玻色爱因斯坦凝聚和激光冷却汇总课件

Atoms

in

Unison

in

the

CoolestGas

in

theUniverse超冷世界的原子大合唱1Laser

Cooling激光冷却What

is

the

significance

of

the

2001

and1997Nobel

Prize

in

Physics?The

Nobel

Prize

(2001)“for

the

achievement

of

Bose-Einstein

condensation(玻-愛因斯坦凝聚態)

indilute

gases

of

alkali

atoms(碱原子),and

for

early

fundamental

studies

of

theproperties

of

the

condensates"2The

WinnersEric

A.

Cornell康奈爾JILA

&NIST,Boulder,

Colorado.1961-Wolfgang

Ketterle3克特勒MIT1957-Carl

E.

Wieman維曼JILA

&UniversityofColorado,Boulder.1951-The

GodfatherRamsey(1989)Kleppner

(1H)Wieman(87Rb)Hulet(7Li)Chu(1997)Ketterle

(23Na)The

Sons

Phillips(1997)Pritchard

The

GrandsonsCornell

(87R4b)Q1:

What

Is

Bose-Einstein

Condensation?De

Broglie

德布羅意(1929

Nobel

Prize

winner)proposed

that

all

matter

iscomposed

of

waves.Their

wavelengths

are

givenby

=

de

Brogliewavelengthh=Planck’s

constant

普朗克常數m

=

massv

=

velocity5Against

Our

Intuition?!

In

most

everyday

matter,

the

de

Broglie

wavelength

is

much

shorter

than

thedistance

separating

the

atoms.

In

this

case,

the

wave

nature

of

atoms

cannot

benoticed,

and

they

behave

as

particles.

The

wave

nature

of

atoms

become

noticeable

when

the

de

Broglie

wavelength

isroughly

the

same

as

the

atomic

distance.

This

happens

when

the

temperature

is

low

enough,

so

that

they

have

lowvelocities.

In

this

case,

the

wave

nature

of

atoms

will

be

described

by

quantum

physics,

e.g.they

can

only

stay

at

discrete

energy

states

(energy

quantization).6Bose

and

EinsteinIn

1924

an

Indian

physicist

named

Bose

studied

the

quantum

behaviour

of

acollection

of

photons.Bose

sent

his

work

to

Einstein,

who

realized

that

it

was

important.Einstein

generalized

the

idea

to

atoms,

considering

them

as

quantum

particleswithmass.Einstein

found

that

when

the

temperature

is

high,

they

behave

like

ordinarygases.However,

when

the

temperature

is

very

low,

they

will

gather

together

atthelowest

quantum

state.

This

is

called

Bose-Einstein

condensation.7Fermions

(費米子) and

Bosons

(玻 子)

Not

all

particles

can

have

BEC.

This

is

related

to

the

spin

of

the

particles.

The

spin

quantum

number

of

a

particle

can

be

an

integer

or

ahalf-integer.

Single

protons,

neutrons

and

electrons

have

a

spin

of

½.

They

are

called

fermions.They

cannot

appear

in

the

same

quantum

state.

BEC

cannot

take

place.

Some

atoms

contain

an

even

number

of

fermions.

They

have

a

total

spin

of

wholenumber.

They

are

calledbosons.

Bosons

show

strong

“social”

behaviour,

and

can

haveBEC.

Example:

A23Na

atom

has

11

protons,

12

neutrons

and

11

electrons.8The

Material

For

BEC

BEC

was

found

in

alkali

metals

e.g.87Rb(金如),23Na(鈉),7Li(鋰)because:

They

are

bosons.

Each

atom

is

a

small

magnetic

compass,

so

that

a

cooling

technique

calledmagnetic

cooling

can

work.

The

atoms

have

a

small

repulsion,

so

that

they

do

not

liquefy

or

solidify

downto

a

very

lowtemperature.9Cooling

Down

the

Atoms

See

theanimation:/physics/2000/bec/what_is_it.html

When

the

temperature

is

high,

the

atoms

have

high

energies

on

average.

