Coherent Enhancement of Linewidth and its ! ! Utilization in Optical - PowerPoint PPT Presentation

Coherent Enhancement of Linewidth and its ! ! Utilization in Optical Determination of 229m Th isomer transition Sumanta Das Wen-Te Liao Adriana Palffy Christoph H. Keitel EMMI Workshop , 26 th Sept 2012 sumanta.das@mpi-hd.mpg.de

! ! Quest for a Nuclear Frequency standard Why ?? Better accuracy and stability Minimum perturbation - thus easier interrogation Candidate : is = 3 / 2 + J π eV 229 Th 7 . 8 ± 0 . 5 g = 5 / 2 + J π B.R. Beck et. al. LLNL-PROC-415170 (2009) W.G. Rellergert et. al. PRL 104, 200802 (2010) C. J. Cambell, A. G. Radnaev and A. Kuzmich, PRL 106, 223001 (2011).

! ! Principle obstacles !! Uncertainty of isomeric energy Weak signal compared to background Signature of Fluorescence ambiguous α - background Incoherent 4 π Γ VUV 229 Th Signal Detector

! ! Possible Solution Measuring the signal in the forward direction Signal High background Incoherent 4 π Γ VUV 229 Th ξ Γ Detector Coherent scattering in the forward direction leads enhancement of linewidth

! ! Possible Solution Measuring the signal in the forward direction Signal High background Incoherent 4 π Γ VUV 229 Th ξ Γ Detector But what about Coherent scattering in the measuring the forward direction leads transition energy ? enhancement of linewidth

! ! Measuring the Transition energy Coherent fast decay in forward direction ∆ Probe Couple coherent FS time spectra of Probe

! ! Measuring the Transition energy Coherent fast decay in forward direction ∆ Probe Couple coherent FS time spectra of Probe Measurement of transition energy with high accuracy

! ! Coherent Forward Scattering - 57 Fe the perfect testbed Coherent Forward Scattering and enhancement of line-width in 229 Th Measurement of Isomeric transition energy using coherent enhancement of line-width

! ! Coherent forward scattering in Nuclei 8329+25 ! !"#"$%&'$()*+,$ !"#"$#%& ! -.,/0123423/$2+56+463/7 ! ()*&+),&$-$!"!$./ ! !"#"$%&' !

! ! NFS of Synchroton radiation !"#$%&'&%'()*+&& )$,'-&#.+$/ ! !"#$%&' ! !"#"$#%& ! Single photon emissison !"#$%&'(&)*%!"+',+'%&+#-$#,$'%&./0121 ! !"#!$%&'()*+)*,#-../,#01*23+)*45)*&6+#7899:;#

! ! Nuclear Exciton ! ! ! ! ! ! ! ! | e � Exciton State recoil-less 1 e i � � k · � r i | g � | e i � √ No spin flip N i | g � Explains Forward Emission Coherent scattering Gives coherent line-broadening in emission Timed-Dicke state Quantum Optics J. P. Hannon and G. T. Trammell, Hyp. Int 123/124 , 127 (1999) !"#$"#%&'(()#*+,#-"#-"#%./,0/+12)3#%&/4+&4#5673#8789#:699;<# ="#=>?(1@4AB4A3#CDD23#%EA/+B4AFG4A(*B#:699H<#

! ! Semi-classical approach Maxwell - Bloch Transition current !"#$"#%&'()*#+,-"#.*#./01#2.3405# 67"#89:;<=>?*#@A"#BC*#+,D"#E3*#3.FG#2.3335# H"#:BI#D&JK>*#L;)@&M'I@#NIA@&BKA"#.GF*#1OF#2.3335# ,"#,P9C(Q@&R@&*#D??>*#8)&'IR@&ST@&CBR#2G0015# U"SV"#W'B?*#-"#+XCMM;*#%"#L"#Y@'A@C*#B&Z':[.G0E"EE0F:.#2G0.G5#

! ! Time domain spectrum of NFS In absence of magnetic field e − Γ t Spontaneous emission !"#"$#%& ! ξ e − Γ t � ξ Γ t )] 2 [ J 1 (2 Dynamical beats Γ t Coherent Decay J ! "#$%&&%'#()*+,-.*#.(#! &, #/-*0# Γ c � "#12.*,3*%.)&#4%+35#63,%# t < 1 / ( ξ Γ ) Γ c = ξ Γ 7"#6%&.*3*,#89-+/*%&& ! J. P. Hannon and G. T. Trammell, Hyp. Int 123/124 , 127 (1999) !"#$%&#'()*+,#-./0(12&0#3&40(%*4"#567,#897#:5;;;<#

! ! In presence of magnetic field J ! "#$%&&%'#()*+,-.*#.(#! &, #/-*0# ξ e − Γ t � "#12.*,3*%.)&#4%+35#63,%# � ξ Γ t )] 2 [ J 1 (2 7"#6%&.*3*,#89-+/*%&& ! Γ t B Quantum Beats !"#"$#%& ! !"#$"#%&'()*#+,-"#.*#./01#2.3405# 67"#89:;<=>?*#@A"#BC*#+,D"#E3*#3.FG#2.3335 !

