Single Atoms in Rotating Ring Optical Lattices
Mingsheng ZHAN (詹明生 )
State Key Lab of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, CASCenter for Cold Atom Physics, CAS
Oct 15, 2009 Beijing
KITPC: Condensed Matter Physics of Cold Atoms ---- Optical Lattices II
Hubbard Hubbard modelmodel
Approximate model that describes electrons in solids Approximate model that describes electrons in solids
Hamiltonian describes fermions /bosons in a periodic potentialHamiltonian describes fermions /bosons in a periodic potential
Simple, yet hard to solve analytically, numerically or empiricallySimple, yet hard to solve analytically, numerically or empirically
JJ XXUU
i=1i=1 i=2i=2 i=3i=3 i=4i=4 i=5i=5
John C. Hubbard at 1963
J tunneling U in site interaction external potentiali
U.Dorner, T.Calarco, P.Zoller, A. Browaeys and P. Grangier,J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S341–S346U.Dorner, T.Calarco, P.Zoller, A. Browaeys and P. Grangier,J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S341–S346
Need of experimental aspects: • single atoms• cooled to ground state• double-well• readout
Need of experimental aspects: • single atoms• cooled to ground state• double-well• readout
Quantum logic gatesQuantum logic gates
Atom array by dipole trap(bottom-up)
ultracold gas
optical lattices
addressing individual atoms
single atom
dipole trap array
cooling the array
Ultracold atoms in lattices(top-down)
The same goal by different routes (殊途同归 )( for quantum simulation)
2
30
22
30
2
30
3( , ) ( , )
2
3( , ) ( , )
2
3[ ( , )]
2
dip
sc
sc dip
dip
cU r z I r z
cr z I r z
U
cF U I r z
h
h
v
2
2
0
0
0
0
2
( )2
20
2 20
0
020
13.
032
5
1.5
2( , )
( )
( ) 1 ( )
( , ) [1 2(
26.2(2 )
1.3(2 )
) ( ) ]
4
2
U mKw m
U
r
w z
R
dipR
R
zR
mKw m
PI r z e
w z
zw z w
z
r zU r z U
w z
U
mw
U
m
kHz
kHzz
Optical Dipole Trap for Atoms
0
2
, 30
Dressed State Picture (AC-Stark / )
( 1)
,3( ) ( )
,2
g
e
g e
light shift
E n
E n n
for gstatecE r I r
forestate
h
h h h h
:
Atom
Laser
Cylindrically symmetric harmonic oscillator
Superfluidity limit
†
1
ˆ 0NM
SF ii
a
Good phase i,
but Poissonic number
2| | / 2ˆ ; !
i
ni
i i in
a e nn
+ ++ +
+
Mott Insulator State
†
1
0i
M n
Motti
a
0ia
Fock state
++good number,
But no phase
M. Greiner, O. Mandel, T. Esslinger, T. Hansch, I. Bloch, Nature 415 (2002) 39.
+
P.Grangier’s group [IO/CNRS]
Observation of collective excitation of two individual atoms in the Rydberg blockade regime
Nature Phys. 2009
Energy distribution and cooling of a single atom in an optical tweezer
PRA 2008
Two-dimensional transport and transfer of a single atomic qubit in optical tweezers
Nature Phys. 2007
Quantum interference between two single photons emitted by independently trapped atoms
Nature 2006
Controlled Single-Photon Emission from a Single Trapped Two-Level Atom
Science 2005
Collisional blockade in microscopic optical dipole traps PRL 2002
Sub-poissonian loading of single atoms in a microscopic dipole trap
Nature 2001
"Collision blockade”
Phys. Rev. Lett. 89, 023005 (2002) Nature 411, 1024 (2001).
RE: Radiative Escape process FCC: Fine-structure Changing Collision
D.Meschede’s group [Bonn Univ.]
Quantum Walk in Position Space with Single Optically Trapped Atoms
Science 2009
Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging
PRL 2009
Inserting Two Atoms into a Single Optical Micropotential PRL 2006
atom-sorting machine Nature 2006
87Rb
MOT 780nm
dipole trapping 830/852nm
Vacuum system
830/852nm
780nm fluor.
