CN101710001B - Multi-penetration ultrastable interferometer and high-precision phase measurement method thereof - Google Patents

Abstract

The invention relates to a multi-penetration ultrastable interferometer and a high-precision phase measurement method thereof. An interferometer with an ultrastable structure is designed. In two beams of light, one beam of light penetrates a phase shifter (the effect of the phase shifter is to generate an unknown phase shift phi) for multiple times (q times, and q is larger than or equal to 2) to obtain a phase shift qMphi, while the other beam of light does not penetrate the phase shifter, but relative optical paths (optical path difference) of the two beams of light in the whole process keep ultrastable (stable within a wavelet nano-grade range) so as to carry out high-precision measurement on the unknown phase shift phi. When the ultrastable interferometer is used, the phase measurement precision can be improved by utilizing a single photon (M is equal to 1), M entanglement photons or photons distinguishable to time to penetrate the phase shifter for multiple times, and a standard quantum limit can be broken. The interferometer is simple and easy to apply and has ultrastable optical path difference, and the measurement precision can be improved by using the single photon, the M entanglement photons or the photons distinguishable to time for penetrating for multiple times, and the standard quantum limit is broken.

Description

The ultra steady interferometer that repeatedly passes and the method for high-precision phase measurement thereof

Technical field

The invention belongs to the optical phase field of measurement; Relate in particular to the ultra steady interferometer that repeatedly passes and utilize single photon, M entangled photons and time to go up differentiable photon survey phase place; Phase measurement accuracy can be increased substantially, and the method for the Measurement Phase of standard quantum limit can be broken.

Background technology

As everyone knows, measurement is the basis of all quantitative science.For whole realm of science, it is vital accurately measuring.For example, utilize the measurement of optical phase can obtain many physical quantitys,, also can carry out many other application like distance, position, displacement, acceleration and light path etc.

Utilize high-precision measuring method, can find new physical phenomenon, the new physical theory of development.Yet the measuring accuracy of physical quantity can receive the quantum mechanics ultimate principle--the restriction of Heisenberg's uncertainty principle.In the phase measurement relevant with basic physics amounts such as time, distances, the uncertainty of its measuring accuracy and used population N (for example, photon or ion) are inversely proportional to, and full accuracy can reach the 1/N reciprocal of number average particle, i.e. Heisenberg's limit.Proved already that Heisenberg's limit was the upper limit (UL) that quantum mechanics allows.And the standard quantum limit that limit by noise; It is noise margin; Generally be that the subduplicate inverse of number average particle

has had a lot of experiments to show; Phase measurement accuracy can be broken the standard quantum limit, as based on squeezed state and multi-photon interference technique or the like.But because the existence of inherent loss, its measuring accuracy can't be approached Heisenberg's limit, even becomes poorer with the increase of photon number.The measuring accuracy that how to improve physical quantity has become physicist's important subject.Along with development of technology, the measurement level is also constantly improving.Simultaneously, high-precision optical phase measurement has many important use, comprises mensuration and medical science and biological reflection measurement or the like of microscopy, gravitational wave detection, material character.

Below, we introduce two kinds of double beam interferometers: a kind of Mach-Zehnder of being interferometer, as shown in Figure 1, it is by two 50: 50 beam splitter BS1 and BS2, and two level crossings 1 and 2 are formed.Input mould a and mould b photon on BS1, wherein mould d afterwards, makes up on BS2 through phase-shifter (PS, its effect is to produce phase shift φ) again, and is last, on mould e and mould f, surveys.This interferometer is on principle, and the optical path difference of two-beam is not easy control, can not keep the stability of long (nanometer) magnitude of wavelet.In optical interdferometer, if relative optical path difference remains unchanged or remains on the stability that wavelet is grown (nanometer) magnitude, claim that this interferometer has superstability, promptly it has ultra steady structure.

Another kind of interferometer is as shown in Figure 2, is called the Nagata interferometer, and it has the ultra steady structure of inherent inherently stable, and it can guarantee that the optical path difference of mould c and mould d is that wavelet long (nanometer) is stable.But it can only make the light beam single of mould d pass phase-shifter.

Utilizing quantum entanglement to carry out the optical phase measurement can improve measuring accuracy and break the standard quantum limit.Therefore; Recently the many work on interferometer all accumulate in and utilize M entangled photons M00M attitude, i.e.

or improve measuring method.

