Observation of atom pairs in spontaneous four wave mixing of two colliding Bose-Einstein Co

a r X i v :0704.3047v 4 [q u a n t -p h ] 12 M a y 2008

Observation of atom pairs in spontaneous four wave mixing of two colliding

Bose-Einstein Condensates

A.Perrin,H.Chang,V.Krachmalnico?,M.Schellekens,D.Boiron,A.Aspect and C.I.Westbrook ?

Laboratoire Charles Fabry de l’Institut d’Optique,CNRS,Univ Paris-Sud

Campus Polytechnique,RD128,91127Palaiseau cedex

(Dated:May 13,2008)

We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive,time resolved,single atom detector.In analogy to quantum optics,the process can also be thought of as spontaneous,degenerate four wave mixing of de Broglie waves.We ?nd a clear correlation between atoms with opposite momenta,demonstrating pair production in the scattering process.We also observe a Hanbury Brown and Twiss correlation for collinear momenta,which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode.The back to back pairs occupy very nearly two oppositely directed spatial modes,a promising feature for future quantum optics experiments.

PACS numbers:34.50.-s,03.75.Nt

Recent years have seen the emergence of “quantum atom optics”,that is the extension of the many analo-gies between atom optics and traditional optics to the quantum optical domain in which phenomena like vac-uum ?uctuations and entanglement play a central role.In optics the advent of correlated photon pairs [1]has provided a fruitful avenue of investigation,with exam-ples including single photon sources and entangled states [2].Partly inspired by this work,there have been many proposals concerning atom pairs,especially the produc-tion and observation of entanglement [3,4,5,6,7].Many authors have also theoretically investigated other aspects of the pair production mechanism in both atomic collisions and in the breakup of diatomic molecules [7,8,9,10,11,12,13].

As emphasized in Ref.[4],pair production can be stud-ied in two limits.If many atoms are created in a sin-gle mode,stimulated emission of atoms is important,and one can speak of two mode squeezing in analogy with Ref.[14].The opposite limit,in which the occupa-tion number of the modes is much less than unity,cor-responds to the spontaneous production of atom pairs,entangled either in spin or momentum in analogy with Ref.[15,16].Experiments on stimulated atomic four wave mixing [17,18,19]and on parametric ampli?ca-tion in an optical lattice [20,21]are in the ?rst limit,and pairs of “daughter BEC’s”with opposite velocities have been clearly observed.Experiments in the regime of individual atom pairs include the many experiments in-vestigating the scattered halo in collisions of cold atoms either in the s-wave regime [22,23,24]or for higher par-tial waves [25,26].None of these experiments however,has demonstrated correlated pairs.The only evidence of atom pair production with cold atoms has been re-ported in absorption images of atoms from the breakup of molecules near a Feshbach resonance [27].

Here,we report on the observation of individual atom pairs with opposite velocities produced in the collision

FIG.1:(Color online)(a)View of the magnetically trapped condensate (in the m x =1state)and the three laser beams which create two cigar shaped counterpropagating free con-densates (in the m x =0state)by σ?/πRaman transfers induced by L 1?L 2and L 1?L ′2respectively (see inset).L 1is

π?polarized (along x )while L 2and L ′2are σ?

-polarized.(b)Representation in velocity space of the expected atomic den-sity after the collision.The scattered atoms are on a sphere and the remaining condensates,pancake-shaped after expan-sion,lie on the edge of the sphere along the x axis.

of two condensates.A time and position resolved,sin-gle atom detector [28]permits us to reconstruct the 3dimensional distribution of the scattered atoms:a spher-ical shell in velocity space.We also reconstruct the two-particle correlation function in 3D and ?nd a strong cor-relation between atoms emitted back to back.This pro-cess can be interpreted as a spontaneous four wave mix-ing process constrained by a phase matching condition as in the non linear optical analog which produces twin photons [2].It can also be seen as the result of pairwise elastic collisions between atoms,constrained by momen-tum conservation.We measure the width of the velocity correlation function for a back to back atom pair and show that it can be roughly understood from the uncer-tainty limited momentum spread of the colliding BECs.This interpretation is con?rmed by the observation of

2

the velocity correlation function for two atoms scattered in

the same direction.This latter e?ect,predicted in Refs.[7,10,13],is another manifestation of the Hanbury Brown-Twiss e?ect (HBT).As in high energy collisions [29],the e?ect allows us to measure the size of the colli-sion volume.

