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: T 1, T 2, T 2 * –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 T 1 longitudinal lifetime De-population T 2 transverse homogeneous lifetime De-coherence T 2 * 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 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). & Wave Packet Motional atoms in optical lattice Motional wave packets in optical lattice

10. Experimental Setup: Vertical Optical Lattice 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

11. 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 Measuring State Population

12. dephasing due to lattice depth inhomogeneities ~ T2* 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 measurement shift θ Measuring Coherence: Oscillations in the Lattice

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

14. 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%

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

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

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. 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 Summary