Recently, Nagata research group of Hokkaido, Japan university has realized the high-accuracy optical phase measurement experimentally, uses and tangles four interference of photons, and it interferes visibility to be higher than the threshold value visibility and to break the standard quantum limit.This achievement is published on [Science 316 (2007) 726].Their result uses the new approach of having started for high-acruracy survey.Yet they have only considered that the entangled photons single passes phase-shifter.Therefore, single photon or time are gone up differentiable photon, use their method all can not break the standard quantum limit.

In order to overcome above-mentioned deficiency, we expect the appearance of novel ultra steady interferometer, thereby use single photon, M entangled photons and time to go up differentiable photon survey phase place, all can improve phase measurement accuracy, and find the phase measurement method of breaking the standard quantum limit.

Summary of the invention

The phase measurement method that the object of the present invention is to provide a kind of ultra steady interferometer that repeatedly passes and break the standard quantum limit.The technical solution adopted for the present invention to solve the technical problems is:

The ultra steady interferometer that repeatedly passes comprises that a bundle divides device BS and the first single face level crossing 1, the second single face level crossing 2, the 3rd single face level crossing 3, places on the surface level, and has the optical element of the ultra steady structure of repeatedly passing and form.The optical element of ultra steady structure is after repeatedly passing phase-shifter, can guarantee that mould c and mould d optical path difference are stabilized in the nanoscale scope.

Wherein specifically designed two optical elements that ultra steady structure is arranged, represented that respectively 2 times (q=2) and 4 times (q=4) passes phase-shifter.Wherein, the component structure of 2 times (q=2) is: A is a two-sided planar mirror, and its available two back-to-back single-surface mirror replaces, and also has four single face level crossing B, C, D and E, and these five level crossings are fixed in the vertical plane.The component structure of 4 times (q=4) is: A is a two-sided planar mirror; Its also available two back-to-back single-surface mirror replaces; Also have eight single face level crossings; I.e. the 4th single face level crossing B, the 5th single face level crossing C, the 6th single face level crossing D, the 7th single face level crossing E, the 8th single face level crossing F, the 9th single face level crossing G, the tenth single face level crossing H and the 11 single face level crossing I, these nine mirrors are fixed in the vertical plane.Pass for four times, its concrete light channel structure is following:

Light is respectively input point a with mould a and mould b with input point b imports corresponding photon exactly by input point a and input point b input, and after acting on through bundle branch device (BS); Part light is called mould d, arrives the first single face level crossing 1 inwards, passes phase-shifter (PS) for the 1st time to the right and the upper surface of arrival two-sided planar mirror A; Upward to the 11 single face level crossing I, level is passed phase-shifter (PS) the 2nd time left and is arrived the tenth single face level crossing H, afterwards; Upward to the 9th single face level crossing G, pass phase-shifter (PS) the 3rd time to the right and arrive the 8th single face level crossing F, upward to the 7th single face level crossing E; The 4th is passed phase-shifter (PS) and is arrived the 6th single face level crossing D left, down to the 5th single face level crossing C, to the right to the 4th single face level crossing B; Lower surface upward to two-sided planar mirror A; Arrive the second single face level crossing 2 to the right, outwards arrive the 3rd single face level crossing 3, incide bundle left again and divide device (BS);

Another part light is called mould c, arrives the 3rd single face level crossing 3 to the right, arrives the second single face level crossing 2 inwards; Arrive the lower surface of two-sided planar mirror A left, arrive the 4th single face level crossing B downwards, left to the 5th single face level crossing C; Upwards arrive the 6th single face level crossing D, do not pass phase-shifter (PS) to the right and, arrive the 8th single face level crossing F downwards to the 7th single face level crossing E; Do not pass phase-shifter (PS) left to the 9th single face level crossing G; Down to the tenth single face level crossing H, do not pass phase-shifter (PS) to the right to the 11 single face level crossing I, arrive the upper surface of two-sided planar mirror A downwards; Do not pass phase-shifter (PS) left and, outwards incide bundle branch device (BS) again to the first single face level crossing 1; After light passes phase-shifter (PS) for 4 times, can guarantee that mould c and mould d optical path difference are stabilized in the nanoscale scope, the above-mentioned two-beam that arrives bundle branch device (BS) once more, after the process bundle divided device (BS) effect, the light of exporting left was mould e, the light of downward output is mould f.

For other more optical elements that pass the ultra steady structure of number of times (q＞4), can obtain through similar method more.

The method that adopts the ultra steady interferometer repeatedly pass to carry out phase measurement is: establishing total useful photon number that experiment adopts is N=qM, promptly once tests the product of used photon number M and the number of times q that repeatedly passes, q >=2 here, M >=1, then N >=2.For example, if repeatedly pass q=2, utilize single photon M=1, then N=1 * 2=2 utilizes two-photon M=2, then N=2 * 2=4; If repeatedly pass q=4, utilize single photon M=1, then N=4 * 1=4 utilizes two-photon M=2, N=4 * 2=8 then, the rest may be inferred.

