Cold atoms in Optical lattice, vibrational states, coherent control via interference between one- and two-phonon excitation, and a little bit about decoherence, Chao Zhuang Quantum Optics Day 2009 Department of Physics University of Toronto Aephraim Steinberg Luciano Cruz Samansa Maneshi Nick Chisholm Ardavan Darabi XiaoXian Liu Chris Paul

Outline Experiment Setup Things I will talk about Interference between one- and two-phonon excitation Coherent control using one- and two-phonon Possible way of probing decoherence Things I will talk a little about Echo experiment Pump-probe experiment

Experiment Setup

1D vertical lattice 1D optical lattice: interference of two laser beams g

Cold atoms in optical lattice g Dilute gas No interaction between atoms Fluorescence image Optical Lattice: Lattice spacing : a ~ 0.93μm ER ~ 32nK, U0 =(18-20)ER = (580-640)nK =103 atoms/plain Photon scattering rate ~ 60ms to 100ms MOT: Cold 85Rb atoms T ~ 10μK =1010atoms/cm3

Prepare and measure the states Initial Lattice After adiabatic decrease Thermal state Well Depth t(ms) t1 t1+40

Prepare and measure the states Initial Lattice After adiabatic decrease t1+40 2 bound states t1 7 ms 1 bound state Well Depth t(ms) Isolated ground state

Prepare and measure the states Initial Lattice After adiabatic decrease t1+40 2 bound states t1 7 ms 1 bound state Well Depth t(ms) Isolated ground state

Operations of lattice Use AOM to control the relative phase between the two lattice beams equivalent to displace the lattice in the real space Use AOM to control the intensity of the lattice beam equivalent to change the lattice depth

PM and AM Phase modulation (PM) Amplitude modulation (AM) Relative phase Amplitude modulation (AM) Intensity of laser beam

Things I will talk about

Interference! No Interference No interference Constructive Destructive

One- v.s. two- phonon excitation Interference between the transition probability of the one-phonon excitation and two-phonon excitation aPM aAM

Typical Experiment Data! AM 20% 8cyc TAM = 100ms PM 6o 4cyc TPM = 200ms

How to change the PM loss Experiment Data Simulation aPM aPM

Search with different PM loss Experiment Data Simulation

Coherent control, one v.s. two Branching Ratio

Only relative phase is varied Experiment Data Simulation Red lines indicate different Branching Ratio

Decoherence probe?

Things I will talk a little about

Decoherence Coherence Possible source of decoherence The ability to interfere A stable relative phase Possible source of decoherence Atoms see different lattice depths Atoms move in transverse plain Tunneling from one well to another Photon scattering

Echo experiment Atoms see different lattice depths, but each atom sees only one lattice depth relative phase between ground and excited states Decoherence: dephasing Reverse the ground state and excited state at time T, rephase at 2T, by probing at different 2T, decoherence due to other sources can be observed Each runner has a different constant running speed

Higher-order echo Each runner with a constant acceleration Atoms are moving, which means the lattice depth each atom sees is changing N-th order echo can fix (N-1)-th time depend frequency drift 2nd order echo: T-reverse-2T-reverse-T-revive 3rd order echo: T-reverse-(1+√2)T-reverse - (1+√2)T-reverse-T-revive

Pump-probe experiment 2D contour plot

Generic way to predict echo decay 2ms Delay 5ms Delay 0 1 2 N t ...

Thank you! One more comment: Interference is EVERYWHERE and USEFUL!