The fact that the width of the HBT peak is close to that of the back to back correlation con?rms that for a given atom on the collision sphere,its partner is scattered into a single mode of the matter wave ?eld.This observa-tion is crucial for future experiments in which one would like to bring pairs back together in order to con?rm their entanglement in the spirit of Ref.[16]or observe other quantum e?ects [30].

We produce condensates of 104?105atoms in the m x =1sublevel of the 23S 1state of metastable helium (He*).The condensates are stored in a cylindrically sym-metric magnetic trap with axial and radial trapping fre-quencies of 47Hz and 1150Hz respectively.The bias ?eld is 0.25G in the x direction (see Fig.1),and de?nes the quantization axis.The uncertainty limited velocity spread of the colliding atoms is thus anisotropic and we calculate it numerically using the Gross-Pitaevskii equa-tion [31].For a condensate with 3×104atoms,we ?nd

rms axial and radial velocity spreads of v rms

x

=0.0044v rec and v rms

yz =0.091v rec ,where v rec =9.2cm/s is the sin-gle photon recoil velocity, k/m where k is the photon wavevector and m is the atomic mass.The spread in these values due to the spread in condensate number is about ±20%.

To generate two colliding Bose-Einstein condensates,we use two stimulated Raman transitions with di?erent momentum transfers,produced by phase coherent laser beams L 1,L 2and L ′2,as shown in Fig.1[31].These transitions have two purposes:?rst they transfer atoms to the magnetic ?eld insensitive state m x =0so that they freely fall to the detector and second,they sepa-rate the condensate into two components with velocities v rec (e 1±e 2),where e 1and e 2are the unit vectors along the propagation axes of the laser beams L 1and L 2re-spectively.The beams are pulsed on for a duration of ～500ns and couple about 60%of the atoms to the m x =0state.We do not switch o?the magnetic trap,therefore atoms remaining in m x =1stay trapped.The two colliding condensates travel with a relative velocity of 2v rec ,at least 8times larger than the speed of sound in the initial condensate.This ensures that elementary excitations of the condensate correspond to free particles.Since they are no longer trapped,the two colliding con-densates expand radially,reducing the collision rate.A numerical model [8],assuming an expansion identical to that of a single condensate with the same total number of atoms,shows a roughly exponential decrease in the pair production rate with a time constant of ～150μs.

After the collision,atoms fall onto a 8cm microchan-nel plate detector placed 46.5cm below the trap center.

This detector measures the arrival time of the atoms and their positions in the x ?y plane [28,32].Figure 2shows successive 2.4ms time slices showing the atom positions as they cross the detector plane.The time of ?ight for the center of mass to reach the detector is 320ms.Since this time of ?ight is large compared to the collision du-ration,and the observed patterns are large compared to the collision volume,the observed 3D atom positions ac-curately re?ect the velocity distribution after collision.In the following,we will only refer to the velocities of the detected atoms.

FIG.2:(Color online)(a-i)Images of the collision of two condensates.Each frame represents a 2.4ms time slice of the atomic cloud as it passes the plane of the detector (x ?y ).150shots have been averaged to obtain these images.The two colliding condensates I,II and the collision sphere are clearly visible.Other features visible in the images are discussed in the text.The axes are marked in units of the recoil velocity.

In Fig.2,one clearly sees a spherical shell of radius of v rec ,represented by circles of varying diameter.In the mid plane of the sphere one can see the unscattered,pancake-shaped condensates I,II which locally saturate the detector.Other features are also visible in Fig.2.In frames (a,b)one sees a condensate,III,which underwent no momentum transfer,possibly due to the imperfect po-larization of the Raman beams which can produce an o?resonant,single beam Raman transition [31].A fourth condensate,IV,probably resulting from four-wave mix-ing [17]of condensate III and the main unscattered con-densates I,II is visible in frames (h,i).Frames (b,c)show a collision sphere due to the collision of I with atoms re-maining trapped in m x =1and with condensate III.The two spots within the sphere in frames (d-f)are not understood.