Based on the above-mentioned ultra steady interferometer that repeatedly passes q >=2; Utilize single photon M=1, M entangled photons and the differentiable photon of M to go to measure the phase an of the unknown; The present invention has provided and wherein a branch ofly in a kind of two-beam has repeatedly passed same phase-shifter; Each photon whenever passes phase-shifter and once produces phase shift φ, and once the phase shift of experiment acquisition is respectively q * 1 φ=N φ, qM φ=N φ and qM φ=N φ; And another Shu Guang does not pass phase-shifter, but the relative light path difference of two-beam is stabilized in the nanoscale scope.Once the useful photon number of experiment is respectively q * 1=N, qM=N and qM=N.Then the precision of Measurement Phase φ is respectively 1/ (q * 1)=1/N, 1/ (qM)=1/N and 1/ (qM)=1/N.Their corresponding standard quantum limits do $1/\sqrt{q\×1}=1/\sqrt{N},$ $1/\sqrt{\mathrm{QM}}=1/\sqrt{N}$ With $1/\sqrt{\mathrm{QM}}=1/\sqrt{N}.$ Can find out, because N>=2 are repeatedly passed and can be broken the standard quantum limit.

The method that adopts single to pass, establishing total useful photon number that experiment adopts is N=qM, q >=2 here, M >=1, N >=2 then, this with repeatedly pass once to test corresponding used useful photon number identical.In theory, if utilize the phase of differentiable photon survey one the unknown of single photon (M=1), M entangled photons and M, the phase shift that each experiment produces is respectively φ, M φ and M φ.Testing used photon number each time is 1, M and M, and the number of times of experiment is respectively N, q and q, then total photon number of experiment use is respectively 1 * N=N, qM=N and qM=N.Therefore, measuring φ precision Δ φ is respectively

With $1/\left(M\sqrt{q}\right)=1/(N/\sqrt{q}).$

So; In theory; The measuring accuracy of repeatedly passing will be higher than the precision that single passes; Utilize the differentiable photon survey phase of single photon (M=1), M entangled photons and M, improved

and

respectively doubly.Repeatedly pass and to improve phase measurement accuracy, and can break the standard quantum limit.

In experiment, through repeatedly passing, the M photon is imported in q>=2, and the useful photon number is N=qM, after on same beam splitter (BS), reconfiguring, is P if on mould e, survey the probability of M photon _e=η (1-cosqM φ)/2, or survey x photon on the mould e and on mould f the probability of y photon of detection be P _Xeyf=η (1-cosqM φ)/2, wherein, M=x+y, x and y represent the photon number surveyed, x, y>=0.Wherein, η is inherent intrinsic efficiency.Utilize the photon detection probability, but evaluation phase φ.If experimentally recording the visibility of interference fringe is V, the precision of Measurement Phase φ is Δ φ=1/ (VqM)=1/ (VN).The corresponding threshold visibility does

If V _Th>=1, experimentally, gained measuring accuracy Δ φ can not break the standard quantum limit, because V can not be greater than 1; If V＞V _Th, Δ φ＜(Δ φ) just arranged _SQL, corresponding measuring accuracy Δ φ has just broken the standard quantum limit.

Because

When q increases or increase η, V _ThJust diminish.Experimentally, always can find a suitable q, make V＞V _ThSet up.Like this, corresponding measuring accuracy Δ φ just can break the standard quantum limit.

Experimentally, pass through single, input M entangled photons after on same beam splitter (BS), reconfiguring, is P if on mould e, survey the probability of M photon _e=η (1-cosM φ)/2, wherein, the inherent intrinsic efficiency of η.Carry out q experiment, the useful photon number is N=qM, utilizes the photon detection probability, but evaluation phase φ.The visibility of interference fringe is V ', and corresponding precision of repeatedly passing Measurement Phase φ is Δ φ=1/ (VqM) to the precision of Measurement Phase φ for

.

Can establish single and pass identically with the visibility V that repeatedly passes or very approaching, because according to relevant report, can know, when q=1～16, V is almost constant, and when q=16～32, V has only minor alteration.Because q>=2; Can find suitable q;

just arranged so; The measuring accuracy of experimentally, repeatedly passing will be higher than the precision that single passes.

The good effect that the present invention can reach is: the interferometer structure made from method for making of the present invention is simple; The optical path difference good stability; It is stable to remain on nanometer scale; The method of repeatedly passing can improve phase measurement accuracy, particularly uses single photon, M entangled photons and differentiable photon can both break the standard quantum limit.Be high-precision phase measurement, the present invention is very ingenious, ultra steady and feasible.

