June 03, 2009

Ultracold - Two Ion Quantum Computer Proposal

Apparatus for generating a two-color optical lattice. Co-propagating beams at both wavelengths are incident on a diffractive optical element (DOE) shown in (a), formed by a photolithographed gold-coated fused silica surface consisting of a regular array of raised equilateral triangles. The image shown was obtained with an atomic force microscope. In (b), reflected light is diffracted, primarily into three first-order beams at each wavelength in a triangular pattern. These beams are then routed by a pair of lenses to form a pair of triangular optical lattices shown in (c), on the image plane of the DOE. The relative position of the two lattices is controlled with a set of electro-optic phase modulators, formed by patterned deposition of mirror/electrodes onto the rear surface of a single lithium-niobate crystal. The lattice structure shown was imaged with a microscope objective onto a CCD camera.

Ultracold molecules: vehicles to scalable quantum information processing in the New Journal of Physics

In this paper, we describe a novel scheme to implement scalable quantum information processing using Li–Cs molecular states to entangle 6Li and 133Cs ultracold atoms held in independent optical lattices. The 6Li atoms will act as quantum bits to store information and 133Cs atoms will serve as messenger bits that aid in quantum gate operations and mediate entanglement between distant qubit atoms. Each atomic species is held in a separate optical lattice and the atoms can be overlapped by translating the lattices with respect to each other. When the messenger and qubit atoms are overlapped, targeted single-spin operations and entangling operations can be performed by coupling the atomic states to a molecular state with radio-frequency pulses. By controlling the frequency and duration of the radio-frequency pulses, entanglement can be either created or swapped between a qubit messenger pair. We estimate operation fidelities for entangling two distant qubits and discuss scalability of this scheme and constraints on the optical lattice lasers. Finally we demonstrate experimental control of the optical potentials sufficient to translate atoms in the lattice.

A truly scalable quantum computer information processing remains an elusive goal. This is due in part to the stringent requirements on long coherence times, the technical difficulties in implementing high fidelity entangling operations, and the challenge to store and control interactions between many quantum bits (qubits). While neutral atoms provide a natural advantage in coupling weakly to their environment and to other atoms at long distance, atomic interactions at short-range, well described by contact interactions, can be strong, coherent and their effect can be controlled by overlapping the atomic wavefunctions. In particular, the strength of this contact interaction is highly sensitive to underlying molecular structure, and can be precisely manipulated by introducing direct coupling mechanisms between free atoms and molecules.

A system using both ultracold molecules and atoms held in an optical lattice may be a promising system to realize a scalable quantum computer due to the high degree of control available in these systems.

The proposal presented here is a novel approach to use two atomic species, each manipulated by a separate optical lattice potential. Highlighted is the fabrication of lattice structure independent of optical wavelength, use of molecular states to induce entanglement between atoms and introduction of single site addressability without the need for spatially resolved manipulations.

A key aspect of this approach is the introduction of auxiliary messenger atoms used both to probe and to manipulate quantum states and entanglement in an array of qubit atoms. By utilizing two separate species of atom for these two roles and carrying information in their internal states, it becomes technically feasible to manipulate spatial overlap of atoms and thereby their interactions, without disrupting the sensitive quantum coherences. We propose to use fermionic 6Li atoms as qubits, prepared in the lattice with ideally one atom per site. Bosonic 133Cs will act as messenger atoms to aid in the gate operations and mediate entanglement among the qubits, and will be less densely populated, on average, by one atom per 100 sites of a separate lattice potential of identical structure to the first. By shifting the relative alignment of the lattices through optical phases, each 133Cs atom can, in principle, be transported to any distant 6Li atom; similar schemes can be found. Since there may be many 133Cs atoms, multiple copies of the same computation can proceed in parallel.

Implementation of the necessary gates via coupling to a molecular state |M. Not only does the molecular state allow entangling operations to be carried out between the atoms, but it also allows single qubit addressing. Part (a) shows how to execute a targeted single qubit rotation. When the atoms are overlapped, rf pulses allow the qubit atom to be rotated into a superposition state. Part (b) shows the sequence to entangle two distant qubits. After entangling messenger and qubit (step 1), the messenger can be transported to a second qubit and subsequently entanglement can be exchanged (step 2).

We have presented a scheme for scalable quantum information processing based on two species of ultracold atoms held in controlled bichromatic optical lattice potentials, including methods to entangle 6Li and 133Cs atoms locally through coupling to bound 6Li–133Cs molecules, and methods to transport entanglement to distant atoms through multiple quantum manipulations. We have identified simple quantum logic gate operations possible in this scenario. Methods are based on the production of translatable optical lattices at two wavelengths with identical structure, for which we have demonstrated a novel realization utilizing diffractive optics and electro-optic modulation. We have discussed gate operations in detail, identifying necessary timescales for entangling via a molecular state and transporting atoms adiabatically. This compares favorably with the expected coherence time, including the effects of off-resonant scattering, qubit tunneling, external field instabilities and state-dependent light shifts. Finally, we have analyzed the effects of realistic experimental uncertainties to ascertain expected fidelities, and compared this with measured errors in lattice construction; with incremental improvement in passive stability, fidelities of > 97% are achievable in entangling distant qubits.

Plot of limits on the intensities of the 681 nm optical lattice L1 versus the 1064 nm optical lattice L2. The diagonal black lines show the bounds imposed by requiring independent control of L1 over 6Li and L2 over 133Cs. Also shown are the tunneling rate limit and off-resonant scattering rate limit for both 6Li (blue lines) and 133Cs (red lines) for a decoherence rate of 2 s–1. The green shaded box shows the available parameter space satisfying all of the above conditions. The black dot corresponds to conditions assumed for calculations in the text.

The capability to independently control the two atomic species allows us to have single site addressability of the qubit atoms. This is accomplished by shifting the optical phases of the messenger lattice, allowing the 133Cs messenger atom to be translated to any 6Li qubit atom. This is a necessary step for many operations in this proposal, including detection and creation of a universal gate set.

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