CN104407485A - Quantum correlated imaging method based on angular position entanglement - Google Patents

Quantum correlated imaging method based on angular position entanglement Download PDF

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CN104407485A
CN104407485A CN201410724877.5A CN201410724877A CN104407485A CN 104407485 A CN104407485 A CN 104407485A CN 201410724877 A CN201410724877 A CN 201410724877A CN 104407485 A CN104407485 A CN 104407485A
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CN104407485B (en
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赵生妹
梁文强
陈超
董小亮
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Nanjing Post and Telecommunication University
Nanjing University of Posts and Telecommunications
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    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35Non-linear optics

Abstract

The invention discloses a quantum correlated imaging method based on angular position entanglement. According to the quantum correlated imaging method, the information of an object to be imaged is coded into angle seams different in angle and the different angle seams are loaded to a light beam. Due to a monotonic function relationship between coincidence counting and the angles of the angle seams, the information of the object can be obtained from a reference light path according to a coincidence counting value and then the image of the object can be obtained, and therefore, the quantum correlated imaging method based on the angular position entanglement is gained. The new correlated imaging method has the following advantages: on one hand, the concept of angular position entanglement is introduced into the field of correlated imaging so that the research direction of correlated imaging can be expanded, and meanwhile, a good imaging effect is also obtained; on the other hand, the research of the angular position entanglement provides a new thought for subsequent research, for example, the fields of multiple-access optical communication and optical identification; the method is simple to implement and has an excellent imaging effect on multi-grayscale image objects.

Description

A kind of Quantum Correlation formation method tangled based on Angle Position
Technical field
The present invention relates to a kind of Quantum Correlation formation method tangled based on Angle Position, belong to the interleaving techniques field of quantum optics and imaging technique.
Background technology
Relevance imaging (Correlated Imaging, referred to as CI), also claims terrible imaging (Ghost Imaging, referred to as GI), be studied in quantum optics field in the last few years one of forward position and focus.Relevance imaging can obtain object picture rich in detail not having the reference path of object.It can break through classical diffraction limit, has high resolving power and high-visibility, has broad application prospects, and as satellite remote sensing, laser radar, medical imaging, military, the various fields such as industrial imaging and survey of deep space, obtain at present and pay close attention to widely.
1988, what under Klyshko foundation Spontaneous Parametric, conversion (SPDC) photon was right tangled behavior, proposes relevance imaging scheme.Nineteen ninety-five, the people such as Pittman change the entangled photon pairs of generation under utilizing Spontaneous Parametric, and " ghost " imaging experiment completed based on quantum entanglement is verified.The characteristic that correlation theory subsequently and experiment show to tangle relevance imaging or the momentum being embodied in momentum-position Heisenberg uncertainty relation tangles, otherwise the position being embodied in momentum-position Heisenberg uncertainty relation is tangled.Photon trajectory angular momentum (OAM) and (angle) position are also that one tangles source.Compared with only having two kinds of values with photon polarization state, the OAM value of single photon from negative infinite to just infinite, can substantially increase the ability of single photon transmission information.2009, the people such as Back used for reference photon polarization state and tangle relevance imaging method, completed the relevance imaging experiment of tangling based on OAM, and had pointed out the quantum essence of relevance imaging from OAM aspect.On this experiment basis, we proposed a kind of method and experimental verification of many gray scales " ghost " imaging of tangling based on OAM in 2011.This imaging process being phase object provides a kind of simple scheme.On the other hand, the people such as Jha are a pair indeterminacy physical quantitys in experimental verification Angle Position in 2010 and angular momentum, obtain the interference based on Angle Position by two angle seam.Compared with tangling with angular momentum, the relation between the coincidence counting of tangling based on Angle Position and angle seam angle will be simpler.Therefore, the present invention proposes a kind of relevance imaging scheme of tangling based on Angle Position, object to be imaged information coding is become the angle seam of different angles, and different angle seams is loaded on light beam by phase place.Owing to there is dull funtcional relationship between coincidence counting and angle seam angle, the information of object can be obtained according to coincidence counting value in reference path, obtain the imaging of object.The present invention gives and a kind ofly novel tangle relevance imaging method, there is important theory significance and using value.
