QUANTUM COMPUTING: Trapped sodium atoms lose remaining degrees of freedom

A technique demonstrated by researchers at the National Institute of Standards and Technology (NIST; Gaithersburg, MD) appears to complete a decades-long quest for total control of atomic motion. For many years scientists have controlled atomic internal states through nuclear-magnetic resonance and Raman scattering to change the spin. And in the last 20 to 25 years, laser cooling and trapping has been used to control the linear-momentum state. Now, the NIST researchers have demonstrated control of the orbital angular momentum (OAM) or the rotation state around a center of mass; finally it appears that all degrees of freedom have been accounted for.

The researchers used a two-photon stimulated-Raman process to transfer OAM from photons in two counterpropagating laser beams to a cloud of sodium atoms trapped in a Bose-Einstein condensate (BEC). The NIST team is the first to actually demonstrate a process that has been described theoretically during the past decade numerous times, according to team member Kristian Helmerson. But unlike theoretical proposals for making up and down Raman transitions between different spin states, the NIST group went from at-rest to in-motion between two different OAM states. This was essentially a matter of practicality, Helmerson said. Because the atoms were confined in a magnetic trap, changing spin states would have released them from the trap. The team is currently looking into demonstrating the theoretically proposed method also, he said.

Raman stimulation was applied to the cloud of trapped sodium atoms by counterpropagating Laguerre-Gaussian (LG) and Gaussian (G) laser beams with the same linear polarization and a variable frequency difference. The wavelengths of the two counterpropagating beams were detuned slightly from the 589 nm excited-state resonance for sodium.¹

The variable frequency difference imparted a linear momentum to the atoms in the Bose-Einstein condensate, and orbital angular momentum was imparted by the OAM difference between the longitudinal Gaussian beam and the radial intensity profile and helical phase of the LG beam. The vehicle for linear-momentum transfer was diffraction of atoms through a moving optical dipole potential generated by the frequency-difference-induced interference of the counterpropagating beams. The optical-dipole potential was not sinusoidal, however, because of the orbital angular momentum of the LG beam. Interference between the two counterpropagating beams created an interference pattern in the shape of a corkscrew instead of the standing wave that would have been created between two plain Gaussian beams. The pitch of the corkscrew was determined by the wavelength of the beams.

Any desired 2-D atomic state

Diffraction from this optical-corkscrew pattern produced a rotating state in the condensate, a matter wave diffracted by the corkscrew into a donut-shaped cloud of atoms, in essentially the reverse of the diffraction process that generated the rotating LG beam from a plane Gaussian. Helmerson described this as the atom-optics analogue of a phase hologram, enabling one to generate any desired 2-D atomic state using a suitable hologram. “In this case we’ve actually made a grating out of light and diffracted the matter wave to create a donut shape,” he said. “We have a program in atom optics to create atomic analogues of optical phenomena.”

They also demonstrated the coherence necessary for quantum processing, by creating superpositions of different rotation states within the BEC, where the relative phase between the states was determined by the relative phases of the optical fields. “People have already used the orbital angular moment of photons for quantum information processing,” Helmerson said. “Now we can do it with atoms.”

The process offers a new and well-controlled way of creating a vortex state in a BEC and generating arbitrary superpositions of atomic rotational states; thereby complementing existing tools for controlling linear momentum and spin angular moment, and thus enabling total control of an atom, Helmerson said. “But this is just the first experiment and more refinements are yet to come,” he added.

In addition to superposition of macroscopic states in atomic vapors for quantum information processing, potential applications include generating superflows in which, for instance, the orbital angular momentum of condensate atoms confined to a ring-shaped trap lossless flow, similar to the toroidal superflow of liquid helium or to the lossless flow of electrons in a superconductive material.

The research team included staff from NIST and the Joint Quantum Institute operated by NIST and the University of Maryland (College Park, MD), and guest researchers from the Indian Institute of Science (Bangalore, India) and the Institut für Experimentalphysik, Universität Wien (Vienna, Austria).

REFERENCE

1. M.F. Andersen et al., Phys. Rev. Lett. 97, 107406 (DOI: 10.1103/PhysRevLett.97. 170406) week ending Oct. 27, 2006.