3

To avoid e?ects of local saturation of the detector in our analysis,we exclude regions around the4conden-sates,representing about40%of the sphere.On the remaining area of the sphere we detect between30and 300atoms on each shot,with an average of about

100 per shot.Assuming a detection e?ciency of10%[32], this means that～5%of the atoms are scattered from the two condensates.This number is consistent with the expected s?wave cross section[33]and the estimated evolution of the density during the collision.

We examine the pair correlation function for atoms in back to back directions by constructing,within the set of all the scattered atoms in one shot,a three dimen-sional histogram containing all the pairs with a velocity sum V=V1+V2close to zero.We then sum the his-tograms over1100shots.Another histogram containing all the pairs of the sum of all shots gives the accidental coincidence rate for uncorrelated atoms and is used as a normalization.We thus recover the normalized second order correlation function,averaged over the sphere[31], g(2)(V)of the distribution of relative velocities of atom pairs on the sphere.Figure3(a)shows the behavior of g(2)(V)around V=0projected along the three space axes.The peak indicates that,given the detection of an atom on the sphere,there is an enhanced probability of detecting a second one on the opposite side.Cartesian coordinates are best suited to plotting the data because of the competing spherical symmetry of the scattering process and the cylindrical symmetry of the source.

To analyze these results further,we perform a three-dimensional Gaussian?t to the normalized histogram:

g(2)(V x,V y,V z)=1+ηe?V x 2

2σyz2.(1)

The?t givesηBB=0.19±0.02,σBB

x =0.017±0.002v rec

andσBB

yz =0.081±0.004v rec.The observed width in the

x direction is limited by the rms pair resolution of the detector,0.014v rec[31,36].In the y and z directions, the observed width is close to the uncertainty limited ve-

locity scale v rms

yz discussed above.It is therefore reason-

able to conclude that the anisotropy in the correlation

function is closely related to the anisotropy of the mo-mentum distribution in the source.Detailed modelling accounting accurately for this width is in progress,but

for purposes of this letter,we will simply compare the width with that of the correlation function for collinear

atoms as described below.

The procedure to construct the correlation function for nearly collinear velocities(the HBT e?ect)is the same as

that for the back to back correlation function.De?ning the relative velocity V′=V1?V2we show in Fig.3b the correlation function g(2)(V′)around V′=https://www.wendangku.net/doc/12259881.html,ing

the?tting function,Eq.1,we?nd:ηCL=0.10±0.02,σCL x=0.016±0.003v rec andσCL yz=0.069±0.008v rec. As in the back to back case,the width in the x direction is limited by the resolution while in the y?z plane it FIG.3:Back to back(panel a)and collinear(panel b)cor-relation peaks.(a)Projection of g(2)(V=V1+V2)along the di?erent axes of the experiment and around V=0. The projection consists in averaging the correlation in the two other directions over a surface equal to the products of the corresponding correlation lengths.This averaging makes the height smaller than the3D?tted valueηBB=0.19±0.02. The peak is the signature for correlated atoms with oppo-site velocities.(b)Projection of g(2)(V′=V1?V2)along the di?erent axes of the experiment.This peak is due to the Hanbury Brown and Twiss bunching e?ect.All velocities are expressed in units of the recoil velocity.

is close to v rms

yz

.If we think of the HBT e?ect as giving a measure of the size of the pair production source,the

width of the collinear correlation function de?nes the size of a mode of the scattered matter wave?eld.The fact that the back to back and collinear widths are so close, at least in the directions we can resolve,is further,strong evidence that,at least in the directions we resolve,the pairs we produce are in oppositely directed modes.

