactification” 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) Oscar Klein 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 Phys. Lett. B 429 , 263–272 (1998) Hierarchy problem: Why is gravity so much weaker? Or: Why is the Planck mass M pl so much bigger? 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 << R n Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Gravity in Extra Dimensions with compactification ADD Newton m m 1 r � R � � V ( r ) G 1 2 for n ( � ADD 3 n ) n R r comp 1 � � V Newton ( r ) G m m Gravity outside Klein radius 3 1 2 r 1 r � R � � V ( r ) G m m for n � ADD ( 3 n ) 1 2 � n 1 r Gravity inside Klein radius � � n � n G R G derive � ( 3 ) comp 3 n � � R m m Enhancement factor � � � � comp V ( r ) G 1 2 for gravity in n extra � � ADD 3 r r � � dimensions Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

A Cavendish torsion balance at 1 Å distance 2 protons in H 2 behave quantum mechanically Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

Angstrom-scale Cavendish experiment R 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 Expectation value for the ADD-compactification in a molecule: � � R � 1 1 n � � � � � � � � � n * 2 * 2 V ( r ) N N R ( r ) ( r ) r dr ( r ) ( r ) r dr � � ADD G 1 2 n � n 1 r r � � � � 0 R n Difference between two quantum states: � � 1 1 � � � � V N N � � ADD G 1 2 � � n 1 n 1 r r � � � � � � 1 0 � � � V ADD E Test for: Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

� � � E Constraints from H 2 D 0 n � R comp � � � � ( n 1 ) cN N r � G 1 2 Forbidden region M-theory (10 dim): Compactification on n extra dimensions � m scale !! R c < 0.6 � m E. J. Salumbides, A. N. Schellekens, B. Gato-Rivera, W. Ubachs, New J. Phys. 17 (2015) 033015 Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016

OUTLOOK: A future molecular test system for physics Lifetimes 10 6 seconds (!) Quadrupole transitions ~ 10 14 Hz There is room at the bottom guys Possible precision 20-digit Vrije Universiteit Amsterdam;Ϳ W. Ubachs Lecture Notes ICTP Winter College Trieste 2016