Filter
dichromatic mirror
MOT laser
Single Atom Trap @ WIPM experimental setup
Hanbury Brown and Twiss (HB-T) effect
http://en.wikipedia.org/wiki/Hanbury-Brown_and_Twiss_effectM.O.Scully and M.S.Zubairy, Quantum Optics, CUP 1997, P.307
2(2) 2 20 16
(2) (2)
(2)
( ) =1-( ) = +
( ) (0)
(0)=0
g
g g
g
-3 / 43cos + si n e ( )
4
(1)
(2)2
( ) ( )( ) =
( ) ( ) ( ) ( )( ) =
a t a tg
a a
a t a t a t a tg
a a
(2) (2)
(2) (2)
(2)
( ) (0)
( ) (0)
2
(0) = 1
0
g g
g g
g
classical field
non-classical
thermal
coherent
single photon
Fluorescence of single atom, antibunching:
SPCM : EG&G SPCM-AQRH-14-FCDiscriminator : ORTEC 935 ( Quad 200-MHz Constant-Fraction Discriminator )Coincidence : RoentDek TDC8HP
BS
TTLNIM
TTL
NIM
SPCM
SPCM
Discriminator
Discriminator
Trigger
Δt
Fiber
Single Atom HBT Experiment
2
(2) 3 / 434
2 20 16
( ) 1 (cos sin )
= +
g e
AC shift 39MHzU0 1.9mKRabi Freq 0
26.6MHz ( RL )33.7MHz ( CL22 )79 MHz ( CL23 )
107 total events103 coincidencePhoton antibunching
(single atom)
HBT measurement of single atom in dipole trap
[email protected]@Cooling0.80mw@Repump
(2) (0) 0g
Counting
Cooling and repump laser
MOT magnetic field
Counting clock
∥
∥
∥
∥
ON
OFF
ON
OFF
ON
OFF
threshold
Δt
50ms
1) once counting > threshold, freezing the trap;
2) waiting a time Δt, then check; repeat 100 times;
3) new Δt, then repeat.
Time sequence
Dipole trap laserON
OFF
lifetime of the single atom trap
0 1000 2000 3000 4000 5000 6000 7000 8000
0
20
40
60
80
100
120
实验值 拟合值
Event num
ber
Time(ms)
Equation y = A1*exp(-x/t1) + y0
Adj. R-Squ 0.98372
Value Standard Er
B y0 2.03533 0.67403
B A1 127.786 3.26696
B t1 468.233 18.81894
0 2 4 6 8 10 12 14 16 18 20 22
10
20
30
40
50
60
70
80
90
实验值 拟合值
Pro
babi
lity
of a
tom
stil
l in
trap
(%)
Light off time(s)
Equation y = A1*exp(-x/t1) + y0
Adj. R-Squa 0.98201
Value Standard Err
B y0 -6.43071 10.70524
B A1 116.4062 8.41719
B t1 11.35793 2.21614
Lifetime 468mswith MOT on
Lifetime 11swith MOT off
Laguerre-Gaussian Mode
22 2
2 2
2 2 2exp
( )
lLGLG pp
lll p
C r r rU L
w z w z wu
z w z
2 2 2
12 2 2 2
2 2exp exp exp exp 2 1 tan
( ) 2
lLGlplLG
pl pRR
C r r r ikr z zu L il i p l
w z w z w z w z zz z
Ring Optical Lattice (ROL)
• Superposition of the model
2 2
2 2
2 2
a
2 22 exp cos
rct
( )
an
lLGlplp
C r r rL l
w z w z w z w
y
z
r x yx
,
1l 2l 3l
Trapping atom array with ROL
Single trap
Spatial filter
0 10 20 30 40 50 600
20
40
60
80
100
120
140
160
Cou
nts
/ 20
ms
Time (s)
830nm 64mW 0.9A
Doubletrap
Rotating ROL
1l 2l
Scheme 1: max 60HzContinuous phase pattern animation on the SLM, max refresh rate 60Hz Continuous phase pattern animation on the SLM, max refresh rate 60Hz
single atoms in rotating ROL
Rotating ROL @12Hzwith 1 atom
Rotating ROL @6Hz with 2 atoms
Xiaodong He, Peng Xu, Jin Wang and Mingsheng Zhan, Opt.Express ( accpted, 2009) Xiaodong He, Peng Xu, Jin Wang and Mingsheng Zhan, Opt.Express ( accpted, 2009)
20 40 60 80 100 120 1400
50
100
150
200
250
300
350
sam
ples
counts/40ms
D_traps to G_trap
0 atom
1 atom
0 50 100 150 200 250 3000
100
200
300
400
500
600
sa
mp
les
counts/40ms
D_traps to Ring_trap
Light assisted nonelastic collisions of two atoms in a trap
MOT light on
2 atoms remain
In a Ring trapIn a Ring trap
In a Gaussian trapIn a Gaussian trap
Collisions rareDifficult to meetCollisions rareDifficult to meet
Collisions richEasier to meet Collisions richEasier to meet
Splitting a trap (with an atom) to two traps
oror
Potential or force? (single vs multi: collision)Particle or wave packet? (single atom interferometer)Potential or force? (single vs multi: collision)Particle or wave packet? (single atom interferometer)
Figure 13. Radial insertion of an atom. (a) An atom in the VDT after the extraction. The traps are separated by displacing the HDT along the x-direction. (b) The atom in the VDT is transported to the z-position of the HDT. (c) Thetraps are merged by moving the HDT along the x-direction towards the VDT. d) Evolution of the radial potentials of the traps along the x-axis for steps (b) and (c).
