Production of BECs. JILA June 1995 (Rubidium)

Transcription

1 Production of BECs JILA June 995 (Rubidium) Jens Appmeier EMMI Seminar

2 Defining the Goal: How cold is ultracold? T 300 K Room Temperature.7 K CMB Temperature ~ mk 3 He becomes superfluid ~0 µk Photon Recoil ~00 nk Occurance of BEC

3 Production of BECs Defining the Goal: BEC Atom Sources Laser Cooling Evaporative Cooling and Optical Traps Observing a BEC

4 Condition of Degeneracy interparticle distance ~ extension of the wavefunction n /3 required background pressure for lifetimes of ~ s: p 0-9 mbar mean free path: 0 km BEC condition: nλ 3 db = n π mk B T 3 =.6 assume n = 0 cm -3 Tc 00 nk

5 Ideal Bose gas in a Trap mean occupation number: h.o. trapping potential: n i = exp[β(ɛ i µ)] V = m ( ω xx + ω yy + ω zz ) critical Temperature Tc: condensate fraction: µ = ɛ 0 k B T c = ω N 0 = N ( ) /3 N 0.94 ωn /3 ζ(3) ( ( T T c ) 3 ) with ω 3 = ω x ω y ω z

6 Atom Sources several types of sources for cold atom experiments: loading a MOT from the background gas and transferring the atoms to the UHV part

7 Atom Sources several types of sources for cold atom experiments: loading a MOT from the background gas and transferring the atoms to the UHV part 3D MOT using desorption D+ MOT / 3D MOT configuration 3D MOT & magnetic transport

8 Atom Sources several types of sources for cold atom experiments: loading a MOT from the background gas and transferring the atoms to the UHV part 3D MOT using desorption D+ MOT / 3D MOT configuration 3D MOT & magnetic transport Oven & Zeeman Slower to feed the 3D MOT

9 Laser Cooling Slowing a hot atomic beam Atom-Light Interaction optical Molasses Magneto-Optical Trap (MOT) Limits of laser cooling

10 Slowing a hot atomic beam velocity red detuned laser Doppler shift: Zeeman shift: ω Doppler = k v ω Zeeman = µ B (m jeg je m jg g jg ) B

11 Slowing a hot atomic beam velocity red detuned laser Doppler shift: Zeeman shift: ω Doppler = k v ω Zeeman = µ B (m jeg je m jg g jg ) B Scattering Rate (force)! laser " &! Doppler! laser % &! Doppler! laser! atom Frequency Figure. Atomic scattering rate versus laser frequency.

12 Slowing a hot atomic beam velocity red detuned laser Doppler shift: Zeeman shift: ω Doppler = k v ω Zeeman = µ B (m jeg je m jg g jg ) B Resonance Condition: The decreasing Doppler shift due to the decelerated atom must be compensated by an inhomogeneous magnetic field to keep the atom in resonance with the incident laser. Scattering Rate (force)! laser " &! Doppler! laser % &! Doppler 0 = 0 + ω Doppler (ν) ω Zeeman (r)! laser! atom Frequency Figure. Atomic scattering rate versus laser frequency.

13 Slowing a hot atomic beam different configurations possible & used (a) Decreasing-Field-Sower Magnetfeld B B 0 3 P 3/ 3 S / Position z 0 L s D -Linie +! B0 (b) Increasing-Field-Slower 0 L s D -Linie --! B 0 -B b (c) Spin-Flip-Slower Nulldurchgang 0 L -B s b D -Linie --! Umpumpen +! Abb..7. Slowing down a hot atomic beam: Theoretisch berechnetes Magnetfeld eines Zeeman-Slowers und die genutzten Übergänv initial = 700 m s v final = 30 m s

14 Atom-Light Interaction resonant with the atomic transition off-resonant

15 Atom-Light Interaction resonant with the atomic transition off-resonant

16 Atom-Light Interaction resonant with the atomic transition off-resonant Absorption / ρ ee I sat I probability to find an atom in the excited state: s 0 / ρ ee = + s 0 + ( /Γ) typical numbers: 87 Rb Isat =.7 mw cm - 3 Na Isat = 6.3 mw cm - s 0 = I/I sat Γ linewidth

17 Atom-Light Interaction resonant with the atomic transition off-resonant Absorption / ρ ee photon scattering rate R = Γρ ee deceleration up to ~ 0 5 g I sat I probability to find an atom in the excited state: s 0 / ρ ee = + s 0 + ( /Γ) typical numbers: 87 Rb Isat =.7 mw cm - 3 Na Isat = 6.3 mw cm - s 0 = I/I sat Γ linewidth

18 Atom-Light Interaction resonant with the atomic transition off-resonant e > g > ω 0 two-level atom & classical light field described by Jaynes-Cummings Model bare states

19 Atom-Light Interaction resonant with the atomic transition off-resonant e > g > ω 0 bare states two-level atom & classical light field described by Jaynes-Cummings Model Assumptions: two level atom (good for most Alkalis) dipole approximation ( λ r Atom ) rotating wave approximation ( ω 0 ω L ω 0 )

