Wave Packet Echo in Optical Lattice and Decoherence Time

1. Wave Packet Echo in Optical Lattice and Decoherence Time Chao Zhuang U(t) Aug. 15, 2006 CQISC2006 University of Toronto

2. 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

3. 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

4. Something General T1 longitudinal lifetime De-population T2 transverse homogeneous lifetime De-coherence T2* transverse inhomogeneous lifetime De-phase

5. Pulse echo: How it works

6. Pulse echo: Timeline

7. 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.

8. Pulse echo: What system • Spin Echo • Nuclear Magnetic Resonance • E. L. Hahn, Phys. Rev.80, 580 (1950) • Photon Echo • 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)

9. 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

10. 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 Experimental Setup:Vertical Optical Lattice

11. Measuring State Population 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

12. Measuring Coherence: Oscillations in the Lattice 0.8 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 measurement shift t(μs) dephasing due to lattice depth inhomogeneities ~ T2*

13. Anatomy of an Echo original oscillation oscillation from echo pulse the echo itself Dephasing due to primarily lattice inhomogeneities

14. 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

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

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

17. Initial Results drive freq. [Hz] observed oscillation freq. [Hz] driven ‘monochromatically’ with 10 cycles

18. What if we try “bang-bang”? (Repeat pulses before the bath gets amnesia; trade-off since each pulse is imperfect.)

19. “bang-bang” pulse sequences...Some coherence out to > 3 ms now...

20. 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 Quasi-monochromatic 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