Summary of the invention
The object of the invention is to provide a kind of Quantum Correlation formation method tangled based on Angle Position, and Angle Position tangles and is applied to relevance imaging technology by the method first.In the method, Gauss's pump light is changed under carrying out parameter by bbo crystal, produces an entangled photon pairs.If signal light path is LG -l, 0pattern, then idle light path will be LG + l, 0pattern.The different information of object to be imaged are encoded into the angle seam θ of different angles, and different angle seams is loaded in the phase place of signal beams.Owing to there is dull funtcional relationship between coincidence counting and angle seam θ, by arranging specific region, the one-to-one relationship between coincidence counting and object information can be obtained.So can obtain the information of object in reference path according to coincidence counting, obtain the imaging of object, the method realizes simple, has good imaging effect for multi-grey image object.
The present invention solves the technical scheme that its technical matters takes: the invention provides a kind of Quantum Correlation formation method tangled based on Angle Position, the method comprises the steps:
Step one: a branch of Gauss's pump light is through Ι type degenerate non-linear phase matcher crystal, and it is right to be tangled for a pair by parametric down conversion generation.The photon entanglement produced is to being expressed as wherein s and i representation signal light path and idle light path; | l> represents that exponent number is the eigenstate of the orbital angular momentum of l; | c l| 2it is the probability under exponent number is respectively l and-l pattern.
Step 2: the Quantum Correlation formation method tangled based on Angle Position set up as shown in Figure 1 realizes schematic diagram, the idle light path of order is |+l> pattern, signal light path is |-l> pattern.
Step 3: first the gray-coded of the object to be imaged is become different angle seam θ in signal light path, and be loaded into signal light path with the form of fan-shaped phase place.The present invention selects the value of angle seam angle to be 0 to π, if the gray shade scale of object is M, the then gray-scale value of imaging object correspondence 0 respectively, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), with the M such as π different angle seam θ, different gray-scale value is encoded into different angle seam θ.
Step 4: by the information of the object to be imaged, namely different angle seam angle θ is loaded in signal light path, and carries out coincidence measurement to signal light path and idle light path, obtains coincidence counting.From Such analysis, there is single-valued relationship in the angle theta of the fan-shaped phase place that signal light path loads and coincidence counting value, c lall constant with A.The angle seam θ size of loading can be obtained by coincidence counting value.
Step 5: the coding corresponding relation of the gray-scale value produced by step 3 and angle seam, recovers the gray-scale value of each pixel in idle light path, obtains object to be imaged information.
The method of the invention tangles a kind of relevance imaging method based on theory by the Angle Position of entangled photon pairs; Exist premised on single-valued relationship between the fan-shaped angle seam phase place of carrying added by coincidence counting value and signal light path.
The method of the invention can be applicable to the relevance imaging of many gray scales object to be imaged.
There is strictly monotone relation between the method for the invention coincidence counting value and the added fan-shaped angle seam phase place of carrying of signal light path, imaging precision is high.
Beneficial effect:
1, the concept that Angle Position tangles by the present invention first introduces relevance imaging field, extends the research direction of relevance imaging.
2, good imaging quality of the present invention, resolution is high, and the image for different gray scale has general applicability.
Accompanying drawing explanation
Fig. 1 the present invention is based on the Quantum Correlation imaging scheme schematic diagram that Angle Position tangles.
Fig. 2 is the phase diagram that signal light path of the present invention loads.
Fig. 3 is | Ψ s> and | Ψ idegree of conformity C (the Ψ of > s, Ψ i) and the graph of a relation of fan-shaped angle.
Fig. 4 is 2 gray scales " NUPT ", 4 gray scales " LENA ", the numerical simulation of the present invention of the object to be imaged such as 8 gray scales " LENA ".
Fig. 5 is 8 gray scales " LENA " figure (signal to noise ratio (S/N ratio)) under different noise conditions, the Y-PSNR variation diagram of imaging object of the present invention.
Fig. 6 is the process flow diagram of the inventive method.
Embodiment
Below in conjunction with Figure of description, patent of the present invention is described in further detail.
Embodiment one
As shown in Figure 1, idle light path is LG to the schematic diagram of a kind of Quantum Correlation formation method tangled based on Angle Position of the present invention + l, 0pattern, signal light path is LG -l, 0pattern, wherein LG + l, 0and LG -l, 0pattern be a branch of Gauss's pump light through Ι type degenerate non-linear phase matcher, produced by parametric down conversion process.Gray-scale values different according to object in signal light path selects the fan-shaped phase place of different angle seam θ, and is loaded in signal light path.Such as, suppose that the gray shade scale of the object to be imaged is M, namely the gray scale value of the object to be imaged is 0,1 ... M-2, M-1.The angle of angle seam θ is selected to be changed to 0 to π this interval (because the coincidence counting corresponding to 0 to π interval is a monotonic quantity), M the angle seam θ value from 0 to π will be obtained, namely angle seam θ can be set to 0 respectively, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), and π, M gray-scale value of imaging object and M angle seam θ one_to_one corresponding.Then signal light path and idle light path are carried out coincidence measurement and obtain coincidence counting, finally obtain the half-tone information of the object to be imaged according to funtcional relationship dull between coincidence counting and angle seam angle, thus recover the object to be imaged in reference path.
