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Wave Packet Echo in Optical Lattice and Decoherence Time Chao Zhuang U(t) University of Toronto Aug. 15, 2006 CQISC2006 Aephraim Steinberg Matthew Partlow Samansa Maneshi Jalani Kanem Department of Physics, Center for Quantum Information and Quantum Control, Institute for Optical Sciences University of Toronto Outline • Pulse echo – Two level system – Life time: T1, T2, T2* – How it works & in What system • Wave packet echo in optical lattice – Setup and Measurement – Optimize echo pulse – Decoherence and coherence control Something General w a 0 b 1 1 1 Ω 0 0 0 1 1 0 0 u T1 longitudinal lifetime v 0 1 0 De-population T2 transverse homogeneous lifetime De-coherence T2* transverse inhomogeneous lifetime De-phase Pulse echo: How it works w pulse, t3 t1t2 pulse, Free Evolution 2 20 0 δ( ) δ 0 ρ(0 ) after pulse, t3 t1t2 after pulse, 2 20 ρρ(0 ) ρ Ω0 u * t4 overlap t2 T2 revive to max T1 T2* v t(1 )t ρ T2 t pulse Pulse echo: Timeline 2 0 pulse t1 pulse t2 t3 t4 t T2* T2* t P T2* Pulse echo: Why it’s important Inhomogeneous decay due to dephasing can be reversed! (De)coherence time due to homogeneous decay can be measured directly. Coherence time decides how long quantum information can be stored in a quantum system. Pulse echo: What system Spin Echo Photon Echo Nuclear Magnetic Resonance E. L. Hahn, Phys. Rev. 80, 580 (1950) Optical Resonance N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964) Wave Packet Echo F. B. J. Buchkremer, R. Dumke, H. Levsen, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 85, 3121 (2000) Optical Lattice & Wave Packet Optical lattices are periodic potentials formed by the ac Stark shift (light shift) seen by atoms when they interact with a set of interfering laser beams. I. H. Deutsch and P. S. Jessen, Phys. Rev. A 57, 1972(1998). Motional atoms in optical lattice Motional wave packets in optical lattice Experimental Setup: Vertical Optical Lattice AOM2 PBS TUI Amplifier Grating Stabilized Laser AOM1 PBS 85Rb Cold atoms T ~ 8μK Lattice spacing ~ 0.93μm Spatial filter Function Generator PBS Controlling phase of AOMs allows control of lattice position Measuring State Population Thermal state Initial Lattice Ground State 1st Excited State After adiabatic decrease Well Depth Isolated ground state 0 t1 t(ms) Preparing a ground state t1+40 2 bound states 1 bound state 7 ms 0 t1 t1+40 Measuring Coherence: Oscillations in the Lattice P0 y = m3*sin(m0*2*3.14/m1+m2)*... 0.8 0.7 Value 208.54 1.801 0.33918 0.46156 238.96 0.43667 0.9413 Error 1.1254 0.027114 0.0072664 0.0015033 5.6669 NA NA dephasing due to lattice depth inhomogeneities ~ T2* m1 m2 m3 m4 m5 Chisq R decaying oscillations 0.6 0.5 0.4 w 0.3 0.2 200 400 600 800 1000 1200 1400 1600 t(μs) coherence preparation shift 0 t=0 v θ t t measurement shift u Anatomy of an Echo 0.8 original oscillation 0.7 0.6 oscillation from echo pulse 0.5 0.4 0.3 0.2 0.1 the echo itself 0 0 500 1000 1500 2000 2500 t Dephasing due to primarily lattice inhomogeneities Echo in the Lattice (using lattice shifts and delays as coupling pulses) θ 0 1 echo (amp. ~ 9%) ; max. 13% (see also Buchkremer et. al. PRL 85, 3121(2000)) single shift t Losssingle~80% 0.8 θ 0 echo (amp. ~ 16%) 0.6 double shift + delay tp~ (2/5 T) t 0.4 0 0.2 Lossdouble~60% θ echo (amp. ~ 19%) rms~ (T/8) t(s) 1000 1200 1400 1600 1800 2000 2200 2400 Uo =18ER ,T = 190μs, tpulse-center = 900s Gaussian pulse t LossGaussian~45% Preliminary data on Coherence time in 1D and 3D Lattice 0.08 1D 0.07 echo amplitude 3D 0.06 0.05 0.04 0.03 0.02 0.01 0 2000 2200 2400 2600 2800 echo at (s) Decoherence due to • transverse motion of atoms • inter-well tunneling, 3000 3200 2D Fourier Spectroscopy echo pulse apply exc detect det echo pulse detect det apply exc memory det det memory exc 1 T2* exc drive freq. [Hz] Initial Results observed oscillation freq. [Hz] driven ‘monochromatically’ with 10 cycles What if we try “bang-bang”? (Repeat pulses before the bath gets amnesia; trade-off since each pulse is imperfect.) “bang-bang” pulse sequences... Some coherence out to > 3 ms now... Summary • Optimisation of certain class of echo pulses • Preliminary work on 3D lattice • Preliminary work on characterization of frequency response of the system due to Quasimonochromatic excitation • Observation of higher-order Echoes Future work • Characterize homogeneous and inhomogeneous broadening through 2D FT spectroscopy • Design adiabatic pulses for inversion of states • Study decoherence due to tunneling