TIQC Research

Entanglement of Ultracold Ions

One of the areas of current research is in using lasers to manipulate and probe entangled states of trapped cadmium ion qubits, relying on the mutual Coulomb repulsion between ions. Qubits are stored in particular hyperfine states of the Cd⁺ ground state, and multiple qubits are coupled through their mutual Coulomb repulsion in the trap, mediated by appropriate external laser fields. Implementing these types of entangling quantum logic gates requires exquisite control of the motional state of the ions, including the laser cooling of ions to near the ground state of motion. Worldwide heating measurements of trapped ions.

Recent highlights in this project include:

Laser cooling to the ground state of motion for multiple ions, and the characterization of motional heating from the ground state in 100-200 micron trap structures.
Identification and demonstration of a particular entangling quantum gate that is insensitive to phase noise from optical and magnetic fields.
Entanglement of two ¹¹¹Cd⁺ ion "clock states" and full tom ographic recons truction of the entangled state with single-qubit rotations and near-perfect detection of multiple qubits with a CCD camera.

The execution of the Grover quantum search algorithm on two qubits, or four states. Univ. of Michigan Press Release on this experiment

Heating in Ion Traps

Many groups have measured heating of trapped ion motion, in terms of the rate dn/dt of vibrational quanta added to the system. Below is a record of all known measurements in traps with motional frequencies between 0.6-6.0 MHz. (If you have a new measurement, please send it to us to be included.)

Assuming that this heating stems for a noisy resonant electric field, we can infer the electric field noise spectral density S_E(w) [units: (V/m)²/Hz], removing the dependence on the atomic ion mass and the trap frequency:

Below is a history of inferred electric field noise scaled from from the above heating measurements in 0.6-6.0 MHz traps, as a function of the distance d to nearest electrode. A simple model of thermal heating (Johnson noise) predicts a 1/d² scaling (or 1/d³ scaling when the skin depth of the electrode material is large compared to d). For fluctuating "patch" potentials of size << d, a 1/d⁴ scaling is expected. See Turchette, et al., and Deslauriers, et al. for a more detailed discussion. Future measurement will hopefully fill the lower left corner of this plot!