Bose-Einstein Condensation

1. Experimental setup:
   
   Bose-Einstein condensation (BEC) of trapped alkali atoms is presently one of the frontier areas of physics which requires a great deal of understanding of interaction of atoms with laser radiation and magnetic field and manipulation of atoms using those. Many research groups worldwide have taken initiative for research and development activities in this exciting field. It is believed that Bose condensate can serve as coherent source of atoms in a similar way as a laser serves the coherent source of photons.

   
   
   Fig-1. Photograph of setup for BEC.

   In Laser Physics Applications Division (LPAD) at RRCAT, we have developed a set-up for generating BEC of Rb⁸⁷ atoms in a QUIC magnetic trap. Our set-up consists of a standard double-MOT system in which two MOTs configured vertically one below the other have been made operational. In this set-up both MOTs are operating at different background pressure. The upper MOT is a vapor-cell MOT (VC-MOT) which is loaded from the background vapor of Rb at pressure 2x10^-8 Torr generated from a getter source. The trapped and cooled atoms in the upper MOT are then transferred using a push beam to load the lower MOT which is in a UHV chamber (~2x10^-10 torr). The atoms in lower MOT (or UHV-MOT) will be finally trapped in QUIC magnetic where RF evaporation will be used for further cooling.

   The following are the highlights of the setup:

   • About 1x10⁸ atoms are trapped in the upper MOT (VC-MOT) which are subjected to push laser beam to load UHV-MOT. We are able to collect ~1x10⁷ atoms in UHV-MOT with suitable choice of parameters. Further work is in progress to enhance the number in the UHV-MOT.

   • The magnetic QUIC trap has been designed and measurements of magnetic field have been performed to characterize trap parameters. The loading of magnetic trap is in progress. After getting appropriate life-time of magnetic trap, RF evaporation experiments will be performed.

   • We are using different techniques such as fluorescence imaging, absorption probe imaging, free expansion method, etc to assess number and temperature of atoms in MOT and in magnetic trap.

   • All the controls on MOTs and magnetic trap are implemented electronically through PC and LabView.

2. Generation of hollow conic beam using an axicon mirror:

   Generation and characterization of hollow beams has attracted considerable attention recently because of their applications in diverse areas such as atom guiding and trapping, optical tweezers, laser machining, and generation of beams with large depth of focus (i.e. non-diffracting beams).

   Fig-2: Experimental set-up for generation of hollow beam. DL: diode laser, AP: aperture, M: high reflectivity mirror, AX: axicon mirror, l/4: quarter wave plate, PBS: polarizing beam splitter, S: screen.		Fig-3: CCD image and intensity profile of the generated conic beam at z = 153 mm.

   We have developed a new reflecting element, all-metal axicon mirror, and demonstrated its use to generate hollow conic beam. The cone angle of axicon mirror governs the divergence of the generated conic hollow beam. We have developed mirrors of different base angle (0.5 to 3.0 degree) which are made from copper. The axicon mirrors were fabricated in Laser Workshop of RRCAT, polished on a diamond turning machine in Machine Dynamics Division of BARC and gold coated in the Optical Workshop of RRCAT. Using an axicon mirror in experimental setup as shown in Fig-2, a good quality hollow conic beam has been generated (Fig-3) with a power conversion efficiency of ~ 85% for transformation of a Gaussian beam into a hollow conic beam [Opt. Eng. 46(8),-084002 (2007)].

3. Use of hollow beam for enhancement of number of atoms in lower MOT:

   We have demonstrated a significant enhancement in the transfer of atoms between upper MOT to lower MOT (i.e. VC-MOT to UHV-MOT) by use of an appropriately tuned and aligned hollow beam. A weakly focused hollow laser beam propagating opposite to the direction of the ejected atomic flux was aligned such that both the MOTs were in the dark region of the hollow beam.

   Fig-4. Schematic of setup used for enhancement of number of atoms transferred to lower MOT using hollow beam (left side). Dependence of number in lower MOT (UHV-MOT) on hollow beam frequency detuning (right side graph).

   A hollow beam generated from a home-made metal axicon mirror was aligned as shown in the schematic figure (Fig-4). The peak to peak intensity diameter and ring-width (FWHM) of the hollow beam were, respectively, ~14.3 mm and ~1.4 mm at the lower MOT and ~3.2 mm and ~1.24 mm at the upper MOT. This corresponds to peak intensities at the lower and the upper MOT planes of ~50 mW/cm² and ~230 mW/cm², respectively, for a beam power of 30 mW. In the presence of the hollow beam the number of atoms in the lower MOT changed significantly and the change depended on both the power as well as the frequency of the hollow beam (see graph in Fig-4). The enhancement in number of atoms in lower MOT in presence of hollow beam was suggested due to few processes involved [Phys. Rev. A 77 (6), 065402 (2008)]. First, availability of more atoms (away from MOT centre) for trapping, due to optical pumping by hollow beam among Zeeman sub-levels. The atoms which are not accessible to the trapping beams due to larger Zeeman shifts are now trappable due the hollow beam. Second, the slowing down of atoms ejected from the upper MOT by the counter propagating hollow beam to bring the speed of ejected atom flux smaller than the capture speed of the lower MOT. And third, a possible reduction in the divergence of the atomic flux because of the transverse cooling and also because of guiding effect for blue detuning of the hollow beam.

4. Measurement of spot-size of a narrow Bessel beam by scanning a CCD-pixel:

   A non-diffracting Bessel beam can acquire and maintain its central spot as small as compared to the wavelength, over a propagation distance much larger than the corresponding Rayleigh range. Because of this remarkable property it has a lot of research and technological applications such as atom guiding, laser machining, etc.