We now turn to the height of the peaksη.In the collinear case we expect the value ofηCL to be unity for a detector resolution much smaller than the peak width. Since in the x direction the width is clearly limited by the resolution,a crude estimate forηCL is the ratio of the

ideal width to the observed one:ηCL≈v rms

x

/σx=0.3. The discrepancy with the?tted value may have to do with our crude estimate of the e?ective source size along

x and therefore of v rms

x

.

In the back to back case,the height of the peak is not limited to unity.A simple model of the peak height com-pares the number of true pairs to random coincidences in a volume?V de?ned by the widths observed in Fig.3:

1+ηBB=

true+random

N?V

(2) Here N is the number of atoms scattered on a single shot (but not necessarily detected)and V is the volume of the scattering shell.A rough estimate of?V/V is1/1400. As mentioned above,we detect on average100atoms on

4

the analyzed 60%of the sphere.Assuming again a quan-tum e?ciency of 10%,a rough estimate of the average number N is 1700so that we ?nd ηBB ≈0.8which gives the correct order of magnitude.We emphasize that ?V is limited by the detector resolution in the x direction and is therefore about 10times larger than the volume corresponding to a single mode.Thus as stated in the introduction,the number of scattered atoms per mode is small compared to unity,and we are in the separated en-tangled pair

production regime.We can verify the 1/N dependence of Eq.(2)by binning the data according to the number of scattered atoms per shot.Dividing the 1100shots into 3bins of di?erent atom numbers we do observe the expected trend as shown in Fig.4.

FIG.4:Projections of g (2)(V )along the x axis and around V =0.Bin of mean number of detected atoms of (a)50,(b)125and (c)190.

A detailed model of the pair production process must include a more careful description of the collision geome-try of colliding and expanding condensates as well the e?ect of the condensates’mean ?eld on the scattered atoms,something which is neglected in the above dis-cussion.A rough estimate of the mean ?eld e?ect is found by adding the chemical potential to the kinetic en-ergy of a scattered atom.This gives an additional veloc-ity broadening of order 0.03v rec ,not entirely negligible compared to the observed widths.Several workers are developing such models.The correlation functions we observe lend themselves to an investigation of Cauchy-Schwartz inequalities [2].A cross correlation (back to back)greater than an autocorrelation (collinear)violates a Cauchy-Schwartz inequality for classical ?elds.Sub-Poissonian number di?erences between opposite direc-tions should also be present [7].A future publication will discuss these aspects of the experiment.

We acknowledge valuable discussions with K.Kheruntsyan,K.M?lmer and M.Trippenbach.Our group is a member of the IFRAF institute,and is supported by the french ANR,the QUDEDIS program and the SCALA program of the European Union.

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英语中的比较级与最高级 详解

比较级与最高级 1.as...as 与(not) as(so)...as as...as...句型中，as的词性 第一个as是副词，用在形容词和副词的原级前，常译为“同样地”。第二个as是连词，连接与前面句子结构相同的一个句子(相同部分常省略)，可译为“同..... He is as tall as his brother is (tall) . (后面的as 为连词) 只有在否定句中，第一个as才可换为so 改错: He is so tall as his brother.（X） 2.在比较状语从句中，主句和从句的句式结构一般是相同的 与as...as 句式中第二个as一样，than 也是连词。as和than这两个连词后面的从句的结构与前面的句子大部分情况下结构是相同的，相同部分可以省略。 He picked more apples than she did. 完整的表达为: He picked more apples than she picked apples. 后而的picked apples和前面相同，用did 替代。 He walked as slowly as she did.完整表达为: He walked as slowly as she walked slowly. she后面walked slowly与前面相同，用did替代。

