Studies of Bose-Einstein Condensates

Investigators: Kevin Wright, Suzanne L. Leslie, and Nicholas P. Bigelow.

Latest Project News:

Recent short term project: Redesigned and manufactured the 3 sets of coils for the magnetic trap. Due to this we now ihave better control over the magnetic fields and better repeatibility in our results.

Current experimental focus: The BEC lab is working to transfer orbital angular momentum to a BEC through use of Laguerre-Gaussian beams and a coherent population transfer technique called STIRAP (Stimulated Raman Adiabatic Passage)

We are using two near-resonant Raman detuned beams of differing optical angular momentum (OAM) to couple two different internal atomic spin states and coherently transfer OAM to the center-of-mass motion of a BEC.

Ultracold atomic vapors with momentum distributions much narrower than the photon recoil momentum have created new opportunities to study atom-photon interactions with unprecedented precision. There has been increasing interest in studying interactions involving photons with nonzero orbital angular momentum (OAM), in addition to the more familiar spin and linear momentum degrees of freedom. Investigation of the details of such interactions have revealed a number of interesting phenomena, including the coupling of electromagnetic orbital angular momentum to the atomic center-of-mass motion.

In order to transfer OAM to an ultracold atomic cloud without heating it and destroying the coherence, it is necessary to devise a coupling scheme which avoids excitation and spontaneous emission. There have been a number of theoretical proposals suggesting using a two-photon interaction to accomplish this. [1,2,3] Several References are listed below. Andersen et. al. have demonstrated coherent OAM transfer to an BEC using a Bragg scattering method, in which appropriately detuned counterpropagating OAM beams couple the stationary atoms in the BEC to a state characterized by the difference in linear and angular momentum of the two beam modes. [4] This approach necessarily results in transfer of considerable linear momentum to the atoms in addition to the OAM transfer, but because the atoms remain in the same magnetic sublevel, it has the advantage of being insensitive to the magnitude and stability of the background magnetic field. The method we have explored uses a pair of near-resonant Raman detuned OAM beams in a STIRAP configuration to adiabatically transfer atoms between two magnetic sublevels of the atomic ground state. When the lasers are co-propagating the atoms acquire negligible linear momentum, and it is possible to transfer purely angular momentum to the atoms. One drawback of this method is that the two-photon detuning is exquisitely sensitive to small changes in the magnitude of the magnetic bias field. Because the linewidth of the two-photon resonance is generally extremely narrow, achieving sufficient magnetic field control and stability is a significant technical consideration.

Although the selection of excited state should be relatively unimportant to achieve STIRAP in the ideal case, the multilevel nature of the system can cause complications in the STIRAP dynamics. We use the 87Rb D1 transitions instead of the D2 because the larger hyperfine splitting and simpler structure of the D1 lines help avoid problems associated with dressed state crossings. [5] This is addressed in reference given below. Our system presently is configured to produce a BEC in the |F = 2,mF = 2ñ state, although it should be possible to configure it for the |F = 1,mF = −1ñ state. The  magnetic quantization axis and collinear beam geometry restrict the beam polarization choices to σ+ for the stokes laser and σ− for the pump laser. We can choose either the |F = 2,mF = 0ñ or the |F = 2,mF = −2ñ as the final state by varying appropriate experimental parameters to construct either a three-state Λ system or a five-state M system. Once a BEC is produced in the initial state, the magnetic trap is turned off and the BEC is allowed to expand and fall under the influence of gravity for 9 ms. This allows the trapping fields to decay and be replaced by a uniform magnetic bias field. Once the magnetic environment has stabilized, the appropriately detuned stokes and pump pulses are applied, causing coherent transfer of the atoms to the final state. The difference in OAM between the beams is imparted to the atoms in the final state, while those remaining in the initial state are nonrotating. We have explored a range of experimental parameters, and have found good results with pulse durations of 10-40 μs, Rabi frequencies of several MHz, and Zeeman splittings of > 10 MHz. After the coherent population transfer, the two clouds still physically overlap, and because absorption imaging is not sensitive to the change in distribution of the population among the magnetic sublevels, we use a modified imaging technique. Immediately following the STIRAP pulses, a strong magnetic field gradient is applied by briefly pulsing our trapping fields. The different magnetic sublevels are thereby separated without distorting the clouds significantly. If the BEC has been successfully transferred to a rotating cloud in the final state, absorption imaging along the STIRAP beam axis shows a toroidal cloud displaced a fixed, repeatable distance from the remnants of the initial cloud. Coherence of the process can be inferred from the lack of population in any other state than the initial and final, and by the size (and therefore temperature) of the rotating cloud in comparison to the recoil limit.

The primary objective of this experiment has been to demonstrate that quantized exchange of pure orbital angular momentum is possible between OAM photons and a BEC. The stimulated Raman scheme presented may be useful for repeatably preparing an initially non-rotating BEC in various well-defined angular momentum states, including coherent superpositions of counter-rotating angular momentum states. Although our work so far has been done with untrapped expanding clouds, we expect it should be possible to modify the method to spin a BEC still held in a magnetic trap, which would open up a number of new possibilities for study.

For more background refer to these references:

  1. 1. K. Marzlin, W. Zhang, and E. M.Wright, “Vortex coupler for atomic bose-einstein condensates,” Physical Review Letters, vol. 79, no. 24, pp. 4728–4731, 1997.

  2. 2. E. L. Bolda and D. F. Walls, “Creation of vortices in a bose-einstein condensate by a raman technique,” Physics Letters A, vol. 246, no. 1-2, pp. 32–36, 1998.

  3. 3. G. Nandi, R. Walser, and W. P. Schleich, “Vortex creation in a trapped bose-einstein condensate by stimulated raman adiabatic passage,” Physical Review A, vol. 69, no. 6, pp. 63606–1–8, 2004.

  4. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Physical Review Letters, vol. 97, pp. 170406/1–4, 27 Oct 2006.

  5. B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. i. numerical studies,” Physical Review A, vol. 52, no. Atomic, Molecular, and Optical Physics, pp. 566–82, 1995.

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For more, click link below:

Exchange of Spin and Orbital Angular Momentum Between an Ultracold Bose Gas and Optical Angular Momentum Beams

Future projects: Bragg scattering with the BEC, experimental verification of the production of Rb2 molecules via Feshbach resonances