Figure 12. Axial insertion. An atom trapped in one of the potential wells of the standing wave of theVDT is inserted into the Gaussian potential well of the HDT by axially moving the VDT along the z-direction.
Y Miroshnychenko et al., New J. Phys. 8(2006)191
Moving trapStatic trap
PZT
dichroic mirror
To SPCM
Moving trap
Static trap
fluorescence
PZT scan speed: 10um/40msPZT scan speed: 10um/40ms
Cooling&Repump ∥∥80ms
PZT ∥ ∥ -2V
5V
160ms
10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2
10
20
30
40
50
60
70
80
原子
还在
静止
阱中
的几
率
mw移动阱光强( )
12mw静止阱光强
The depth of the moving well affects the rate carrying the atomThe depth of the moving well affects the rate carrying the atom
??
Time evolution of the trap intensity profile
Initial
exposure time 1ms readout time 2.5ms
??
The final position of the atom is determined by force not the depth of potential. The final position of the atom is determined by force not the depth of potential.
Atom transfer between traps
Gaussian trapGaussian trap
Merging Merging Splitting Splitting
ring trapring trap
Time sequence: double Gaussian double
Off
On
Cooling lightrepumping light MOT coil
Interaction time: N*1/60 s N =1,2,3 …variable
Off
On
Cooling lightrepumping light MOT coil+ L (or – L) SLM light
Interaction time: N*1/60 s N =1,2,3 …variable
Time sequence: double ring double
Single atom transport ( via a Gaussian trap )
0 10 20 30 40 50 600
100
200
300
400
500
600
sam
ples
counts/20ms
trap_2 trap@gaussian N=1
0 10 20 30 40 50 60 700
100
200
300
400
500
600
700
trap_1 trap@gaussian N=1
Y A
xis
Titl
e
X Axis Title
0 10 20 30 40 50 60 70 800
100
200
300
400
500
trap_1 trap@gaussian N=3
sam
ples
counts/20ms0 10 20 30 40 50 600
50
100
150
200
250
300
350
trap_2 trap@gaussian N=3
sam
pels
counts/20ms
1/60 s
3/60 s
2 1
0 10 20 30 40 50 600
50
100
150
200
250
300
350
400 trap_2 trap@LG N=1
sam
pels
counts/20ms
0 10 20 30 40 50 600
50
100
150
200
250
300
350
400trap_2 trap@LG N=3
sam
ples
counts/20ms
0 20 40 60 80 1000
50
100
150
200
250
300
trap_1 trap@LG N=1
sam
pels
coutns/20ms
0 20 40 60 80 1000
50
100
150
200
250
300
350
400 trap_1 trap@gaussian N=3
sam
pels
counts/20ms
3/60 s
1/60 s
2 1
Single atom transport ( via a ring trap )
cooling atom to ground state + internal state control
making interaction of atoms in/between sites
entanglement, quantum simulation / computing
……
single atom AI, HBT…
cooling atom to ground state + internal state control
making interaction of atoms in/between sites
entanglement, quantum simulation / computing
……
single atom AI, HBT…
Next …
Optical vector beam ( OVB)
• The focused pattern can be much smaller than the diffraction limit
Tailoring of arbitrary optical vector beamsNew Journal of Physics 9 (2007) 78
Phys. Rev. Lett. 91, 233901 (2003)Phys. Rev. Lett. 100, 123904 (2008)Phys. Rev. Lett. 91, 233901 (2003)Phys. Rev. Lett. 100, 123904 (2008)
Primary results with OVB
0 20 40 60 80 100 1200
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Sa
mp
les
Counts/20ms
20ms 14.8mW@830nm ovb1
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Sa
mp
les
Counts/20ms
14.8mW@830nm ovb2
0 20 40 60 80 1000
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7000
Sa
mp
les
Counts/20ms
20ms 14.8mW@830nm Ring1
0 20 40 60 80 100 120 1400
2000
4000
6000
8000
Sa
mp
les
Counts/20ms
20ms 14.8mW@830nm Ring2
OVB trapOVB trap
Lifetime longerTighter potentialLifetime longerTighter potential
Normal ring trapNormal ring trap
Lifetime shorterLifetime shorter