3.谓语的替代 在as和than 引导的比较状语从句中，由于句式同前面 主句相同，为避免重复，常把主句中出现而从句中又出现的动词用do的适当形式来代替。 John speaks German as fluently as Mary does. 4.前后的比较对象应一致 不管后面连词是than 还是as,前后的比较对象应一致。The weather of Beijing is colder than Guangzhou. x than前面比较对象是“天气”，than 后面比较对象是“广州”，不能相比较。应改为: The weather of Bejing is colder than that of Guangzhou. 再如: His handwriting is as good as me. 应改为: His handwriting is as good as mine. 5.可以修饰比较级的词 常用来修饰比较级的词或短语有: Much,even,far,a little,a lot,a bit,by far,rather,any,still,a great deal等。 by far的用法: 用于强调，意为“...得多”“最最...”“显然”等，可修饰形容词或副词的比较级和最高级，通常置于其后，但是若比较级或最高级前有冠词，则可置于其前或其后。

The way常见用法

The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because

人教版(新目标)初中英语形容词与副词的比较级与最高级

人教版（新目标）初中英语形容词与副词的比较级与最高级 （一）规则变化： 1．绝大多数的单音节和少数双音节词，加词尾-er ，-est tall—taller—tallest 2．以不发音的e结尾的单音节词和少数以-le结尾的双音节词只加-r，-st nice—nicer—nicest , able—abler—ablest 3．以一个辅音字母结尾的重读闭音节词或少数双音节词，双写结尾的辅音字母，再加-er，-est big—bigger—biggest 4．以辅音字母加y结尾的双音节词，改y为i再加-er，-est easy—easier—easiest 5．少数以-er，-ow结尾的双音节词末尾加-er，-est clever—cleverer—cleverest, narrow—narrower—narrowest 6．其他双音节词和多音节词，在前面加more，most来构成比较级和最高级 easily—more easily—most easily （二）不规则变化 常见的有： good / well—better—best ; bad (ly)/ ill—worse—worst ; old—older/elder—oldest/eldest many / much—more—most ; little—less—least ; far—farther/further—farthest/furthest

用法： 1．原级比较：as + adj./adv. +as（否定为not so/as + adj./adv. +as）当as… as中间有名字时，采用as + adj. + a + n.或as + many / much + n. This is as good an example as the other is . I can carry as much paper as you can. 表示倍数的词或其他程度副词做修饰语时放在as的前面 This room is twice as big as that one. 倍数+as+adj.+as = 倍数+the +n.+of Your room is twice as larger as mine. = Your room is twice the size of mine. 2．比较级+ than 比较级前可加程度状语much, still, even, far, a lot, a little, three years. five times,20%等 He is three years older than I (am). 表示“（两个中）较……的那个”时，比较级前常加the（后面有名字时前面才能加冠词） He is the taller of the two brothers. / He is taller than his two brothers. Which is larger, Canada or Australia? / Which is the larger country, Canada or Australia? 可用比较级形式表示最高级概念，关键是要用或或否定词等把一事物（或人）与其他同类事物（或人）相分离 He is taller than any other boy / anybody else.

英语中的比较级和最高级

大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基础上变化的。分为规则变化和不规则变化。 规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加 -er 和 -est 构成。 great (原级) (比较级) (最高级) 2) 以 -e 结尾的单音节形容词的比较级和最高级是在词尾加 -r 和 -st 构成。wide (原级) (比较级) (最高级) 3)少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和 -est 构成。 clever(原级) (比较级) (最高级) 4) 以 -y 结尾,但 -y 前是辅音字母的形容词的比较级和最高级是把 -y 去掉,加上 -ier 和-est 构成. happy (原形) (比较级) (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该辅音字母然后再加 -er和-est。 big (原级) (比较级) (最高级) 6) 双音节和多音节形容词的比较级和最高级需用more 和 most 加在形容词前面来构成。 beautiful (原级) (比较级) (比较级) difficult (原级) (最高级) (最高级) 常用的不规则变化的形容词的比较级和最高级: 原级------比较级------最高级 good------better------best many------more------most much------more------most bad------worse------worst far------farther, further------farthest, furthest 形容词前如加 less 和 least 则表示"较不"和"最不 形容词比较级的用法: 形容词的比较级用于两个人或事物的比较,其结构形式如下: 主语+谓语(系动词)+ 形容词比较级+than+ 对比成分。也就是, 含有形容词比较级的主句+than+从句。注意从句常常省去意义上和主句相同的部分, 而只剩下对比的成分。

