Ion-trap quantum computation Summer School of CQIQC 2012

Laser Lab Prof. Vasant Natarajan Department of Physics Indian Institute of Science Bangalore May 25, 2012

Paul trap – dynamic stabilization Mathieu equation

Mechanical analogue of the stabilization – from Paul’s Nobel lecture

Mathieu stability plot

Spectrum from harmonically-oscillating particle fm modulation with depth of modulation kx 0 Tight confinement – Lamb-Dicke regime x 0 << λ

,,,, Cooling laser tuned to lower motional sideband Sideband cooling | e > | g>

Ca + energy levels 4P 3/2 4P 1/2 Shelving 850 nm 397 nm Cooling 866 nm Repumping 3D 5/2 3D 3/2 4S 1/2

Life time measurement • Shelving technique by Dehmelt observation of quantum jumps to determine the lifetime • Both lasers run continuously and we observe the fluorescence photons at a rate of a few kHZ. • For a time in order of 1 s we apply a third laser at 4P 3/2 –3D 3/2 transition.

• By decay of 4P 3/2 level the ion may fall into the metastable 3D 5/2 the fluorescence vanishes. state and • Repeat the process and determine the time intervals where no fluorescence is observed after blocking the shelving laser.

Life time measurement Histogram of the dark periods for a single ion. The experimental data are fitted by an exponential

Linear Paul trap design Each section length = 15mm Rod diameter = 6 mm r 0 = 2.66 mm For axial trapping additional DC field = 150 V RF between diagonal rods for radial trapping V 0 ω 0 = 100 V = 2 MHZ UHV= 10 -10 torr Ions get trapped in a linear chain on the axis of the trap

Photos of linear ion trap

Experimental requirements • Need three lasers working simultaneously – Cooling (397), Repumping (866), and shelving (850) • Use 397 nm fluorescence from hollow cathode lamp to lock cooling laser • Mix all the beams in a hollow-core fiber and transport them to the experiment • Use an ICCD Camera for detection

Experimental Schematic

Ca + energy levels 4P 3/2 4P 1/2 Shelving 850 nm 397 nm Cooling 866 nm Repumping 3D 5/2 3D 3/2 4S 1/2

Why Calcium • Has a lambda level scheme with two lying metastable 3D states • Ca+ has a closed shell plus a single valance electron. • No outer correlation exist but core effects play an important role • Electric field of the valence electron causes a core polarization leading to modified nuclear electric field seen by the outermost electron to explore new physics.

Advantages of trapped ions for quantum computation • Near-perfect two level system formed of a ground level and a metastable excited level • Decoupled from the environment and well isolated in vacuum for long storage times • Internal states can be initialized and measured with extremely high accuracy • Laser pulses can be used to manipulate electronic and motional degrees of the ion string

Acknowledgements Workshop – Manohar, Sharief Students – Ayan Banerjee, Dipankar Das, Dipankar Kaundilya, Lal Muanzuala, Durgesh Datar, Zeba Naqvi Money – DST and CQIQC

Sideband Cooling