! ! 229 Th doped VUV crystals 229 Th:LiCaAlF 6 229 Th:CaF 2 Transparent around the probable isomeric wavelength ~ 160 nm High doping density of Thorium ~ 10 18 -10 19 /cm 3 achievable Electronic band gap of 10 eV , no internal conversion 229 Th in the crystal lattice confined to Lamb-Dicke regime, Lamb-Mossbauer factor ~ 1 W.G. Rellergert et. a. PRL 104, 200802 (2010) G. A. Kazakov et. al. NJP 14, 083019 (2012)

! ! Shifts and Broadening Spontaneous line-width of isomeric transition ~ 0.1 mHz Temperature dependent shifts due to electric monopole interaction ~ 10 kHz/K Temperature dependent shifts due to 2nd order doppler effect ~ 70 Hz (77 k) Temperature dependent inhomogeneous broadening due to 2nd order Doppler effect ~ 70 Hz (77k) Inhomogeneous broadening due to magnetic dipole interaction ~ Few hundred Hz Homogeneous broadening ?? W.G. Rellergert et. a. PRL 104, 200802 (2010) C. J. Cambell, A. G. Radnaev and A. Kuzmich, PRL 106, 223001 (2011) G. A. Kazakov et. al. NJP 14, 083019 (2012)

! ! Coherent Line-broadening in 229 Th Why ?? High density of Thorium ~ 10 18 -10 19 /cm 3 229 Th in the crystal lattice confined to Lamb-Dicke regime Mossbauer like transition - no recoil Narrow line-width, weak coupling - favourable condition for formation of exciton Coherent forward scattering same as Fe can be used How much is the coherent broadening ? W.G. Rellergert et. a. PRL 104, 200802 (2010) C. J. Cambell, A. G. Radnaev and A. Kuzmich, PRL 106, 223001 (2011) G. A. Kazakov et. al. NJP 14, 083019 (2012)

! ! σ − [3 m 2 − I is ( g ) ( I is ( g ) + 1)] E is ( g ) ≃ Q is ( g ) (1 − γ ∞ ) φ zz m 4 I is ( g ) (2 I is ( g ) − 1)] E. V. Tkalya, PRL 106, 162501 (2011) G. A. Kazakov et. al. NJP 14, 083019 (2012)

! ! Coherent Line-broadening in 229 Th τ = Γ t ξ = 1 4 σ NL Effective resonance thickness � � c � σ = 2 π 2 I e + 1 1 Nuclear resonance 1 + α f LM cross-section 2 I g + 1 E n Immediately after excitation t < 1 / ( ξ Γ ) ξ Coherent enhancement of decay rate by a factor

σ ≃ 10 − 12 cm 2 ! ! L = 10 mm N = 10 18 - 10 19 / cm 3 ξ ≃ 10 6 − 10 7 Coherent enhancement of Decay Homogeneous line broadening ξ Γ ≃ 0 . 1 − 1 kHz ms time scale for signal collection, high repetition rate of events, lot more data collection Possible issues in measurement VUV pulse train Detector blinded by VUV pulse Th doped crystal Weak Fluorescence Signal

! ! Chopper rotating at Solutions: kHz freq VUV pulse Detector Using a chopper 229 Th to block the VUV excitation pulse Weak Fluorescence signal VUV pulse Rotation of Crystal in ms time scale Th doped crystal Detector Weak Fluorescence signal

! ! Utilization of line-broadening towards determination of the isomeric transition energy

! ! Two field spectroscopy Strong couple, weak probe Autler-Townes Splitting Splitting induced Quantum beats Maxwell - Bloch Equations 1 η = Γ ξ c ∂ t Ω p + ∂ y Ω p = i η a 31 ρ 31 2 L Poster by Wen-Te Liao, EMMI Worshop

! ! Clebsch - Gordon co-efficients of allowed transition √ � ( a 31 , a 32 ) = ( 2 / 3 , − 2 / 15) 3 Relaxation and decoherence rates ( γ 31 , γ 32 , γ 21 ) = 2 π × (251 , 108 , 30) Hz 2 1 Rabi Frequency � 1 / 2 I eff k L − 1 � Ω p ( c ) = 4 √ π p ( c ) ( L + 1) B ( µL ) (2 L + 1)!! Exp [ − n τ 31(2) 2 T ] √ � c ǫ 0 L T = 10 µs n = 1 for probe, = 0 for control Wen-Te Liao, S. Das, A. Palffy and C. H. Keitel, arxiv: 1210.3611 (2012) G. A. Kazakov et. al. NJP 14, 083019 (2012), Poster by Wen-Te Liao, EMMI Worshop

! ! | 3 / 2 , 3 / 2 � ∆ p Ω p E = � ( ω p + ∆ p ) | 5 / 2 , 5 / 2 � Poster by Wen-Te Liao, EMMI Worshop

! ! E = � ( ω p + ∆ p ) Poster by Wen-Te Liao, EMMI Worshop Wen-Te Liao, S. Das, A. Palffy and C. H. Keitel, arxiv: 1210.3611 (2012)

! ! Conclusions Coherent scattering from Th-ensemble in forward direction leads to faster decay - in ms time scale Forward direction suitable for signal measurement, high signal to background ratio, more signal collection in a time interval NFS time spectra of the probe in a couple-probe scheme gives quantum beat - a clear signature of isomeric transition Energy of the isomeric transition can be evaluated to an accuracy of 10Hz by fitting the detuning dependent measured NFS time spectra with theory Thanks for your interest