Report

Experimental Quantum Correlations in Condensed Phase: Possibilities of Quantum Information Processing Debabrata Goswami CHEMISTRY*CENTER FOR LASERS & PHOTONICS*DESIGN PROGRAM Indian Institute of Technology Kanpur Funding: * Ministry of Information Technology, Govt. of India * Swarnajayanti Fellowship Program, DST, Govt. of India * Wellcome Trust International Senior Research Fellowship, UK * Quantum & Nano-Computing Virtual Center, MHRD, GoI * Femtosecond Laser Spectroscopy Virtual Lab, MHRD, GoI * ISRO STC Research Fund, GoI Students: A. Nag, S.K.K. Kumar, A.K. De, T. Goswami, I. Bhattacharyya, C. Dutta, A. Bose, S. Maurya, A. Kumar, D.K. Das, D. Roy, P. Kumar, D.K. Das, D. Mondal, K. Makhal, S. Dhinda, S. Singhal, S. Bandyopaphyay, G. K. Shaw… Laser sources and pulse characterization What is an ultra-short light pulse? τΔν = constant ~ 0.441 (Gaussian envelope) Laser Time-Bandwidth Relationship • For a CW Laser 5. 1 ) x *2 (ni s 1 5. 0 0 Delta function ~0.1 nm 5 .0 - 1- 0 5- time 01 - 5 .1 51 - 02 - wavelength • An Ultrafast Laser Pulse • Coherent superposition of many monochromatic light waves within a range of frequencies that is inversely proportional to the duration of the pulse Short temporal duration of the ultrafast pulses results in a very broad spectrum quite unlike the notion of monochromatic wavelength property of CW lasers. e.g. Commercially 10 fs (FWHM) available 94 nm Ti:Sapphire Laser at 800nm wavelength time Pulse Characterization: Intensity Autocorrelation 800 Spectral intensity (a.u.) Non-collinear Intensity autocorrelation M1 SPITFIRE PRO 600 400 200 0 600 650 700 750 800 850 900 950 100 150 1000 Wavelength(nm) M1 BS M1 L M1 1.2 M Mirror L Lens BS Beam Splitter PD Photo Diode Delay BBO PD 1.0 SHG Intensituy (a.u.) M1 M1 0.8 0.6 30 fs 0.4 0.2 0.0 -200 -150 -100 -50 0 50 Delay (fs) 200 Laser Pulse Profile Laser central wavelength ~730 nm, Pulse width: ~180 fs Pulse Characterization Under Different Repetition rate 1.4 1 kHz raw dtata 1 kHz fitted data 500 Hz raw data 500 Hz fitted data 333 Hz raw data 333 Hz fitted data 250 Hz raw data 250 Hz fitted data 200 Hz raw data 200 Hz fitted data 100 Hz raw data 100 Hz fitted data 50 Hz raw data 50 Hz final data 25 Hz raw data 25 Hz fitted data 20 Hz raw data 20 Hz fitted data 10 Hz raw data 10 Hz fitted data 5 Hz raw data 5 Hz fitted data 1.2 SHG Intensity (a.u.) 1.0 0.8 0.6 0.4 0.2 0.0 -400 -300 -200 -100 0 100 Pulsewidth (fs) 200 300 400 Laser repetition rate (Hz) 1000 500 333 250 200 100 50 25 20 10 5 Pulse width (fs) 47 52 58 59 62 67 69 80 81 88 111 Ideal Two-Level System F∆ + ∅ Ω N (t )) G 2 GΩ 0 G H2 2 1 H FM ℏ ∗ * 1 1 E(t ) 0 (t )ei.t i (t ) I J J 0 J K 1 2 R N 1(t)=k(eff.(t))N/ N N eff n R 2 1 n d (t ) dt i 2 [ (t ), H FM (t )] Phys. Rep. 374(6), 385-481 (2003) 1 Electric Field Rabi Frequency Intensity Time Resonance offset (Detuning) Effect of Transform-limited Guassian Pulse Excited state population w.r.t Rabi frequency and detuning Effect of Transform-limited Hyperbolic Secant Pulse Excited state population w.r.t Rabi frequency and detuning Consider a & let the be For Rotating Wave Approximation (RWA) to hold: Though this may hold for the central part of the spectrum for a very spread-out spectrum (e.g., few-cycle pulses), it would fail for the extremities of the spectral range of the pulse. To prove this point, lets rewrite the above equation as: At the spectral extremities FAILS FAILS RWA Failure When we go to few cycle pulses, we need to evolve some further issues… Few cycle limit? 150 150 With RWA 100 Without RWA Area Area 100 50 -1.5 -1.0 -0.5 0 0.5 1.0 Detuning 1.5 0 -1.5 -1.0 -0.5 Pulse in Time Domain with FWHM = 1.016576e+02 fs 0 0.5 1.0 Detuning 300 1.5 200 Intensity (arbitrary units) 0 50 100 Secant Hyperbolic Pulse 6-cycles limit 0 -100 -200 -300 0 50 100 150 200 250 Time (fs) 300 350 400 450 Observations & Problem Statement… • The constant area theorem for Rabi oscillations, at zero detuning, fail on reaching the higher areas (and hence, intensity). • This is dependent on the number of cycles in each pulse. So, let us define a threshold function for the area, for each type of profile: where n is the number of cycles, and the minimum is taken over the inversion contours of the corresponding proﬁle. Study the DEPENDENCE of ‘χ’ on ‘n’ for DIFFERENT pulse envelop profiles Effect of Six-Cycle Gaussian Pulse Effect of Eleven-Cycle Gaussian Pulse Effect of Thirty-six Cycle Gaussian Pulse χ(n) χ(n) Typical Example: cosine squared χ(n) characterizes the critical limit of area, after which the cycling effect dominates the envelop profile effect, for few-cycle pulses This measure is DEPENDENT on the envelop profile under question. Present Status • Many cycle envelop pulses: • Area under pulse important • Interestingly, • Envelop Effect still persists even in the few cycle limit results • Measure of nonlinearity has to be consistent over both the domains… The plane wave equations for the two photons and the combined wave function is given by: Hamiltonian. Thus This two-photon transition probability is independent of δ, the time delay between the two photons • Relative Photon delay is immaterial • Virtual state position is also not extremely significant • Coherent Control • Bioimaging • Multiphoton Imaging • Optical Tweezers • 2-D IR Spectroscopy Femtosecond Pulse Shaper Measurement of Nonlinearities