Absorption and Fluorescence Studies on Hyperfine Spectra of Rb and Dressed state picture Sabyasachi Barik National Institute of Science Education and Research, Bhubaneswar Project guide- Prof. C.S.Unnikrishnan Tata Institute of Fundamental Research, Mumbai VSRP-2012 talk
Motivation Improve resolution of spectroscopy to study lightmatter interaction To get a clear picture treat both light and atom quantum mechanically To explain Autler-Townes doublets, Mollow triplet (observed in lab ) full quantum mechanical treatment of Light- atom interaction has to be done.
Spectral line splitting Fine structure splitting : spin angular moment(s) interacts with orbital angular moment(l) to give total angular moment(j) j=s+l and l-s <j<l+s Selection rules: Δj = ±1 or 0 For Rb:[Kr]5s 1 (ground state) and [Kr]5p 1 (excited state) Hyperfine splitting : Magnetic moment of nucleus interacts with total angular moment of electron to give hyperfine levels F=j+I and j-i <F<j+I Selection rules : ΔF = ±1 or 0
5 2 P3/2 Hyperfine splitting of Rubidium(Rb Rb) Hyperfine energy level diagram of 87 Rb for D2 line 780.023 nm 266.65 MHz 156.947 MHz 72.218 MHz F =3 F =2 F =1 F =0 Hyperfine energy level diagram of 85 Rb for D2 line 5 2 P3/2 780.023 nm 121.0 MHz 63.4 MHz 29.3 MHz F =4 F =3 F =2 F =1 F=2 5 2 S1/ 2 6.384 GHz 5 2 S1/ 2 3.04 GHz F=3 F=1 F=2
Doppler broadened spectra of Rb Doppler broadening= due to thermal motion of atoms Theoretically At room temperature ν D ~ 0.5 GHz From expt ν D(87) = 0.5214 GHz and ν D(85) = 0.5217 GHz Theoretically ν 12(87) = 6.38 GHz and ν 23(85) =3.04 GHz From expt ν 12(87) = 6.72 GHz and ν 23(85) =2.99 GHz
Doppler free saturation absorption spectroscopy Doppler-free saturation spectroscopy technique allows to resolve the energy levels with much more precision, limited only by the natural line width. Probe beam Detector Pump beam Rb atom vapor cell Put intense pump and less intense probe from opposite direction At the cross point :both interacts with zero velocity atom. Atoms with non zero velocity whose Doppler shift is midway between the transition lines Crossovers
Absorption spectrum Theoretically ν 12(87) = 156.95 MHz ν 23(87) = 266.65 MHz Experimentally ν 12(87) = 158.70 MHz ν 23(87) = 269.33 MHz Theoretically ν 01(87) = 72.22 MHz ν 12(87) =156.95 MHz Experimentally ν 01(87) = 78.33 MHz ν 12(87) = 158.50 MHz
Fluorescence Theoretically ν 12(87) = 156.95 MHz Experimentally ν 12(87) = 156.56 MHz Theoretically ν 34(85) = 121 MHz Experimentally ν 34(85) = 121.66 MHz
Power Broadening => y intercept = Γ 2 = 56.21 MHz 2 Γ= 7.497 MHz τ= (21.23 ±6.54) ns literature value = 27.70 ns
Dressed state picture When we go to atoms and photons then fully quantized theory can only explain that. Hamiltonian for SHO and electromagnetic field looks the same electric field canonical position magnetic field canonical momentum for quantization Jaynes-Cummings Model(fully quantized Rabi model) en ± =(n + ½ )ħω±ħω(δ) Ω(δ) Rabi frequency Ω(δ) = new states- dressed states
Autler -Townes effect Two transitions between a> and b>, b> and c> Drive the a and b transition with ω L frequency pump laser. A very weak field with frequency ω probes the transition b c. how the absorption of the probe field is modified when the transition a b is driven by the field ω L.
Experimental data from a previous experiment Atomic beam experiment Pump and probe are perpendicular to atomic beam line. No Doppler broadening. Autler-Townes effect in Na a> = F=2, M F = 2 of 3S1/2 level b> = F=3, M F = 3 of 3P3/2 level c> = F=4, M F = 4 of 4D5/2 level Laser A as pump at 589 nm Laser B as probe which scans around 568.8 nm as the resonance Reference : AUTLER-TOWNES EFFECT IN DOUBLE OPTICAL RESONANCE,H.R. GRAY and C.R. STROUD, Optics Communication 25 (1978) 3.
Autler -Townes Effect proposed experimental setup Pump unused Rb cell unused Probe 5 2 P3/ 2 780.023 nm 5 2 S1 / 2 pump probe F =3 F =2 F =1 F =0 F=2 PD F=1 If I = 10 mw/mm 2 as the pump then Γ pow = 150 MHz but Ω =212.132 MHz so we can resolve the Autler-Townes doublet.
Conclusions The hyperfine levels of Rb were studied by Absorption and fluorescence. Lifetime was measured from power broadening. Autler-Townes effect study was done. Future step Set up an experiment to see the Autler-Townes effect. Acknowledgements Prof. Unnikrishnan, project guide Dr. Rajalaksmi, Dr. Raghavan, Dipankar Dr J. Dasgupta, VSRP coordinator VSRP and IAS friends THANK YOU
References [1] B.H. Bransden and C.J. Joachain :Physics of Atoms and [2] Christopher J. Foot: Atomic [3] Wolfgang Demtroder :Laser Spectroscopy [4] William Thomas Silfvast :Laser Fundamentals [5] Christopher C. Gerry and Peter L. Knight :Introductory Quantum Optics [6] J. Ye, S. Swartz, P. Jungner, and J. L. Hall, Opt. Lett. 21(16),1280 (1996). [7] DL100 Manual(Toptica)[http://www.toptica.com]