Description of drawings

Fig. 1 is the structural representation of prior art Mach-Zehnder interferometer;

Fig. 2 is the structural representation of prior art Nagata interferometer;

The structural representation of the ultra steady interferometer q=2 that Fig. 3 repeatedly passes for the present invention;

The structural representation of the ultra steady interferometer q=4 that Fig. 4 repeatedly passes for the present invention.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is done further detailed explanation.

The ultra steady interferometer of the interferometer that the present invention designed for repeatedly passing; Like Fig. 3 or shown in Figure 4: the ultra steady interferometer that repeatedly passes; Comprise that a bundle divides device BS and three single face level crossings 1,2,3, place on the surface level, and also comprise the optical element of a ultra steady structure and form.The optical element of ultra steady structure is for after repeatedly passing phase-shifter, can guarantee that mould c and mould d light path are stabilized in wavelet scope (nanoscale).Designed two optical elements,, represented that respectively 2 times (q=2) and 4 times (q=4) passes phase-shifter like Fig. 3 and shown in Figure 4 with ultra steady structure.Wherein, the component structure of 2 times (q=2) is: A is a two-sided planar mirror, and its available two back-to-back single-surface mirror replaces, and also has four single-surface mirror B, C, D and E, and these five mirrors are fixed in the vertical plane.The component structure of 4 times (q=4) is: A is a two-sided planar mirror, and its also available two back-to-back single-surface mirror replaces, and also has eight single-surface mirror B, C, D, E, F, G, H and I, and these nine mirrors are fixed in the vertical plane.For other ultra steady component structure that repeatedly passes, like q=4,6,8 ... .. can obtain through similar method.

Based on the above-mentioned ultra steady interferometer that repeatedly passes, input M=m+n photon | mn＞ _Ab, m, n>=0 promptly has the input of n photon at mould a input m photon at mould b, and through beam splitter (BS) afterwards, photon state becomes

Then, mould d passes after the phase-shifter φ through q time, and its attitude develops and arrives

After on same beam splitter (BS), reconfiguring, be P if on mould e, survey the probability of M photon _e=η (1-cosqM φ)/2, wherein, η is inherent intrinsic efficiency.Utilize the photon detection probability; But evaluation phase φ; Through one-shot measurement; In theory; Precision for

promptly

useful photon number be qMN, the standard quantum limit of corresponding precision is

Be located at reconfigure on the same beam splitter (BS) after, survey x photon on the mould e and on mould f the probability of y photon of detection be P _Xeyf=η (1-cosqM φ)/2, wherein, M=x+y, x and y represent the photon number surveyed.Utilize the photon detection probability; But evaluation phase φ; Through one-shot measurement; In theory; Can get identical conclusion: precision is qM for

useful photon number, and the standard quantum limit of corresponding precision is

Experimentally, once experiment, the visibility of interference fringe is V, and the precision of Measurement Phase φ is Δ φ=1/ (VqM), and the corresponding threshold visibility does

If V _Th>=1, experimentally, gained measuring accuracy Δ φ can not break the standard quantum limit, because V can not be greater than 1; If V＞V _Th, Δ φ＜(Δ φ) just arranged _SQL, corresponding measuring accuracy Δ φ can break the standard quantum limit.

In theory; Total photon number is N=qM; Pass for single; Through q experiment; Corresponding precision Δ φ repeatedly passes for

; Q>=2; Precision Δ φ for

because arranged so, in theory, the measuring accuracy of repeatedly passing will be higher than that single passes.

Below, we specify the phase measurement method of breaking the standard quantum limit:

1. use single photon

Based on the above-mentioned ultra steady interferometer that repeatedly passes, the input single photon does not promptly have the photon input at mould a input single photon and at mould b, and the photon state of its input does | 10＞ _Ab, single photon M=1, through beam splitter (BS) afterwards, quantum state becomes

Then, mould d passes after the phase-shifter φ through q time, and its attitude develops and arrives

After on same beam splitter (BS), reconfiguring, the probability of on mould e, surveying single photon is P _e=η (1-cosq φ)/2=(1-cosq φ)/2, wherein, η is inherent intrinsic efficiency, here η=1.Utilize the photon detection probability; In theory; Through once experiment, use total number of light photons to be N=qM=q, Measurement Phase φ precision is

because M=1; η=1, then Δ φ=1/ (qM)=1/q.In one-shot measurement, effectively population is N=qM=q * 1=q, and corresponding standard quantum limit does ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=\sqrt{\mathrm{\η}}/\sqrt{\mathrm{QM}}=1/\sqrt{q}.$

If repeatedly pass, q>=2 just have,

Be Δ φ＜(Δ φ) _SQL, in theory, utilize single photon repeatedly to pass its precision and can break the standard quantum limit.

