1. 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 Preserving Coherence of Atoms and Characterizing Decoherence Processes in an Optical Lattice

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

4. Measuring State Populations Thermal state Ground State 1 st Excited State Initial Lattice After adiabatic decrease Well Depth t (ms) 0 t1t1 t 1 +40 Isolated ground state Preparing a ground state t 1 +40 2 bound states 0 t1t1 7 ms 1 bound state

5. Oscillations in the Lattice displace the lattice dephasing due to lattice depth inhomogeneities 200400600800 10001200 14001600 t (μs) P0P0 decaying oscillations 0.2 0.3 0.4 0.5 0.6 0.7 0.8 coherence preparation shift 0 t t t = 0 pre-measurement shift θ

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

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

8. Higher-Order Echoes (Dynamical Decoupling) P0P0 expected 2 nd order echo 1 st order echo 21of pulse1 oscill’ns due to pulse pulse1pulse2 T = 2.2ms expected 3 rd order echo T ´ = 3ms 500μs 1ms decaying oscillations

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

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

12. 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 Summary