Theenergy

levels

are

almost

continuous.

It

is

sufficient

to

describe

the

systemby

classical

physics.

When

the

temperature

is

low,

the

atoms

have

low

energies

on

average.

It

isnecessary

to

describe

the

system

by

quantum

physics.

When

the

temperature

is

very

low,

a

large

fraction

of

atoms

suddenly

crashinto

the

lowest

energy

state.

This

is

called

Bose-Einstein

condensation.10The

Strange

State

of

BEC

When

all

the

atoms

stay

in

the

condensate,

all

the

atoms

are

absolutely

identical.There

is

no

possible

measurement

that

can

tell

them

apart.

Before

condensation,

the

atoms

look

like

fuzzy

balls.

After

condensation,

the

atoms

lie

exactly

on

top

of

each

other

(a

superatom).11Q2:

How

Is

BECMade?Laser

beam12Other

equipment:

laser

equipment,

computer,

electronicsCost

less

than

US$100,000Laser

Cooling(激光冷卻)

The

technique

of

laser

cooling

was

developed

by

the

winners

of

the

1997

NobelPrize

winners.

In

the

physical

world,

the

lowest

temperatures

approach

a

limit

of

–273oC.

This

iscalled

the

absolute

zero.

Nothing

can

be

as

cold

as

the

absolute

zero

because

allatomic

and

subatomic

motions

stop.

Laser

cooling

can

get

to

the

low

temperature

of

0.18

K(1

K微開=10-6K).Chu

朱棣文

Cohen-Tannoundji13PhillipsSteven

Chu

(朱棣文)Stanford

UniversityUSAThe

Royal

Swedish

Academy

of

Scienceshas

awardedthe

1997

Nobel

Prize

in

Physics

jointly

to:“for

development

ofmethods

to

cool

andtrap

atoms

with

laserlight”Nobel

PrizeinPhysics

1997C.

Cohen-TannoudjiEcole

Normale

Superieure&

College

de

FranceFranceWilliams

PhillipsNational

Institute

ofStandards

&

TechnologyUSA14工作经历：1976-1978在加州大学伯克利分校做博士后研究1978-1983任电磁现象研究贝尔实验室研究人员1983-1987美国电话、电报公司贝尔实验室量子电子学研究部主任。1987至今斯坦福大学物理和应用物理教授。2008年12月被任命为美国能源部长朱棣文朱棣文是继李政道、杨振宁、丁肇中、李远哲之后的第5位华裔诺贝尔奖获得者。生于1948年2月28日 江苏省太仓县人现职：美国斯坦福大学物理学和应用物理教授教育背景：1970年毕业于罗彻斯特大学，获数学学士和物理学学士。1976年获加州大学伯克利分校物理学博士。15Ping-pong

Balls

Photons

are

particles.

They

carry

momenta

like

ping-pong

balls.

You

can

slow

the

motion

of

an

atom

by

bouncing

laser

light

off

the

atoms.

See

the

animation

/physics/2000/bec/lascool1.html.16Tuning

the

Laser

Only

laser

light

with

the

correct

colour

(frequency)

can

be

absorbed

by

theatoms.

If

the

colour

is

wrong,

the

atoms

cannot

absorb

the

photons.

See

the

animation

/physics/2000/bec/lascool2.html17Mechanical

effects

of

light18As

a

consequence

ofthe

conservation

of

energy

andmomentum,

atoms

can

experiencelight-induced

forces

during

their

interaction

with

a

radiation

field.Next,

we

discuss

the

application

of

these

forces

incausing

the

deflection,

cooling

of

the

atomic

beams.1.