In theory, when under Gauss's pump light is by Spontaneous Parametric, conversion obtains signal photon and idle photon entanglement pair, two-photon state can be expressed as:
| ψ ⟩ = Σ n = - ∞ n = + ∞ c n | - n ⟩ s | n ⟩ i , - - - ( 1 )
Wherein, | n> represents the orbit angular momentum state (LG pattern) of l=n pattern, | c n| 2to represent under Spontaneous Parametric that in transfer process, pump photon is converted into ± probability of n photon.Because conversion under Spontaneous Parametric has symmetry, have:
c n=c -n, (2)
In order to provide coincidence counting and the corresponding relation of different angle seam information, derive the expression-form of the coincidence counting when signal light path loads different angle seam phase place below.
Suppose that the basic state of signal light path and idle light path is respectively |-l> and |+l>, in the angle seam phase place as shown in Figure 2 that signal light path loads, wherein white portion phase value is 0, grey parts phase value is π, the angle seam angular dimension of grey parts is θ, then the phase place corresponding to angle seam can be expressed as:
M ( &phi; ) = &pi; 0 &le; &phi; &le; &theta; , 0 &le; r &le; r 0 0 &theta; < &phi; &le; 2 &pi; , 0 &le; r &le; r 0 , - - - ( 3 )
Wherein θ is the angle representing angle seam, its transformation range 0≤θ≤2 π; r 0it is the radial radius size of angle seam.Because the originate mode of signal light path input is the OAM state of-l, its mathematical form is |-l>=Aexp (-il φ), wherein Α is LG pattern radial distribution, has nothing to do with the value of l.Therefore, the OAM state after signal light path loads angle seam θ | Ψ s> is:
s>=Ae -ilφe iM(φ)(4)
Because different l value LG pattern is mutually orthogonal, therefore loading the signal state after angle seam θ deployable is various l value LG patterns, namely
| &psi; s &rang; = &Sigma; l &prime; = - &infin; l &prime; = + &infin; A l &prime; | l &prime; &rang; - - - ( 5 )
Wherein A l 'for:
A l &prime; = 1 2 &pi; d&phi; e - i l &prime; &phi; A e - il&phi; e iM ( &phi; ) - - - ( 6 )
Further for above formula abbreviation can be obtained:
A l &prime; = A - &theta; &pi; e - i ( &theta; / 2 ) ( l &prime; + l ) sin c [ ( &theta; 2 ( l &prime; + l ) ) , l &prime; &NotEqual; - l 1 - &theta; &pi; , l &prime; = - l , - - - ( 7 )
Due to idle light path OAM state | Ψ i> is the OAM state of+l, can be expressed as
i>=|+l>, (8)
According to coincidence counting formula, the coincidence counting C (Ψ of signal light path and idle light path can be obtained s, Ψ i) be:
C(Ψ si)=|<Ψ s|<Ψ i|Ψ>| 2, (9)
Wherein:
&lang; &psi; s | &lang; &psi; i | | &psi; &rang; = [ &Sigma; l &prime; = - &infin; l &prime; = + &infin; A l &prime; &lang; l &prime; | ] &lang; + l | &Sigma; n = - &infin; n = + &infin; c n | n &rang; | - n &rang; = [ &Sigma; l &prime; = - &infin; l &prime; = + &infin; A l &prime; &lang; l &prime; | ] c l | - l &rang;
= A [ 1 - &theta; &pi; ] &lang; - l | c l | - l &rang; = c l A ( 1 - &theta; &pi; ) , - - - ( 10 )
Can be obtained by two formulas above:
C ( &psi; s , &psi; i ) = | &lang; &psi; s | &lang; &psi; i | | &psi; &rang; | 2 = c l 2 A 2 ( 1 - &theta; &pi; ) 2 , - - - ( 11 )
Wherein, c lall constant with A, therefore:
C ( &psi; s , &psi; i ) &Proportional; ( 1 - &theta; &pi; ) 2 , - - - ( 12 )
Fig. 3 is | Ψ s> and | Ψ ithe degree of conformity graph of a relation of >, shows C (Ψ s, Ψ i) and the relation of angle theta.As can be seen from the figure along with angle theta change to π from 0 time, C (Ψ s, Ψ i) be reduced to minimum value from maximal value, along with angle theta change to 2 π from π time, C (Ψ s, Ψ i) be increased to maximal value from minimum value.