20 Atom-Light Interaction resonant with the atomic transition off-resonant e > g > ω 0 bare states shifted states two-level atom & classical light field described by Jaynes-Cummings Model Assumptions: two level atom (good for most Alkalis) dipole approximation ( λ r Atom ) rotating wave approximation ( ω 0 ω L ω 0 ) due to the atom-light interaction, the energies of the levels are shifted by E e/g = ± Ω 4 for Ω ω L ω 0

21 Optical Molasses starting point: resonant atom-light interaction F (v) = k(r(v) R( v)) = k Γ + s 0 + s 0 ( ( kv) Γ ) + s 0 + s 0 ( ) ( +kv) Γ

22 Optical Molasses starting point: resonant atom-light interaction F (v) = k(r(v) R( v)) = k Γ + s 0 + s 0 ( ( kv) Γ ) + s 0 + s 0 ( ) ( +kv) Γ force of single laser force of single laser resulting froce 0.5 F[ hk Γ/ I/I 0 ] v[γ/(k)]

23 Optical Molasses starting point: resonant atom-light interaction F (v) = k(r(v) R( v)) = k Γ + s 0 + s 0 ( ( kv) Γ ) + s 0 + s 0 ( ) ( +kv) Γ F[ hk Γ/ I/I 0 ] v[γ/(k)] force of single laser force of single laser resulting froce Taylor series arround v = 0 F = αv strong damping term due to many scattered photons from one direction

24 Magneto-Optical Trap add a position dependent term to obtain a confinement in real space F = -αv - Dx

25 Magneto-Optical Trap add a position dependent term to obtain a confinement in real space F = -αv - Dx inhomogeneous magnetic field leads to an inhomogeneous Zeeman splitting B $ # 0 $ % J= m=- m=0 m=+ $ % $ # $ % $ # $ % $ # J=0 B<0 force B=0 force=0 B>0 force

26 Magneto-Optical Trap add a position dependent term to obtain a confinement in real space F = -αv - Dx inhomogeneous magnetic field leads to an inhomogeneous Zeeman splitting Advanced Optics Laboratory B $ # $ # Magnetic coils Polarized light $ % $ # $ % $ % Figure 4. Schematic of the MOT. Lasers beams are incident from all six directions and have helicities (circular polarizations) as shown. Two coils with opposite currents produce a magnetic field that is zero in the middle and changes linearly along all three axes. while the!m " #transition shifts to higher frequency. If the laser frequency $ is # below all the atomic transition 0 frequencies and the atom is to the left of the origin, many photons are scattered from the $ % laser beam, because it is close to resonance. The $ # laser beam from the right, however, is far from its resonance and scatters few m=- m=0 photons. Thus the J= force from the scattered photons pushes the atom back to the zero of the magnetic field. If the atom moves to the right of the origin, exactly the opposite happens, and again the $ % atom is $ pushed # $ toward % $ # the center where the magnetic field is zero. Although it is somewhat more complicated J=0 to extend B<0 the analysis B=0 to three dimensions, experimentally force it is simple, as shown force=0 in Figure 4. As in optical molasses, laser beams illuminate the atom from all six directions. Two symmetric magnetic field coils with oppositely directed currents create a magnetic field that is zero in the center and changes linearly along the x, y, and z axes. If the circular polarizations of the lasers are set correctly, a linear restoring force is produced in each direction. Damping in the trap is provided by the cooling forces discussed in section.. It is best to characterize the trap "depth" in terms of the maximum velocity that an atom can have and still be contained in the trap. This maximum velocity v max is typically a few times &' ( &' m=+ $ % $ # B>0 force $ %

27 Magneto-Optical Trap Temperature Limit: max. scatt. Rate = Γ/ k B T D = Γ Doppler Temperature Na: 35 µk typical numbers: n = 0 cm -3 nλdb = 0-6

28 Magneto-Optical Trap Temperature Limit: max. scatt. Rate = Γ/ k B T D = Γ Doppler Temperature Na: 35 µk typical numbers: n = 0 cm -3 nλdb = 0-6

29 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J =

30 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

31 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

32 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

33 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

34 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

35 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4

36 Sub-Doppler Cooling lin lin no external magn. field ground state degenerate Zeeman levels, even in the J = J = Suppose σ - : ground state population: -/ light shifts: E / = Ω 4 E / = Ω 3 4 pumping process takes a finite time τp Sisyphus cooling

37 Sub-Doppler Cooling Recoil Limit ω L emission in a random direction Limit: Absorption of Photon Atom in Rest Acceleration due to reemission Recoil Temperature: ~ 3 µk for 3 Na

38 Limits of Laser Cooling Atomic Level structure sub-doppler cooling degenerate limited by photon recoil k B T r = k m T r 3 µk T r 350 nk 3 Na 87 Rb non-degenerate doppler cooling in a MOT limited by finite scattering rate k B T D = Γ T D 35 µk T D 46 µk phase space density: ~

