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

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

Ca + energy levels Cooling Shelving Repumping

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 state and the fluorescence vanishes. 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 = 100 V ω 0 = 2 MHZ UHV= 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 Cooling Shelving Repumping

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