The way的用法及其含义(二)

The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中

英语比较级和最高级的用法归纳

英语比较级和最高级的用法归纳 在学习英语过程中，会遇到很多的语法问题，比如比较级和最高级的用法，对于 这些语法你能够掌握吗？下面是小编整理的英语比较级和最高级的用法，欢迎阅读！ 英语比较级和最高级的用法 一、形容词、副词的比较级和最高级的构成规则 1.一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级 在后面加-est; (1)单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest (2)双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2.以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st; 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3.在重读闭音节(即：辅音+元音+辅音)中，先双写末尾的辅音字母，比较级加-er，最高级加-est; 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4.以“辅音字母+y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est; 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5.其他双音节词和多音节词，比较级在前面加more，最高级在前面加most; 如：bea utiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily 注意：(1)形容词最高级前通常必须用定冠词 the，副词最高级前可不用。 例句： The Sahara is the biggest desert in the world. (2) 形容词most前面没有the，不表示最高级的含义，只表示"非常"。 It is a most important problem. =It is a very important problem.

(完整版)the的用法

定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

英语比较级和最高级的用法

More than的用法 A. “More than+名词”表示“不仅仅是” 1)Modern science is more than a large amount of information. 2)Jason is more than a lecturer; he is a writer, too. 3) We need more than material wealth to build our country.建设我们国家，不仅仅需要物质财富. B. “More than+数词”含“以上”或“不止”之意，如： 4)I have known David for more than 20 years. 5)Let's carry out the test with more than the sample copy. 6) More than one person has made this suggestion. 不止一人提过这个建议. C. “More than+形容词”等于“很”或“非常”的意思，如： 7)In doing scientific experiments, one must be more than careful with the instruments. 8)I assure you I am more than glad to help you. D. more than + (that)从句，其基本意义是“超过（=over）”，但可译成“简直不”“远非”.难以，完全不能（其后通常连用情态动词can） 9) That is more than I can understand . 那非我所能懂的. 10) That is more than I can tell. 那事我实在不明白。 11) The heat there was more than he could stand. 那儿的炎热程度是他所不能忍受的 此外，“more than”也在一些惯用语中出现，如： more...than 的用法 1. 比……多，比……更 He has more books than me. 他的书比我多。 He is more careful than the others. 他比其他人更仔细。 2. 与其……不如 He is more lucky than clever. 与其说他聪明，不如说他幸运。 He is more （a）scholar than （a）teacher. 与其说他是位教师，不如说他是位学者。 注：该句型主要用于同一个人或物在两个不同性质或特征等方面的比较，其中的比较级必须用加more 的形式，不能用加词尾-er 的形式。 No more than/not more than 1. no more than 的意思是“仅仅”“只有”“最多不超过”，强调少。如： --This test takes no more than thirty minutes. 这个测验只要30分钟。 --The pub was no more than half full. 该酒吧的上座率最多不超过五成。-For thirty years，he had done no more than he （had）needed to. 30年来，他只干了他需要干的工作。 2. not more than 为more than （多于）的否定式，其意为“不多于”“不超过”。如：Not more than 10 guests came to her birthday party. 来参加她的生日宴会的客人不超过十人。 比较： She has no more than three hats. 她只有3顶帽子。（太少了） She has not more than three hats. 她至多有3顶帽子。（也许不到3顶帽子） I have no more than five yuan in my pocket. 我口袋里的钱最多不过5元。（言其少） I have not more than five yuan in my pocket. 我口袋里的钱不多于5元。（也许不到5元） more than, less than 的用法 1. （指数量）不到，不足 It’s less than half an hour’s drive from here. 开车到那里不到半个钟头。 In less than an hour he finished the work. 没要上一个小时，他就完成了工作。 2. 比……（小）少 She eats less than she should. 她吃得比她应该吃的少。 Half the group felt they spent less than average. 半数人觉得他们的花费低于平均水平。 more…than,/no more than/not more than (1)Mr．Li is ________ a professor; he is also a famous scientist． (2)As I had ________ five dollars with me, I couldn’t afford the new jacket then． (3)He had to work at the age of ________ twelve． (4)There were ________ ten chairs in the room．However, the number of the children is twelve． (5)If you tel l your father what you’ve done, he’ll be ________ angry． (6)－What did you think of this novel? －I was disappointed to find it ________ interesting ________ that one． 倍数表达法 1. “倍数+形容词（或副词）的比较级+than+从句”表示“A比B大（长、高、宽等）多少倍” This rope is twice longer than that one.这根绳是那根绳的三倍（比那根绳长两倍）。The car runs twice faster than that truck.这辆小车的速度比那辆卡车快两倍（是那辆卡车的三倍）。 2. “倍数+as+形容词或副词的原级+as+从句”表示“A正好是B的多少倍”。

