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

Motivation

quantum simulation

quantum computing

single photon source

single atom physics

quantum simulation

mimic an unknown system

using a controllable system

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

The single atom trap

@ WIPM

87Rb

MOT 780nm

dipole trapping 830/852nm

Vacuum system

830/852nm

780nm fluor.

Filter

dichromatic mirror

MOT laser

Single Atom Trap @ WIPM experimental setup

Fluorescence of a single Rb atom (2009/02/13)

1 atom

0 atom

10s

0 atom

1 atom

2 atom

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

18.4mw@830nm2.28mw@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

Ring Optical Lattices

by SLM

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

Realizing ROLwith a spatial light modulator (SLM)

SLM

0th order

1l

1th ordermodulated

1l 2l 3l

4l

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 the ROL

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

1l 2l

Scheme 2: up to MHz (EOM driven phase change)

2Hz rotation is shown here

3l

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)

Dynamics of

single atoms in the traps

Loading two atoms to a trap

Ring trapRing trap

Gaussian trapGaussian trap

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 …

a way to bring the atoms closer

—— optical vector beam (OVB)

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)

Experimental Arrangement

SLM

PBS

HW

HW

HW

Dipole trap laser

to trap

PW

Primary results with OVB

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

7000

8000

Sa

mp

les

Counts/20ms

20ms 14.8mW@830nm ovb1

0 20 40 60 80 1000

1000

2000

3000

4000

5000

Sa

mp

les

Counts/20ms

14.8mW@830nm ovb2

0 20 40 60 80 1000

1000

2000

3000

4000

5000

6000

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

Ministry of Sci & Tech of China (MOST)Chinese Academy of Sciences (CAS)Natural Science Foundation of China (NSFC)

Acknowledgments Acknowledgments

All of you, for your attention!

许鹏 何晓东王谨 刘敏