In experiment, the visibility of establishing interference fringe is V, and the precision of then being surveyed is Δ φ=1/ (VqM).The corresponding quantum standard limit does

Breaking the standard quantum limit, is exactly to want Δ φ＜(Δ φ) _SQL, promptly

The threshold value visibility does

If V _Th>=1, its measuring accuracy can not be broken the quantum standard limit, because the experimentally actual visibility that records can not be greater than 1; As V＞V _ThThe time, Δ φ＜(Δ φ) _SQLSet up, its precision is just broken the quantum standard limit.

Here, because q >=2, η=1, M=1, N >=1.Therefore,

Current, experimentally, when q=2, visibility V ₁₂(V _MqFirst footnote is photon number M, and crus secunda is designated as and passes number of times q) can reach 98% ± 0.5%, V is just arranged _Mq=V ₁₂＞V _Th, V here _MqIn first footnote be photon number M, crus secunda is designated as and passes number of times q.So, experimentally, use single photon, can break the standard quantum limit through repeatedly passing.

If utilize the single photon single to pass, total photon number is N=qM=q * 1, does not have the photon input at mould a input single photon and at mould b, and the photon state of its input does | 10＞ _AbAfter on same beam splitter (BS), reconfiguring, the probability of on mould e, surveying single photon is P _e=η (1-cos φ)/2=(1-cos φ)/2, η=1 here.Experiment number is q time, then

Corresponding standard quantum limit does Hence one can see that, Δ φ=(Δ φ) _SQLTherefore, use the single photon single to pass, in theory, its precision can not be broken the standard quantum limit.

Experimentally, since M=1, η=1, then

And the visibility V of current experiment ₁₁Although can reach 98% ± 0.5%, the visibility V that experimentally records ₁₁Can not be greater than 1, that is, and V ₁₁＜V _ThSo, experimentally, use single photon, pass through single and can not break the standard quantum limit.

2. use and tangle two-photon

Based on the above-mentioned ultra steady interferometer that repeatedly passes, the input two-photon | 11＞ _Ab, i.e. M=2 can obtain high precision and breaks the standard quantum limit.Experimentally import single photon simultaneously at each input end, it just can produce the two-photon attitude | 11＞ _Ab, passing after the BS for the first time, photon state does

Wherein, the interference of the amplitude of two-photon has been eliminated | 11＞ _CdItem-Hong-Ou-Mandel effect.If pass phase-shifter (each photon passes and once produces unknown phase shift φ) for q time, attitude | 2002＞develop and arrive

On mould e and f, the probability of surveying two photons is P _Ef=η (1-cos2q φ)/2=(1-cos2q φ)/2, here, η=1, but utilize probability evaluation phase φ, through one-shot measurement, in theory, precision is Δ φ=1/ (qM), because M=2 has Δ φ=1/ (2q).In one-shot measurement, effectively population is qM=2q, and the standard quantum limit does ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=\sqrt{\mathrm{\η}}/\sqrt{\mathrm{QM}}=1/\sqrt{2q},$ Since M=2, η=1.

Because repeatedly pass, q>=2, so,

Be Δ φ＜(Δ φ) _SQL, in theory, the measuring accuracy of repeatedly passing can be broken the standard quantum limit.

Experimentally, the precision of measurement is Δ φ=1/ (VqM)=1/ (2Vq), and the corresponding quantum standard limit does ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=\sqrt{\mathrm{\η}}/\sqrt{\mathrm{QM}}=1/\sqrt{2q},$ Since η=1, M=2.The threshold value visibility does $V_{\mathrm{Th}}=1/\sqrt{\mathrm{\η\; QM}}=1/\sqrt{2q},$ Since repeatedly pass, q>=2, therefore, V _Th≤1/2=50%.And the visibility V of current experiment ₂₂Can reach 96% ± 1%.Because V _Mq=V ₂₂＞V _Th, V here _MqIn first footnote be photon number M, crus secunda is designated as and passes number of times q, so, experimentally, use two-photon, can break the standard quantum limit through repeatedly passing.