“the way+从句”结构的意义及用法

“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法

不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.

初中英语比较级和最高级讲解与练习

初中英语比较级和最高级讲解与练习 形容词比较级和最高级 一．绝大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 1. 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 2. 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基 础上变化的。分为规则变化和不规则变化。 二．形容词比较级和最高级规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加-er 和-est 构成。 great (原级) greater(比较级) greatest(最高级) 2) 以-e 结尾的单音节形容词的比较级和最高级是在词尾加-r 和-st 构成。 wide (原级) wider (比较级) widest (最高级) 3) 少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和-est构成。 clever(原级) cleverer(比较级) cleverest(最高级)， slow(原级) slower(比较级) slowest (最高级) 4) 以-y 结尾,但-y 前是辅音字母的形容词的比较级和最高级是把-y 去掉,加上-ier 和-est 构成. happy (原形) happier (比较级) happiest (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该 辅音字母然后再加-er和-est。 原形比较级最高级原形比较级最高级 big bigger biggest hot hotter hottest red redder reddest thin thinner thinnest 6) 双音节和多音节形容词的比较级和最高级需用more 和most 加在形容词前面来构 成。 原形比较级最高级 careful careful more careful most careful difficult more difficult most difficult delicious more delicious most delicious 7)常用的不规则变化的形容词的比较级和最高级: 原级比较级最高级 good better best 好的 well better best 身体好的 bad worse worst 坏的 ill worse worst 病的 many more most 许多 much more most 许多 few less least 少数几个 little less least 少数一点儿 （little littler littlest 小的） far further furthest 远（指更进一步，深度。亦可指更远） far farther farthest 远（指更远，路程）

way 用法

表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法

英语比较级和最高级

形容词比较级和最高级的形式 一、形容词比较级和最高级的构成 形容词的比较级和最高级变化形式规则如下 构成法原级比较级最高级 ①一般单音节词末尾加 er 和 est strong stronger strongest ②单音节词如果以 e结尾，只加 r 和 st strange stranger strangest ③闭音节单音节词如末尾只有一个辅音字母， 须先双写这个辅音字母，再加 er和 est sad big hot sadder bigger hotter saddest biggest hottest ④少数以 y, er(或 ure), ow, ble结尾的双音节词， 末尾加 er和 est(以 y结尾的词，如 y前是辅音字母， 把y变成i，再加 er和 est，以 e结尾的词仍 只加 r和 st) angry Clever Narrow Noble angrier Cleverer narrower nobler angriest cleverest narrowest noblest ⑤其他双音节和多音节词都在前面加单词more和most different more different most different 1) The most high 〔A〕mountain in 〔B〕the world is Mount Everest，which is situated 〔C〕in Nepal and is twenty nine thousand one hundred and fourty one feet high 〔D〕 . 2) This house is spaciouser 〔A〕than that 〔B〕white 〔C〕one I bought in Rapid City，South Dakota 〔D〕last year. 3) Research in the social 〔A〕sciences often proves difficulter 〔B〕than similar 〔C〕work in the physical 〔D〕sciences. 二、形容词比较级或最高级的特殊形式：

高中英语的比较级和最高级用法总结

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The way的用法及其含义(一)

The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.

(完整版)初中英语比较级和最高级的用法

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