Quantum Computation II Experimental Realization

In this article the experimental prerequisites for ion trapping will be explained. The experimental setup, including a ultra-high vacuum chamber, photoionization, detection and Doppler cooling lasers will be discussed. The experimental control of the trap electrode voltages via a FPGA-based DAC board will be introduced.

Overview

1. Place the ion trap in ultra-high vacuum (UHV) chamber

2. Lower the pressure of UHV chamber down to $10^{-12} \, \mathrm{mbar}$.

   • bake the vessel for several weeks in an oven at $150 ^\circ\mathrm{C}-200 ^\circ\mathrm{C}$ reduce pressure to $10^{-10} \, \mathrm{mbar}$.

   • connect with a residual gas analyzer (RGA) monitor residual volatile molecules.

   • connect with an ion gauge to monitor pressure.

   • use a titanium sublimation pump coat the inner surfaces of the chamber with a titanium layer.

     /* Explanation: Clean titanium is very reactive, serving as a getter material. Sublimed titanium molecules can chemically react with reactive gases, like O₂ and N₂ , and disassociate and diffuse H₂ . */

   • use an ion pump to emit electrons and ionize residual molecules or atoms by collisions. The ionized molecules are then directed to and bounded by titanium layer, using strong magnetic field.

   Maintenance: vent under argon reflow

3. Load neutral calcium.

   • Crystalline calcium is placed into an evaporative oven placed below the trap and then evaporated.
   • The neutral calcium beam is directed into the main vacuum chamber and loaded above the trap through that $100 \, \mathrm{\mu m}$ wide slit.

4. Ionize calcium

   • First, a blue $423 \,\mathrm{nm}$ laser excites the atoms from the $^1S_0$ ground state to the $^1P_1$ state

   • Second, a red $732 \,\mathrm{nm}$ laser exciting $^1P_1$ to the $^1D_2$ state.

   • Last, a infrared $832 \,\mathrm{nm}$ laser is used for exciting the neutral atoms beyond the ionization limit of 6.1130 eV and creating positively charged $^{40}\mathrm{Ca}^+$ ions.

     /* Note: Spectroscopic notation $^{2S+1}L_J$ */

   

5. Doppler Cooling

Qubit

$^{40}\mathrm{Ca}^+$ could serve as an optical qubit. In the figure above, the electronic energy levels of $^{40}\mathrm{Ca}^+$ ion are depicted (neglecting the Zeeman splitting sublevels). The qubit is formed by the $S_{1/2}$ and $D_{5/2}$ levels and provides an excited state lifetime of $\tau = 1.2 \,\mathrm{s}$.

Readout of the qubit state is achieved by detection of fluorescence on the $S_{1/2} \harr P_{1/2}$ transition: if the qubit is in the ground state, the $397\, \mathrm{nm}$ laser will transfer the ground state population into the $P_{1/2}$ state and the fluorescence counts can be detected with a photomultiplier tube. The excited state will not yield fluorescence due to its long lifetime.

In order to deplete the excited state population and de-excite the qubit, the $D_{5/2} \harr P_{3/2}$ transition is driven.

In order to drive the $S_{1/2} \harr D_{5/2}$ transition, extremely narrow band lasers with line widths below $200 \,\mathrm{mHz}$ are used. Achieving
this accuracy requires laser-locking to ultra-high finesse cavities.

Doppler Cooling

To be continued.