Quantum Logic with Cavity QED

Our current research is focused on realizing neutral atom systems capable of storing and manipulating quantum information. The major thrust of our experimental effort is to develop a neutral atom cavity QED system capable of generating controllable quantum entanglements between distinguishable atoms. We have developed atom traps designed to trap small arrays of atoms inside high-finesse optical resonators. Our next step is to incorporate these atom traps into our assembled high-finesse optical resonator. Successful implementation of this plan will enable coherent quantum information processing between atomic qubits readily scalable to ~20 qubits.

Atom-Photon Entanglements

The quantum bus between the atomic qubits in our system will be the single photon quantum field of a high-finesse optical cavity. The atom-cavity (‘cavity QED’) system has been a cornerstone of theoretical quantum optics for the last 40 years. This strongly interacting system intrinsically entangles atomic degrees of freedom with the quantum field of the cavity in the absence of dissipation. It is only in the last 10 years or so that the mirror polishing and coating technology has advanced to the level required to make sufficiently low-loss (or high finesse) cavities needed to successfully realize this system in the laboratory. In addition to the intrinsic atom-photon entanglement, extensions of this system have been suggested and demonstrated for generating atom-atom and photon-photon entanglements. Taken as a whole, the cavity QED system offers considerable flexibility for both generating and transmitting quantum information.

Atom-atom entanglements

One particularly promising idea for generating scalable entanglements is schematically illustrated in the figure to the right and is due to Zoller’s group. In this scheme, an adiabatic passage technique is utilized to create atom-atom entanglements via state transfer between the two atoms. The cavity field serves as a quantum information bus between the two atoms, and, in the simplest sense, the two atoms interact by ‘sharing’ a single photon field of the cavity.

Successfully implementing this or other related ideas in an atom-cavity system requires simultaneously meeting many experimental challenges, including:

•Localization of an array of atoms or ions within the cavity.

•Achievement of large atom-cavity coupling rate g₀ relative to the cavity decay rate k and the atomic spontaneous emission rate G (strong coupling regime).

•Ability to address the atoms individually with external laser fields and prepare and measure ground state coherences of the individual atoms.

•Long coherence times for the atomic ground states and appropriate atomic level-schemes for implementing the adiabatic passage.

Scalable quantum logic

We will employ neutral rubidium atoms confined in the fields of two focused standing-waves formed by retro-reflected CO₂ laser beams. Individual atoms will be trapped at the anti-nodes of the standing wave, which have a periodicity of 5.3 mm (half of the CO₂ laser wavelength). Quantum logic gates between arbitrary atoms can be performed by first linearly translating one or both of the standing waves in the vertical direction to bring the two atoms of interest into the cavity mode. The key point is that the gate operation only involves two atoms at a time; hence there is no need for the other, non-participating, atoms to be inside the cavity mode. It is important to note that the cavity field is typically in the vacuum state and experiences non-zero excitation only during the gate operation itself (~1 ns)—no coherence of the cavity field is required from gate to gate.

Trapping the photon

We have been developing high-finesse resonators suitable for cavity QED experiments. A photo of one of our resonators is shown here. This cavity has a length of 200 mm, and a finesse of 600,000.

Trapping the atom

One of our principal objectives is to develop single atom dipole force traps allowing for individual addressing, long storage time for atomic coherences and compatibility with the small optical cavities. Hence, we have devoted significant effort to develop traps with these capabilities.

We employ a dipole force trap formed by a focused, retro-reflected infrared (CO₂) laser beam. The trapping potential is where is the ground state polarizability of the atom (rubidium) and is the spatially varying laser intensity. The retro-reflected beam forms a standing-wave intensity pattern, , with a waist = 50 mm and a Rayleigh range = 750 mm which yields a 1-D array of miniature traps separated by = 5.3 mm. For typical parameters in our trap, the maximum potential depth is ~1 mK, which is much larger than the temperature of the laser cooled atoms (~10 mK). We load the trap from a vapor-cell magneto-optic trap (MOT), and we initially load ~10⁶ atoms distributed over ~400 different anti-nodes. A typical false-color image of the trap obtained by imaging the resonant florescence of the atoms is shown.

We have also developed more complicated trap geometries required for creating scalable entanglements in the atom-cavity scheme. Three different geometries are shown in Figure 5. Both the 2-D and the 3-D traps are new traps first developed in our laboratory. Both of these traps may be useful for other lattice-based neutral atom quantum information applications in addition to the atom-cavity system we are pursuing.

Images of ultracold rubidium atoms trapped in different configurations of laser beams. Left to right: dual 1-D traps, crossed 1-D traps, and 3-D lattice trap formed at trap intersections.

Magnetic spin-spin interactions for quantum logic

We have proposed an implementation of a quantum logic scheme utilizing the direct magnetic spin-spin interaction between individually trapped neutral atoms. The qubits of this system are stored in the long-lived hyperfine ground states of atoms, and coherent control of the spin-spin interactions is accomplished by controlling inter-atomic spacings. Our proposal is distinctive in that 1) the magnetic spin-spin interaction used to create the inter-atom entanglement is virtually decoherence-free and 2) atom-atom interactions are mediated via a movable ‘‘header’’ atom that serves to transfer quantum information from one qubit to another. The header atom can in fact be a different species, and hence, in contrast to other lattice proposals, the atom trapping potentials are not required to be spin-dependent in order to maintain trap distinguishability for small atom separations and can be realized with far-detuned laser beams. This latter distinction is important because near-resonant laser traps are a significant source of decoherence. (L. You and M.S. Chapman, Phys. Rev. A, 62, 052302 (2000)).