Atomic

deflection19When

an

atom

absorbs

or

emits

a

photon

offrequency

ν

from

a

light

beam,

a

transfer

of

recoilmomentumtakes

place

between

the

atom

and

the

field.If

absorption

is

followed

by

stimulated

emission,

nonet

momentum

is

transferred

to

the

atom

as

themomentum

transferred

in

the

process

of

absorptionis

canceled

by

equal

but

opposite

transfer

ofmomentum

in

the

process

of

stimulated

emission.20If,

however,

absorption

is

followed

by

spontaneousemission,

there

is

a

net

momentum

transfer

to

theatom

as

the

spontaneous

emission

in

arbitrarydirections

gives

no

average

contribution

tothemomentum.If

this

process

takes

place

a

large

number

oftimes,

a

substantial

transfer

of

momentumcanoccur,

from

the

light

beam

to

the

atom,

leading

toatomic

deflection.21As

discussed

above,

an

atom

experience

a

momentumrecoil

of upon

each

radiative

event.

Hencetheabsorptive

force

of

the

atom

is

given

bywhere

r

is

the

rate

of

radiation

decay

or

the

netfluorescence

rate.

For

a

two-level

atomat

rest,

with

atransition

frequency

ω,

the

rate

γ

is

proportional

to

theupper

level

occupancy

ρaa

of

the

atom,

i.e.,22where

Γ

is

the

spontaneous

emission

rate

from

theexcited

state

|a>

to

the

ground

state

|b>.The

interaction

of

a

two-level

atom

with

a

radiation

field

offrequency

ν

is

described

by

the

following

set

of

equationsfor

the

density

matrix

elements:23where

the

detuning

is

Δ=ω-ν,

ΩR

is

the

Rabifrequencyassociated

with

the

light

beam.A

steady-state

solution

of

the

density

matrix

elementsyields24The

absorptive

force

is

thus

given

byand

is

in

the

same

direction

as

the

light

beam.2.

Laser

cooling25So

far

we

have

considered

the

force

of

a

light

beam

onan

atom

atrest.If

the

atom

is

moving

with

a

velocity

v

along

the

lightbeam,

it

seesa

Doppler

shifted

frequency,

ν±kv,

ofthe

light

beam.Here

the

+

(or

-)

sign

corresponds

to

a

situation

whenthe

atom

is

moving

in

the

opposite

(or

same)

directionto

the

light

beam.The

expression

for

the

absorptive

force

Fa

then

becomes26In

the

limit

of

no

saturation(ΩR=0

in

the

denominator)and

a

small

velocity,

we

can

expand

the

denominator.The

resulting

expression

for

Fa

iswhere27is

a

constant

deflecting

force,The

second

term,

proportional

to

atomic

velocity,

actslike

a

friction

term.If

the

atom

is

located

in

a

standing

wave,

it

sees

twooppositely

moving

light

waves,

one

in

the

samedirection

as

the

velocity

of

the

atom

and

other

in

theopposite

direction.We

assume

that

the

forces

due

to

the

two

beams

canbe

superimposed.

Hence

the

total

force

on

the

atomin

a

standing

wave

is28i.e.,

the

deflection

forces

Fo

cancel

and

the

frictionforces

from

the

two

beams

remain.

The

friction

forceisresponsible

for

the

slowing

down

of

the

atom

leadingto

laser

cooling.Physically,

we

can

understand

the

process

of

lasercooling

as

follows.Ifthe

field

moving

in

the

oppositedirection

to

the

atom

will

be

Dopplerup-shifted,

thus

compensating

thedetuning.

The

atom

will

thereforebedecelerated.

By

this

mechanism

theatoms

can

be

slowed

down

to

thepace

of

extremely

sluggish

atomicmolasses.ωνkv29atomlightUsing

the

Doppler

Effect(多普勒效应)

Problem:

The

laser

can

slow

theapproaching

atoms,

but

it

can

alsoblast

off

the

receding

ones.

Solution:

Use

Doppler

shift.

When

the

atom

is

receding

fromthe

laser

source,

the

wavelengthislengthened

and

there

is

a

redshift.

When

the

atom

is

approaching

thelaser

source, the

wavelength

isshortened

and

there

is

a

blueshift.

