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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Implementing qubits in an entangled Bose-Einstein condensate

Michael F. Brown

Published Jul 31, 2002• 0 citations
Publisher

Abstract

An experimentally realized Bose-Einstein spinor condensate is analyzed. The condensate of sodium atoms in their F equals 1 hyperfine state is optically trapped by a focused, near- infrared laser beam which eliminates many limitations associated with magnetic traps. A minimal theoretical description of the system is formulated and solved for motion along one dimension. The significance of the results of the solution, for possible use in quantum computing, is discussed.

DOI
10.1117/12.477422

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An experimentally realized Bose-Einstein spinor condensate is analyzed. The condensate of sodium atoms in their F equals 1 hyperfine state is optically trapped by a focused, near- infrared laser beam which eliminates many limitations associated with magnetic traps. A minimal theoretical description of the system is formulated and solved for motion along one dimension. The significance of the results of the solution, for possible use in quantum computing, is discussed.
Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ condensed atoms were transferred into the optical trap. Densities of up to $3\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$ of Bose condensed atoms were obtained, allowing for a measurement of the three-body loss rate constant for sodium condensates as ${K}_{3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}{\mathrm{cm}}^{6}{\mathrm{s}}^{\ensuremath{-}1}$. At lower densities, the observed 1/e1/e1/e lifetime was longer than 10 s. Simultaneous confinement of Bose-Einstein condensates in several hyperfine states was demonstrated.
Summary form only given. Bose-Einstein condensates (BEC) are generally produced by evaporative cooling of laser cooled atomic samples in magnetic traps. Though magnetic traps are indispensable for the production of a BEC, they pose restrictions on the possible studies with a BEC. Previous experiments of our group have demonstrated that it is possible to trap a BEC in the circular focus of a far-detuned infrared laser beam. This first realization of an optical dipole trap (ODT) for BEC was used to prepare and investigate spinor condensates of Na atoms in the F=1 hyperfine manifold. However, the initial peak density in this ODT after loading from the magnetic trap reached 10/sup 15/ atoms/cm/sup 3/, leading to rapid losses due to three-body collisions. To realize an ODT capable of storing large condensates for a long time, we have used a laser beam with an elliptical beam profile. The optical trap is loaded by superimposing the light field onto the magnetic trap and then slowly turning off the magnetic fields. The transfer efficiency is close to 100%, and thus more than 10/sup 7/ Bose-condensed atoms can be loaded into the ODT.
Summary form only given.We have established an experimental and theoretical program focused on understanding photon atom interactions in condensates with the aim of probing the properties of condensates as well as testing our models of the interactions themselves. With a combination of laser and evaporative cooling, we are routinely creating million atom Bose-Einstein condensates of sodium atoms in the newly designed 4D magnet. Our experimental setup incorporates a candlestick atomic beam source, which provides for recirculation of uncollimated sodium atoms, The laser cooling step involves a zero-crossing Zeeman slower, magneto-optic trap, and polarization gradient cooling. The laser-cooled atom cloud is loaded into the 4D magnetic trap and adiabatically compressed to high density and an evaporative cooling process is initiated. Using a RF magnetic resonance technique, hot atoms are ejected through magnetic spin flips. After formation of the condensate in the tightly confining trap, we manipulate the condensate by adiabatically changing the trapping potential and through interaction with photons. We have developed a technique for probing the condensates directly inside the trap using near-resonant absorption imaging. This imaging technique gives high sensitivity to details of the condensate wavefunction and to its surface structure. Images of pure condensates are compared to calculations of the condensate wavefunction based on a Hartree mean field description of the two-body interaction between condensate atoms.
We created sodium Bose-Einstein condensates in an optically plugged quadrupole magnetic trap. A focused, 532-nm laser beam repelled atoms from the coil center where Majorana loss is significant. We produced condensates containing up to $3\ifmmode\times\else\texttimes\fi{}{10}^{7}$ atoms, a factor of 60 improvement over previous work and a number comparable to the best all-magnetic traps, and transferred up to $9\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms into a purely optical trap. We compare our observations with a simple model of evaporative cooling, concluding that a laser in the range of 1 W (rather than 5 W) may suffice.
Optical trapping as a viable means of exploring the physics of ultracold dilute atomic gases has revealed a new spectrum of physical phenomena. In particular, macroscopic and sudden occupation of the ground state below a critical temperature—-a phenomenon known as Bose-Einstein condensation—-has become an even richer system for the study of quantum mechanics, ultracold collisions, and many-body physics in general. Optical trapping liberates the spin degree of the BEC, making the order parameter vectorial (‘spinor BEC’), as opposed to the scalar order of traditional magnetically trapped condensates. The work described within is divided into two main efforts. The first encompasses the all-optical creation of a Bose-Einstein condensate in rubidium vapor. An all-optical path to spinor BEC (as opposed to transfer to an optical trap from a magnetic-trap condensate) was desired both for the simplicity of the experimental setup and also for the potential gains in speed of creation; evaporative cooling, the only known path to dilute-gas condensation, works only as efficiently as the rate of elastic collisions in the gas, a rate that starts out much higher in optical traps. The first all-optical BEC was formed elsewhere in 2001; the years following saw many groups worldwide seeking to create their own version. Our own all-optical spinor BEC, made with a single-beam dipole trap formed by a focused CO₂ laser, is described here, with particular attention paid to trap loading, measurement of trap parameters, and the use of a novel 780 nm high-power laser system. The second part describes initial experiments performed with the nascent condensate. The spinor properties of the condensate are documented, and a measurement is made of the density-dependent rate of spin mixing in the condensate. In addition, we demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of the condensate, whose populations have been coherently evolved through spin dynamics. We drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, nominally number-correlated through the angular momentum-conserving collision m=0 + m=0 ⇌ m=+1 + m=-1 have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates.
Summary form only given. The optical trapping of sodium Bose condensates has opened the possibility to study spinor condensates which have their hyperfine spin as a new degree of freedom. They represent a superfluid system with a vector order parameter. A host of novel phenomena have been predicted. A spinor condensate such as the one realized by Stamper-Kurn et al. involves all three hyperfine states in the lowest energy f=1 manifold and thus poses challenges towards the understanding of the low energy properties and dynamics of such systems. We consider a Bose condensate which contains atoms with three internal spins in a cigar-shaped trap and approximate the wavefunction of the spin state.