39 Limits of Laser Cooling Atomic Level structure sub-doppler cooling degenerate limited by photon recoil k B T r = k m T r 3 µk T r 350 nk 3 Na 87 Rb non-degenerate doppler cooling in a MOT limited by finite scattering rate k B T D = Γ T D 35 µk T D 46 µk phase space density: ~ further cooling schemes needed to reach BEC

40 Evaporative Cooling and Optical Dipole Traps Cooling scheme Commonly used trap configurations magnetic traps optical dipole traps & lattice potentials

41 Evaporative Cooling remove hottest atoms from the trap E trapping potential

42 Evaporative Cooling remove hottest atoms from the trap E cut potential trapping potential

43 Evaporative Cooling remove hottest atoms from the trap E cut potential runaway evaporation, i.e. temperature decrease due to atom loss leads to an increasing atom density gain in phase space density trapping potential

44 Evaporative Cooling remove hottest atoms from the trap E cut potential runaway evaporation, i.e. temperature decrease due to atom loss leads to an increasing atom density gain in phase space density trapping potential important parameters: truncation R = τ loss η = U parameter Ratio of good to bad collisions k B T 7 0 τ el

45 Evaporative Cooling remove hottest atoms from the trap E cut potential runaway evaporation, i.e. temperature decrease due to atom loss leads to an increasing atom density gain in phase space density trapping potential important parameters: truncation R = τ loss η = U parameter Ratio of good to bad collisions k B T 7 0 τ el BEC occures

46 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F =

47 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F =

48 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F = Rempe MPQ

49 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F = Rempe MPQ

50 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F = Rempe MPQ

51 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F = Rempe MPQ

52 Magnetic Traps V = m F g F µ B B magnetic field maximum in free space forbidden by Maxwells laws need low field seeking states ( mfgf > 0) 3 Na F = - 0 F = Rempe MPQ

53 Far-Off-Resonance Traps light shift of the atomic levels due to laser light: E = Ω Ω = Γ I(r) 4 I sat inhomogeneous intensity profile creates (trapping) potential for the atom

54 Far-Off-Resonance Traps light shift of the atomic levels due to laser light: E = Ω Ω = Γ I(r) 4 I sat inhomogeneous intensity profile creates (trapping) potential for the atom Two cases: blue detuned light (i.e. = ωl - ω0 > 0): repulsive potential, repell atoms from intensity maximum red detuned light (i.e. = ωl - ω0 < 0): attractive potential, single beam acts as a trap

55 Far-Off-Resonance Traps Single Beam Trap: use a focused beam to trap atoms σ(z) I(r) = I 0 exp[ (x + y ) σ 0 σ(z) ] σ(z) = σ 0 + z zr σ 0 z R = πσ 0 λ Rayleigh range trapping frequencies in radial and longitudinal direction: 4 V V ω = mσ0 ω = mzr

56 Optical Potentials Creation of Lattice Potentials by interfering trapping beams tight confinement, single site addressability, variable lattice depth z crossed dipole beam y x waveguide / charger beam ~0 standing light wave

57 Observing a BEC density distirbution of a thermal cloud in the harmonic trap given by Boltzmann distribution during TOF the cloud expands due to its velocity distriburion governed by the Maxwell-Boltzmann distribution, i.e. homogeneous expansion in free space

58 Observing a BEC density distirbution of a thermal cloud in the harmonic trap given by Boltzmann distribution during TOF the cloud expands due to its velocity distriburion governed by the Maxwell-Boltzmann distribution, i.e. homogeneous expansion in free space BEC: additional interaction energy adds during expansion MIT, Ketterle group

59 References H. Metcalf, P. van der Straten: Laser Cooling and Trapping, Springer 999, ISBN: L. Pitaevskii, S. Stringari: Bose-Einstein Condensation, Oxford University Press, ISBN: C.J. Pethick, H. Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press A. Griffin, S. Stringari, D.W. Snoke: Bose-Einstein Condensation, Cambridge University Press C.J. Foot: Atomic Physics, Oxford University Press W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn, Making, probing and understanding Bose-Einstein condensates, Varenna lectrue notes, ArXiv cond-mat/ J. Dalibard, C. Cohen-Tannoudji: Laser cooling below the doppler limit by polarization gradients: simple theoretical models, J.O.S.A. B 6, 03 (989) Y. Castin, H. Wallis, J. Dalibard: Limit of Doppler Cooling, J.O.S.A. B 6, 046 (989) E.W Streed, A.P Chikkatur, T.L Gustavson, M. Boyd, Y. Torii, D. Schneble, G.K. Campbell, D.E. Pritchard, and W. Ketterle: Large atom number Bose-Einstein Condensate machines, Rev. Sci. Instrum. 77, 0306 (006)

60 NaLi KIP Jens Appmeier Fabienne Haupert Jan Krieger Peter Krüger Anton Piccardo-Selg Valentin Volchov Markus K. Oberthaler former members: Elisabeth Brama Marc Repp Stefan Weis