If single passes, M=2, total number of light photons is N=qM=2q, can carry out q experiment.From the above, $\mathrm{\Δ\; \φ}=1/\left(M\sqrt{q}\right)=1/\left(2\sqrt{q}\right),$ ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=1/\sqrt{\mathrm{QM}}=1/\sqrt{2q},$ Δ φ＜(Δ φ) just arranged _SQLTherefore, use the two-photon single to pass, in theory, measuring accuracy also can be broken the standard quantum limit.Because in q>=2 o'clock, the precision that

repeatedly passes will be higher than single and pass again.

The precision that experimentally records is Δ φ=1/ (VqM)=1/ (2Vq), so the precision of repeatedly passing with single is respectively

If q=2,4 o'clock, because V _2q, V ₂₁Be more or less the same, can get

So, experimentally, use two-photon, the precision of repeatedly passing is higher than the precision that single passes.

3. use and tangle four photons

Based on the above-mentioned ultra steady interferometer that repeatedly passes, import four photons | 22＞ _Ab, i.e. M=4 can obtain high precision and breaks the standard quantum limit.Experimentally import two-photon simultaneously, can produce four photon states at each input end | 22＞ _AbThrough after the BS, attitude becomes for the first time

$\sqrt{3/8}|{40>}_{\mathrm{cd}}+\sqrt{3/8}|{22>}_{\mathrm{cd}}+\sqrt{3/8}|{04>}_{\mathrm{cd}}$

Then, pass phase-shifter q time, attitude becomes

$\sqrt{3/8}|{40>}_{\mathrm{cd}}+\sqrt{3/8}{e}^{i2\mathrm{q\φ}}|{22>}_{\mathrm{cd}}+\sqrt{3/8}{e}^{i4\mathrm{q\φ}}|{04>}_{\mathrm{cd}}$

Through after the same BS, attitude develops and arrives for the second time

$|\mathrm{\Ψ}>=\sqrt{6}/16(1-2e^{i2\mathrm{q\φ}}+e^{i4\mathrm{q\φ}})\left(\right|{40>}_{\mathrm{ef}}+\left|{04>}_{\mathrm{ef}}\right)+1/8(3+2e^{i2\mathrm{q\φ}}+3e^{i4\mathrm{q\φ}})\left(\right|{22>}_{\mathrm{ef}}$

$+\sqrt{6}/8(1-e^{i4\mathrm{q\φ}})\left(\right|{31>}_{\mathrm{ef}}+\left|{13>}_{\mathrm{ef}}\right)$

If employing probe method: at 3 photons of mould e detection with at a mould f1 photon, its probability is P _3ef=η (1-cosMq φ)/2=3/8 (1-cos4q φ)/2, (η=3/8 here), but utilize its evaluation phase φ, in theory, through measurement once, precision does

The useful photon number is qM, corresponding standard quantum limit

Here q>=2, M=4, η=3/8, thereby,

Can get Δ φ＜(Δ φ) _SQLSo; In theory; Utilize repeatedly passing of four photons can break the quantum standard limit, precision is

Experimentally; The precision of measuring is Δ φ=1/ (VqM); The corresponding quantum standard limit be that threshold of visibility is here; η=3/8, M=4.Repeatedly pass, q>=2,

And experimentally, visibility can reach V ₄₂=96% ± 1%, can know V ₄₂＞V _Th

Therefore, use four photons, can break the standard quantum limit through repeatedly passing.

In addition, if adopt the Okamoto probe method: survey 3 photons and at mould f1 photon at mould e, simultaneously, also survey 1 photon e and at mould f3 photon at mould.Through above-mentioned detection method, detection probability is P _3e1f+1e3f=3/4 (1-cos4q φ)/2, η can bring up to 3/4 from 3/8.Thereby, can reduce threshold of visibility V _Th, because

Adopting the benefit of Okamoto probe method is the threshold value V that can reduce to break the standard quantum limit _Th, like this, in experiment, can break the standard quantum limit with less visibility.

And pass for single; The useful photon number is N=qM=4q; Can carry out q experiment; Precision is

because

so; In theory; Use four photons, repeatedly pass the precision height that passes than single.

Pass V for single _Th=81.65%, experimentally, visibility can reach V ₄₁=96% ± 1%.Therefore, use four photons, pass also through single and can break the standard quantum limit.Yet, can know by last analysis, use four photons, repeatedly pass the precision height that passes than single.

4. use and on the time mould, can distinguish photon

Top discussion requires two-photon input attitude to be | 11＞ _Ab, promptly its two photon two spatial modes can distinguish with a time mould on undistinguishable, rather than

Attitude be two photons at two spaces and two time moulds, just, two photons all are differentiable on spatial mode and time mould.Top discussion requires four photons input attitude to be | 22＞ _Ab-four photons are at two spaces and a time mould, rather than

-four photons are at two spaces and two time moulds, and just, two photons must be undistinguishables at each mould.Below, use and on the time mould, can distinguish photon.

