Samansa Maneshi, Jalani Kanem, Chao Zhuang, Matthew Partlow Aephraim Steinberg Department of Physics, Center for Quantu

1. Preserving Coherence of Atoms and Characterizing Decoherence Processes in an Optical Lattice Samansa Maneshi, Jalani Kanem, Chao Zhuang, Matthew Partlow Aephraim Steinberg Department of Physics, Center for Quantum Information and Quantum Control, Institute for Optical Sciences University of Toronto

2. Motivation • Controlling coherence of quantum states is the fundamental problem in the field of quantum information processing • Need to characterize real world systems and be able to perform error corrections with no a priori knowledge of the errors Outline • Measuring quantum states in the lattice • Coherence in the lattice and Pulse-echo • 2D spectroscopy and characterization of broadening

3. AOM2 PBS TUI Amplifier Grating Stabilized Laser AOM1  PBS PBS Spatial filter Function Generator Controlling phase of AOMs allows control of lattice position Cold 85Rb atoms T ~ 8μK Lattice spacing ~ 0.93μm VerticalOptical Lattice Experimental Setup

4. Thermal state Initial Lattice Ground State 1st Excited State After adiabatic decrease Well Depth Isolated ground state 0 t1 t1+40 t(ms) Preparing a ground state 2 bound states 1 bound state 7 ms 0 t1 t1+40 Measuring State Populations

5. 0.8 displace the lattice 0.7 0.6 0.5 0.4 0.3 P0 coherence preparation shift 0.2 1000 1200 θ 200 400 600 800 1400 1600 0 decaying oscillations t = 0 t t pre-measurement shift t(μs) Oscillations in the Lattice dephasing due to lattice depth inhomogeneities

6. Echo in the Lattice (using lattice shifts and delays as coupling pulses) 0 θ (see also Buchkremer et. al. PRL 85, 3121(2000)) echo (amp. ~ 9%) single shift Losssingle~80% 0 θ echo (amp. ~ 16%) double shift + delay tp~ (2/5 T) t Lossdouble~60% θ 0 echo (amp. ~ 19%) Gaussian pulse rms~ (T/8) t LossGaussian~45% Uo =18ER ,T = 190μs, tpulse-center = 900s ; max. 13% t

7. Preliminary data on Coherence time in 1D and 3D Lattice Decoherence due to • transverse motion of atoms • inter-well tunneling,

8. • • • • • • expected 2ndorderecho expected 3rd order echo oscill’ns due to pulse 1st order echo 21of pulse1 1ms 500μs 1ms 500μs T ´=3ms T =2.2ms pulse1 pulse2 Higher-Order Echoes (Dynamical Decoupling) P0 decaying oscillations

9. echo pulse echo pulse apply detect detect apply memory memory 2D Fourier Spectroscopy

10. Quasi-Monochromatic Excitation drive with 5-period sinusoid instead of abrupt shift abrupt shift responds at T=210μs drive at  = 150μs responds at T=180μs drive at  = 190μs responds at T=200μs

11. Preliminary data on Linear Fourier Spectroscopy Frequency Power Spectrum Frequency Spectrum width ~1400Hz

12. Summary • Optimisation of certain class of echo pulses: • Larger echo amplitude and less loss of atoms due to Gaussian pulse compared to square and simple pulse • Observation of higher-order Echoes • Preliminary work on characterization of frequency response of the system due to Quasi-monochromatic excitation Future work • Characterize homogeneous and inhomogeneous broadening through 2D FT spectroscopy • Design adiabatic pulses for inversion of states • Study decoherence due to tunneling