See

theanimation:http://www.astro.ubc.ca/~scharein/a3

11/Sim.html30多普勒冷却极限31多普勒冷却原则上可以使原子的热速度从室温下的几百m/s降至很低，但是却不能无限低下去，存在着一个极限TD。因为原子在每次吸收和自发发射光子而获得阻碍其运动的过程中，由于自发发射的随机性，每发射一个光子以后原子都获得一个在时间和方向上都随机的反冲动量，因而导致原子动量的起伏。这种起伏相应于激光对原子的一种加热过程，它是难于消除的。激光对原子的冷却速率与这种加热过程达到平衡的温度，也就

是激光冷却的多普勒极限温度TD

。需要其他的冷却机制将原子冷却至比TD更低的温度，它们基本上都是在“光学粘胶”中依靠其它机制来实现。32Laser

Trapping(激光陷阱)

Suppose

the

laser

has

the

right

colour

for

the

photons

to

be

absorbed

by

anapproaching

atom,

then

the

atom

will

be

slowed

down.

However,

the

laser

will

not

have

the

right

colour

for

the

photons

to

beabsorbed

by

the

receding

atom

because

of

Doppler

effect.

Hence

the

atomwill

not

change

in

this

case.

When

lasers

are

sent

in

from

all

the

different

directions,

the

atoms

can

getcold

very

quickly.

This

is

calledlaser

trapping,

and

the

trapped

atoms

form

an

optical

molass

(光学黏胶).

See

the

animation:

/physics/2000/bec/lascool4.html

33真空中的一束钠原子被迎面而来的激光束阻止了下来，然后把钠原子引进两两相对，沿三个正交方向的六束激光的交汇处。其效果就是不管钠原子企图向何方运动，都会遇上具有恰当能量的光子，被推回到六束激光交汇的区域。于是，在这个小区域里，聚集了大量冷却下来的原子，组成了肉眼看去像是豌豆大小的发光气团。由六束激光组成的阻尼机制就像某种粘稠的流体，原子陷入其中会不断降低速度。这种机制就叫做“光学粘胶”。34光学粘胶35Magnetic

Trapping(磁性陷阱)

Problem:

Laser

cooling

can

cool

the

atoms

down

to

10

K,

because

atoms

canspontaneously

emit

the

absorbed

photon.

This

is

still

too

hot

forBEC.

Solution:

Evaporative

cooling

The

atoms

behave

as

tiny

compasses.

They

can

be

pulled

by

magnetic

fields.

A

magnetic

field

can

be

designed

to

push

the

atoms

inwards

from

both

sides,forming

a

magnetic

trap.

See

the

animation:

/physics/2000/bec/mag_trap.html36在光学粘胶装置的基础上再加上两个磁性线圈，设计了一种很有效的陷阱，叫做磁光陷阱。磁光陷阱会产生一个比重力大的力，从而把原子拉回到陷阱中心。磁光阱37Evaporative

Cooling(揮發冷卻)

Principle:

Evaporation

takes

heat.

A

cup

of

tea

gets

cool

after

steam

escapes,because

faster

atoms

escape

from

the

cup,

leaving

behind

the

slower

ones.

Technique:

Lower

the

height

of

the

trap

quickly,

so

that

there

are

still

enoughatoms

left

in

the

trap

to

get

involved

in

BEC.

Try

to

trap

the

largest

number

of

atoms

in

BEC

in

the

animation:

/physics/2000/bec/evap_cool.html383940Can

You

Break

This

Record?41Q3:

What

Does

a

Bose-Einstein

Condensate

Look

Like?

There

is

a

drop

of

condensate

at

thecentre.

The

condensate

is

surrounded

by

uncondensed

gas

atoms.

The

combination

looks

like

a

cherry

with

a

pit.

See

the

movie

when

it

cools

from

400

nK

to

50

nK(1nK納開=10-9K).:

/physics/2000/bec/what_it_looks_like.html42Atom

Laser(原子激射)

Laser

of

light:

all

the

photons

are

exactly

the

same

in

colour,

direction

and

phase(positions

of

peaks

and

valleys).

Laser

of

atoms:

all

the

atoms

in

the

condensate

are

exactly