(1) uses differentiable two photons on the time mould

If the input attitude does

--two-photon is at two spaces and two time moulds, and just, two photons are differentiable at each mould, if single passes, surveying 2 photons is P at the probability of mould e _2e=1/4 (1-cos2 φ) 2, such method can not be broken the standard quantum limit, because

Carry out q experiment, total number of light photons is N=qM=2q, and the standard quantum limit does

If repeatedly pass, q=2, experimentally surveying 2 photons is P at the probability of mould e _2e=1/4 (1-cos4 φ)/2 are although visibility can not be broken the standard quantum limit up to V=87% ± 1%, because V _Th=1.But if q=4, experimentally probability is P _2eThe standard quantum limit just can be broken in=1/4 (1-cos8 φ)/2, because V=87% ± 1%, and $V_{\mathrm{Th}}=\sqrt{2}/2\≈70.7\%.$

(2) use differentiable four photons on the time mould

If the input attitude does

Repeatedly pass q>=2, survey 3 photons at mould e and 1 photon at mould f, detection probability is P _3ef=1/8 (1-cos4q φ)/2, η=1/8 wherein, M=4.Through one-shot measurement, used the N=qM photon altogether, remove Measurement Phase φ, measuring accuracy

Corresponding standard quantum limit ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=\sqrt{\mathrm{\η}}/\sqrt{\mathrm{QM}}.$ The experiment visibility is V=82% ± 6%, because $V_{\mathrm{Th}}=1/\sqrt{\mathrm{\η\; QM}}=1/\sqrt{q/2},$ When q>=4,

So during q=4, this method can be broken the standard quantum limit.If use the probe method of Okamoto, then $V_{\mathrm{Th}}=1/\sqrt{\mathrm{\η\; QM}}=1/\sqrt{q},$ When q>=2, $V_{\mathrm{Th}}\≤\sqrt{2}/2\≈70.7\%.$ So during q=2, this method can be broken the standard quantum limit, because the visibility of experiment is up to V=87% ± 1%.

If the ultra steady interferometer that uses single to pass, surveying 3 photons is P at mould e and 1 photon at the probability of mould f _3ef=1/8 (1-cosM φ)/2, M=4 here, η=1/8.Use the N=qM photon, can carry out q experiment.Because

this can not break the standard quantum limit.But if use the probe method of Okamoto, probability is P _3ef+e3f=1/4 (1-cosM φ)/2, but with regard to the standard quantum limit, because

And V=82 ± 6%.But the precision of its measurement is less than repeatedly passing.

From the above, use identical M entangled photons, repeatedly number passes than single and passes the measuring accuracy that reaches higher.Particularly outstanding is that based on the ultra steady interferometer that repeatedly passes, differentiable photon also can be broken the standard quantum limit on service time.Be high-precision phase measurement, the present invention is very ingenious, ultra steady and feasible.

The above is merely preferred embodiment of the present invention, is not to be used to limit protection scope of the present invention.All within spirit of the present invention and principle, any modification of being done, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

The interferometer structure that method for making of the present invention is made is simple; The optical path difference good stability; It is stable to remain on nanometer scale, and the method for repeatedly passing can improve phase measurement accuracy, particularly uses single photon, M entangled photons and time to go up differentiable photon and can both break the standard quantum limit.

Claims (3)

1. ultra steady interferometer that repeatedly passes; Comprise that a bundle divides device (BS) and the first single face level crossing (1), the second single face level crossing (2), the 3rd single face level crossing (3) to place on the surface level; And have four times (being q=4) of being fixed in the vertical plane are passed the optical element of the ultra steady structure of phase-shifter (PS); It is characterized in that: said optical element comprises two-sided planar mirror (A), the 4th single face level crossing (B), the 5th single face level crossing (C), the 6th single face level crossing (D), the 7th single face level crossing (E), the 8th single face level crossing (F), the 9th single face level crossing (G), the tenth single face level crossing (H) and the 11 single face level crossing (I) that is 45 with optical axis, and concrete light channel structure is following:

