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# Quantum Computation

### Quantum Manipulation and Quantum Computation

The key parameter for the realization of a non-trivial quantum computor depends on the number of quantum bits, or qubits. Scalable quantum systems with more than a few qubits are not yet realized.

Two species of ultracold atoms in optical lattices constitute a very promising system to realize a scalable quantum computer. Using two sets of optical lattices, we can independently control the two atomic species to transport the quantum information or to induce the entanglement. In particular, molecular state can be used to mediate the entanglement via Feshbach resonance or Raman-coupling.

For the two atomic species, one fermionic can form ideal quantum registors in an optical lattice. The second species is treated as messengers to exchange the quantum information of the registors and to induce the necessary quantum entanglements.

#### Full proposal

Computation in the realm of quantum mechanics can be exponentially faster than its classical counterpart for certain algorithms. In spite of the abundance of proposals to implement quantum computation in various physical systems, few systems have yet been experimentally demonstrated or can in principle be scalable to many quantum bits (qubits). This is due to the stringent requirements on the long coherence time and high efficiency in entangling the qubits.

Ultracold atoms in an optical lattice formed by optical standing waves are a promising system to realize a scalable quantum computation system. By tuning the relative phase of the standing waves, arbitrary two atoms can be entangled by bringing them into close spatial vicinity [1]. Repeating the above entanglement process on different atom pairs, we can establish quantum entanglement of many atoms. Since atoms can be individually trapped in the lattice with a typical periodicity of 0.5um, 1000 qubits can be localized within a very small volume of 5 um^{3}.

To extend the above scheme to a scalable quantum computer, I will confine two atomic species in two sets of optical lattices: atoms of the first kind act as qubits and the second kind as messengers. While the qubits store the quantum information, the messengers move between two qubits in order to induce entanglement between them. To move only the messenger atoms, we externally control their corresponding optical lattice. By repeating the above process for many pairs of qubits, the quantum entanglement between multiple atoms can be realized and scalable. Furthermore, when the two lattices consist of laser beams with commensurate wavelengths, multiple computation machines can function simultaneously.

The three primary objectives of this project are the

- Formation of an optical lattice with specific atomic occupancy number. Ultracold atoms can be loaded into singly-occupied or multiply-occupied lattice sites by an adiabatic transfer into the lattice. The site occupancy number can be experimentally determined by radio-frequency or microwave-frequency transition. For singly-occupied sites, we expect a long coherence time, due to the absence of the atomic collisions. For multiply-occupied site, we will investigate ways to determine the atom number by radio-frequency or microwave spectroscopy.
- Entanglement of two or three atoms at one optical lattice site The collisional shifts at multiply occupied sites allow us to implement quantum entanglement via coherent radiative excitation. Assuming two bosonic atoms are in the motional ground state and can occupy two internal ground states |+> and |->, the system is described by the triplet states |++>, |+->+|-+> and |-->, which in general acquire different collision shifts. The available entangled states |+->+|-+> and |++>+|--> can be prepared by selectively driving the transition to the target state.
- Transportation and entanglement of two atomic species For a scalable system, a system with two atomic species and two independently controlled optical lattices will be investigated. Coherence time of the atoms in the lattice will be examined by precision Ramsey spectroscopy. Studies on the two-species cold collision properties will allow for a best strategy to entangle the atoms.

#### Reference

[1] C. Chin, V. Vuletić, A.J. Kerman and S. Chu, in Proceedings of the XV. International conference on Laser Spectroscopy (World Scientific) (2001).

Related: cesium-lithium mixture experiment.