   
   
   Fig-5. Schematic of experimental setup for the generation of the zero order Bessel beam. AX: axicon mirror of base angle 3⁰, LB: input laser beam, BE: beam expander, L₁ & L₂: lenses of 100 mm focal lengths, M: 45⁰ high reflectivity mirror, GP: polished glass plate, HB: hollow beam, L₃: lens of 500 mm focal length, CCD: charge-coupled device camera.
   
   

   We generated a zero-order Bessel beam by focusing a hollow beam (as shown in experimental setup in Fig-5). The spatial intensity profile of the beam was recorded using a CCD of pixel size of 6.45 mm which are shown in Fig-6 for different V values. Analysis of these CCD-recorded profiles indicated that width (FWHM) of the generated Bessel beam was within one pixel size (6.45 mm). For a narrow beam, such as this, the measurement of the spot-size is a challenging task. The well known scanning knife-edge does not work for measurement of FWHM of the central spot of Bessel beam, due to large contribution of side rings to the signal.

   For an accurate measurement of spot-size of this Bessel beam which has FWHM smaller than size of CCD pixel, we demonstrated a new method [Measu. Sci. Technol. 21(2), 025308 (2010)] in which the CCD camera was scanned transverse to the beam axis and variation in number of counts on a particular (marked) pixel was recorded for each position scanned. This variation in counts on a pixel with its position from the beam axis was fitted with the simulated variation of power P on the pixel with position. The spot-size parameter was obtained from this best-fit. For a pixel, positioned at (x_o, 0, z) at a distance x_o from the beam axis (z-axis), the power P can be evaluated as,

   	(1)
   Fig-6. Transverse intensity profiles of the generated Bessel beam measured with the CCD at different values of V. The inset shows a CCD image of the spot atV = 500 mm.

   where 2a is size of the pixel, I (=J₀²(αρ), for a zero-order Bessel beam and ρ² = x²+y² ) is beam intensity at a point (x, y) in a cross-section perpendicular to beam axis, and a(z) is z-dependent spot-size parameter. The best-fit P(x_o, a) vs. x_o to the measured counts vs x_o resulted the spot-size parameter a(z) as shown in Fig-7. For two values of V (506 mm and 525 mm), the best-fit results yielded a^-1 to be 1.8 mm (for V =506 mm) and 2.1 mm (for V =525 mm). From these, we obtained FWHM to be 4.1 mm (for V =506 mm) and 4.8 mm (for V =525 mm), which are evidently smaller than the size of a CCD-pixel (6.45 mm).

   
   
   Fig-7. Variation in number of counts (normalized) on a pixel with its distance x_o from the beam axis. The data shown by filled circles are for V = 506 mm and those shown by hollow circles are for V = 525 mm. The continuous curves show the simulated P(x_o, a) values best-fit to the measured data.

   We found that on a Gaussian beam of narrow width, our new method (i.e. scanning pixel method described above) gave results as accurate as scanning knife edge method. But scanning pixel method is particularly attractive for a Bessel beam, for which the familiar scanning knife-edge method is difficult to apply due to specific intensity pattern of a Bessel beam. The scanning pixel method also has sub-pixel resolution.

   References:

   1. "Collective modes of a quasi two-dimensional Bose Condensate in large gas parameter regime", S. R. Mishra, S P Ram, Arup Banerjee, Pramana J. Physics 68(6), 913 (2007). (also in arXiv:cond-mat/0603015 v1 1 Mar 2006).
   2. "Generation of hollow conic beam using a metal axicon mirror", S. R. Mishra, S. K. Twari, S. P. Ram and S. C. Mehendale , Opt. Eng. 46(8),-084002 (2007).
   3. "Study of collective mode frequencies of a Q2D Bose gas in large gas parameter regime", S. P. Ram, S. R. Mishra, Arup Banerjee, Proc. Fifth DAE-BRNS National Laser Symposium (NLS-05), Dec 7-10, 2005, Vellore Institute of Technology, Vellore, India.
   4. Design and characterization of a QUIC Trap, S R Mishra, S P Ram, S K Tiwari and S C Mehendale, Proc. Sixth DAE-BRNS National Laser Symposium (NLS-06), Dec 5-8, 2006, RRCAT, Indore.
   5. "Use of a hollow laser beam to improve atom transfer in a double-MOT system", S. R. MISHRA, S. P. RAM, S. K. TIWARI, S. C. MEHENDALE, Proc. National Laser Symposium NLS-07 (Dec.17-20, 2007), Vadodara, India.
   6. "Generation of optical pulses with a variable delay from a single beam using AOMs in tandem: Application to temperature measurement of cold atoms", S. P. RAM, S R MISHRA, S. K. TIWARI, Proc. National Laser Symposium NLS-07 (Dec.17-20,2007), Vadodara, India.
   7. "Measurement of a narrow spot-size by scanning of single pixel of a CCD camera", S. P. RAM, S. K. TIWARI, J. JAYABALAN, S. R. MISHRA, Proc. National Laser Symposium NLS-07 (Dec.17-20, 2007), Vadodara, India.
   8. "Generation of a narrow nondiffracting beam using a metal axicon mirror". S. K. TIWARI, S. P. RAM, S. R. MISHRA, S. C. MEHENDALE, Proc. National Laser Symposium NLS-07 (Dec.17-20, 2007), Vadodara, India.
   9.  “Enhanced atom transfer in a double magneto-optical trap set-up”, S. R. Mishra, S. P. Ram, S. K. Twari, and S. C. Mehendale, Phys. Rev. A 77 (6), 065402 (2008).
   10.  “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel”, S. K. Twari, S. P. Ram, J. Jayabalan and S. R. Mishra, Measu. Sci. Technol. 21(2), 025308 (2010).