Light is respectively input point a with mould a and mould b with input point b imports corresponding photon exactly by input point a and input point b input, and after acting on through bundle branch device (BS); Part light is called mould d, arrives the first single face level crossing (1) inwards, passes phase-shifter (PS) for the 1st time to the right and the upper surface of arrival two-sided planar mirror (A); Upward to the 11 single face level crossing (I), level is passed phase-shifter (PS) the 2nd time left and is arrived the tenth single face level crossing (H), afterwards; Upward to the 9th single face level crossing (G), pass phase-shifter (PS) the 3rd time to the right and arrive the 8th single face level crossing (F), upward to the 7th single face level crossing (E); The 4th is passed phase-shifter (PS) and is arrived the 6th single face level crossing (D) left, down to the 5th single face level crossing (C), to the right to the 4th single face level crossing (B); Lower surface upward to two-sided planar mirror (A); Arrive the second single face level crossing (2) to the right, outwards arrive the 3rd single face level crossing (3), incide bundle left again and divide device (BS);

Another part light is called mould c, arrives the 3rd single face level crossing (3) to the right, arrives the second single face level crossing (2) inwards; Arrive the lower surface of two-sided planar mirror (A) left, arrive the 4th single face level crossing (B) downwards, left to the 5th single face level crossing (C); Upwards arrive the 6th single face level crossing (D), do not pass phase-shifter (PS) to the right and, arrive the 8th single face level crossing (F) downwards to the 7th single face level crossing (E); Do not pass phase-shifter (PS) left to the 9th single face level crossing (G); Down to the tenth single face level crossing (H), do not pass phase-shifter (PS) to the right to the 11 single face level crossing (I), arrive the upper surface of two-sided planar mirror (A) downwards; Do not pass phase-shifter (PS) left and, outwards incide bundle branch device (BS) again to the first single face level crossing (1); After light passes phase-shifter (PS) for 4 times, can guarantee that mould c and mould d optical path difference are stabilized in the nanoscale scope, the above-mentioned two-beam that arrives bundle branch device (BS) once more, after the process bundle divided device (BS) effect, the light of exporting left was mould e, the light of downward output is mould f.

2. the method for the Measurement Phase of the ultra steady interferometer that repeatedly passes according to claim 1 is characterized in that: use single photon

1) input single photon does not promptly have the photon input at mould a input single photon and at mould b, and the photon state of its input does | 10＞ _Ab, single photon M=1 divides device (BS) afterwards through bundle, and quantum state becomes

2) mould d passes phase-shifter (PS) afterwards through q time, and its attitude develops and arrives

Corresponding standard quantum limit is calculated as

When the number of times q=4 that passes, attitude develops and arrives $\left(\right|{10>}_{\mathrm{Ab}}+e^{i4\mathrm{\φ}}\left|01{>}_{\mathrm{Ab}}\right)/\sqrt{2},$ Corresponding standard quantum limit is calculated as ${\left(\mathrm{\Δ\; \φ}\right)}_{\mathrm{SQL}}=1/\sqrt{4}=\frac{1}{2};$

3) in measurement, when the number of times q=4 that passes, single photon M=1, the visibility that records interference fringe is V, the precision of then being surveyed is Δ φ=1/ (VqM)=1/4V; The corresponding quantum standard limit does

The threshold value visibility does

In the measuring process, when q>=2, V is arranged _Mq=V ₁₂＞V _Th, V here _MqIn first footnote be photon number M, crus secunda is designated as and passes number of times q; In measurement, use single photon, the number of times q=4 that passes can break the standard quantum limit, and the precision of its measurement does $\mathrm{\Δ\; \φ}=1/\left(\mathrm{Vq}\right)=\frac{1}{4V}.$

3. the method for the Measurement Phase of the ultra steady interferometer that repeatedly passes according to claim 1 is characterized in that: use two-photon

1) input two-photon | 11＞ _Ab, i.e. M=2 can obtain high precision and breaks the standard quantum limit; In the measuring process, import single photon simultaneously, promptly also import single photon at mould b, can produce the two-photon attitude at mould a input single photon at two input end a and b | 11＞ _Ab

2) pass bundle for the first time and divide device (BS) afterwards, photon state does

Pass phase-shifter (PS) for q time, attitude | 2002＞develop and arrive

Can calculate the standard quantum limit does

When the number of times q=4 that passes, attitude | 2002＞develop and arrive

Can calculate the standard quantum limit and be (Δ φ) _SQL=1/4;

3) in measurement, establishing the visibility that records interference fringe is V, and the precision of measurement is Δ φ=1/ (VqM), and the corresponding quantum standard limit does

The threshold value visibility can be calculated as

For repeatedly passing, then there is V q>=2 _Mq=V ₂₂＞V _Th, V here _MqIn first footnote be photon number M, crus secunda is designated as and passes number of times q; In measurement, use two-photon, the number of times q=4 that passes can break the standard quantum limit, and the precision of its measurement is Δ φ=1/ (2Vq)=1/8V.

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