Optical Dipole Force Trap of87Rb Bose-Einstein Condensates
Department of Physics, Gakushuin University
K. Araki, N. Kikuchi, T. Eno,
T. Kuwamoto, T. Hirano

Abstract•Confinement of BEC in a crossed-FORTControl of trap potential, frequency and aspect ratio⇒ We have realized the parameters that are similar to
the magnetic trap.

•Life time measurements of BEC in a crossed-FORTPotential of optical trap
•Shallow potential depth ⇒ Gravity can’t be ignored.
⇒ Potential is anharmonic.

•Gaussian beam
Potential
Without gravity
With gravityWe considered the effects ofgravity and Gaussian profile,and calculated as follows ・・・Gravity
direction

position

Gravity shiftCalculations of trap depth and frequency (1)< Trap potential >U ( x, y, z ) = U dip ( x, y, z ) + U g ( x)∂U ( x,0,0)
=0
∂x

⇒

x = x0 , x1

( x0 < x1 )U 0 = U ( x1 ,0,0) − U ( x0 ,0,0)∂ 2U (x, y, z )ω q ( x, y , z) =m,2∂q() − 2 x2 + y 2 U z -axis0=exp  222 
1 + (z zr ) wy 0 1 + ( z z r ) (())

 − 2 x2 + z2 +exp  2
22 
1 + ( y yr )
 wz 0 1 + ( y yr ) ()(q : x, y , z)⇒Position dependence
Trap frequencies are defined at thepotential minimum.

ω q = ω q ( x0 ,0,0),

U dip = U z -axis + U y-axis

U y-axis0< Trap frequency >( q : x, y, z ) U z −axis : potential of z − axis beam
 U y −axis : potential of y − axis beam
2
 z r , yr : Rayleigh length , wy 0 , wz 0 : 1 e radius
U z −axis0 , U y −axis0 : maximum potential depthCalculations of trap depth and frequency (2)xPotential

U(x,0,0)x1

gy-axisbeam

z-axisbeam

zx0
U0
x – positiony2wy0zy2wz0

Potential parameters of single-FORTx

Adjustment of aspect ratio 1 ε< Magnetic Trap : MT >1 ε ~ 10, ω ~ 2π × 71 [ Hz ], U 0 ~ 1.2 [ µK]z<Single-FORT>λ ~ 850 [ nm] ( Red tune), 1 ε ~ 10U (x,0,0)
1λw0 =~ 2.8 [ µm]πεAdjustment of frequency ωω ~ 2π × 71 [ Hz ]⇒ P ~ 0 .00576 [ mW ]U 0 ~ 5 .6 × 10 − 7 [ µ K ]Potetial [μK]

⇒ beam waist w0 (1 e 2 radius)

gy0-1

P=0.1mW
P=0.01mW
P=0.00576mW-2-3-4-10-505x – position [μm]10Impossible to adjust single-FORT parameters to the MT’s values.
Crossed-FORTExperimental setupxFORT Beam : δ<0 (Red tune)
Target : BEC of 87Rb (F=2)

zg

mirrory2wy0polarization
polarization

CoilCell

MOT
Beam

FORT
Beamz

y2wz0~5°FORT
Beam2
Probe λz= 845[nm], wz0= 90[μm] (1/e radius), Pz= 6.8[mW]
Beam λ = 851[nm], w = 24[μm] (1/e2 radius), P = 10.6[mW]yy0yTrap potential & frequency (crossed-FORT)x
Trap depth : U0 ~ 1.0 [μK]zg

Trap Frequency : ωx ~ 2π×230 [Hz]ωy ~ 2π×244 [Hz]ω z ~ 2π×21 [Hz]yPotential [μK]

U (x,0,0)420Gravity shift : x0 ~ - 4.2 [μm]Aspect ratio : (ωx ωy)1/2 / ω z ~ 11x0-2-4-6-40

U0-20020x - position [μm]40c.f. Magnetic Trap:MT ωρ/ ωz ~ 10

FORT’s Time Table
MOT→PGC→MT→Evaporative Cooling→
Pure BEC( F=2 ,mF=2 )① ramp up time
② FORT trap time
③ Time-Of-Flight(TOF)① = 50ms

Crossed-FORT TOF imaging (1)Crossed-FORT

Geometric mean trap frequency

Trap Time : 500ms

Calculation

ω FORT ~ 2π × 106 [Hz ]

TOFg

10ms

15ms

MT0.5mmExperimental value
31ms
0.5mm

ω MT ~ 2π × 71 [ Hz]Crossed-FORT TOF imaging (2)Crossed-FORT (TOF : 17ms)
Trap time : 200ms

1000ms

3000ms2000ms

5000ms

g

500ms

330μm

330μm

Number of Condensed Atoms

Life time of BEC（crossed-FORT & MT）
10

BEC in MT
BEC in FORT

6Loss rate for
N < 3×105 [atoms]

105τ MT ~ 7.3 [sec ]τ FORT ~ 1.9 [sec]10402468Trap Time [sec]

10

τ MT
⇒
~ 3 .8
τ FORT

Possible reasons for short life time in crossed-FORT
1．Heating？
① Absorption of photon ?
Absorption rate ~ 560 [sec] ⇒ negligible② Intensity fluctuation or pointing instability of the beam ?
2．Thermal cloud？
BEC
TOF 0ms

Trap Time : 500ms

Ultra cold gas

MTSummary?We could confine rubidium 87 condensates in crossed-FORT.
?Transfer rate of atoms was about 50 % ( ~ 5×105 [atoms] ).
?Life time of BEC in the crossed-FORT was about 1.9 [sec].
⇒enough to perform various experiments in an optical trap.
e.g. : dynamics of BEC with spin degrees of freedom.

Experimental apparatus (1)Optics of laser system

ECLD
slave laser
TC-40(Lower MOT, (Upper MOT) (repump)probe,pump, push)

Magnetic trap coilcoilcellExperimental apparatus (2)Light source of FORTAOM

Fibercoupler< LD >LDP max 〜 100 [mW]λz〜 845 [nm], λ y 〜851 [nm]