Quantum dynamics of evaporatively cooled Bose-Einstein ... - Physics

Correlations all quantum eects enter through the real stochastic noise terms j (t x) without these, the equations correspond to the approximate classicalmean-eld equations the noise terms are independent, Gaussian, and delta-correlated in spaceand time:h i (t x) j (t 0 x 0 )i = ij (x ; x 0 )(t ; t 0 )Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 5

Atom loss hot atoms near the edge **of** the trap escape absorption: ;(x) = ; max d j=1 [sin(x j=L j )] 50Modulated Absorption21.5Γ(x,y)10.50.5 0000.5y−0.5−0.5xDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 7

Initial Conditions the precise initial conditions are not expected to be very signicant subsequent quantum noise dominates initial thermal noise the simplest possible choice is made: a high-temperature **Bose**-**Einstein**grand canonical ensemble in this initial state, no account is taken **of** the trapping or interparticlepotentialsDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 8

Parameters try to choose parameters used in the experiments however computational constraints on the lattice size=) limited number **of** atoms=) limited to either narrow deep traps, or wide shallow traps go for a compromise:{ a 0 = 0:6nm trap size ' 10m{ initial temperature T 0 = 2:4 10 ;7 K{ initial number **of** atoms N 0 ' 500 in 2d{ initial number **of** atoms N 0 ' 15000 in 3dDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 9

Evaporative cooling **dynamics** have done 1d, 2d and 3d simulations nal distribution in k-space is tall (intense) and narrow, because **of**:{ ramped potential{ thermalising eect **of** collisions quantum eects dominate for for these parameters high atom loss rate initially=) change trap shape=) alter evaporative cooling procedureDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 10

Three dimensional simulation - evolution **of** the momentum distributionduring a single trajectory.Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 11

Simulation **of** a three-dimensional **Bose** condensate, showing the ensembleaverage (15 paths) atom density hn(k)i along one dimension in Fourierspace versus time.Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 12

Connement Measure measurable (physical) quantities given by ensemble average want to measure the occupied volume in k-space use higher order correlations to do this dene connement parameter:Q =Rdk h 1 (k) 1 (k) 2 (k) 2 (k)i;Rdk h 1 (k) 2 (k)i2 x 3 0Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 13

2520151/Q1050−50 20 40 60 80 100TimeSimulation **of** a three-dimensional **Bose** condensate, showing the ensembleaverage evolution (11 paths) **of** the connement parameter Q.Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 14

Angular Momentum nonzero nal (angular) momentum =) vortices calculate evolution **of** angular momentum distribution occupation **of** angular modes is given by:wherehn(j)i =X{ n is the index for the radial modes{ j is the index for the angular modesnh ^ jn ^ jniDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 15

1020angular momentum (j)50−5151050n(j))3020100−10−200−100 20 40 60 80 100time (t)−550time (t)1001050−5angular momentum (j)Angular momentum distribution n(j), during the condensation **of** a twodimensionalBEC.−10Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 16

121086420050time (t)1001050−5angular momentum (j)Ensemble average **of** the angular momentum distribution hn(j)i, during thecondensation **of** a two-dimensional BEC.−10Drummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 17

Conclusions rst principles quantum simulation **of** BEC 10 000 atoms (initially) in 32000 trap modescondensateup to 200 atoms in dicult - not impossible with classical computers physics: evaporative cooling with variable potential condensate can form in excited mode can spontaneously form metastable vorticesDrummond & Corney - **Quantum** **dynamics** **of** evaporative **cooled** BECs 18