Can find by Fig. 3, when the primary input state of signal light path and idle light path is |-l> and | during+l>, be the monotonous descending function of loading fan-shaped phase place angle theta in 0 to π interval coincidence counting value.If signal light path is | the OAM light of-l> pattern, idle light path input | the OAM light of+l> pattern.When loading the fan-shaped phase place of different angle theta in signal light path, will different coincidence counting values be obtained in idle light path, and between coincidence counting value and angle seam angle θ, there is dull funtcional relationship.Because different angle seam correspond to the different gray scales of the object to be imaged, therefore can realize the differentiation of the different gray-scale value of imaging object in idle light path, obtain image objects.Specific implementation step of the present invention is as follows:
Step one: a branch of Gauss's pump light, through Ι type degenerate non-linear phase matcher, is produced by parametric down conversion process and tangles light a pair, be respectively flashlight and idle light.The photon produced is to being expressed as wherein s and i represents signal light path and idle light path respectively, | l> represents that exponent number is the eigenstate of the orbital angular momentum of l.| c l| 2it is the probability that two photon exponent numbers are respectively l and-l pattern.
Step 2: set up the Quantum Correlation imaging scheme of tangling based on Angle Position as shown in Figure 1, idle light path input LG + l, 0pattern, signal light path input LG -l, 0pattern.In signal light path, first gray-scale values different for object is encoded into different angle seam angle θ, and being loaded in signal light path with the form of fan-shaped phase place, the present invention selects 0 to this interval of π (0 to π interval corresponding coincidence counting and angle seam angle θ are a monotonic quantity).If the gray shade scale of imaging object is M, i.e. value 0,1, ..., M-2, M-1, then corresponding angle seam angle θ is 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1) and π, evenly be divided into M part by 0 to π interval, M angle seam θ value is corresponding with M gray-scale value.
Step 3: signal light path and idle light path are carried out coincidence measurement, obtains coincidence counting.From Such analysis, there is one-to-one relationship in the angle theta of the fan-shaped phase place that signal light path loads and coincidence counting value, c lbe all constant with A, by coincidence counting value, the corresponding fan-shaped phase theta size loaded can be obtained.
Step 4: the relation between the angle seam size obtained by step 2 and gray-scale value, obtains the gray-scale value of each pixel, by computing machine Recovery image.
Embodiment two
In order to verify the proposed by the invention Quantum Correlation formation method tangled based on Angle Position, now verified by numerical simulation.The wavelength of Gauss's pump light source that this numerical simulation uses is λ=633nm.In order to more objective and accurate the performance that the relevance imaging method of tangling based on Angle Position is described, the present invention introduces Y-PSNR (peak signal-to-noise rate, PSNR), and wherein PSNR is defined as:
PSNR ( X i , j , X i , j &prime; ) = 101 g [ Val max 2 MSE ( X i , j , X i , j &prime; ) ] - - - ( 13 )
Wherein, represent the gray scale maximal value of original objects, MSE is defined as:
MSE ( X i , j , X i , j &prime; ) = &Sigma; 0 &le; i < M &Sigma; 0 &le; j < N ( X i , j - X i , j &prime; ) 2 M &times; N - - - ( 14 )
Wherein, X i,jwith X ' i,jrepresent the half-tone information value of original objects and Recovery image respectively.
As shown in Figure 1, the invention provides a kind of Quantum Correlation formation method tangled based on Angle Position, the method is based on photon Angle Position tangles, signal light path loads different angle seam θ (fan-shaped phase place) according to the gray shade scale of imaging object, utilize angle seam θ and the monotonic functional relationship between idle light path and signal light path coincidence counting value, in idle light path according to coincidence counting value judgement angle seam θ size, the one-to-one relationship of recycling angle seam θ and imaging object gray-scale value, determines imaging object.Described method comprises:
1) a branch of wavelength be λ=633nm Gauss pump light through Ι type degenerate non-linear phase matcher, by parametric down conversion process produce tangle light a pair, be respectively flashlight and idle light.The photon produced is to being expressed as wherein s and i represents signal light path and idle light path respectively, | l> represents that exponent number is the eigenstate of the orbital angular momentum of l.| c l| 2it is the probability that two photon exponent numbers are respectively l and-l pattern.
2) idle light path input LG + l, 0pattern, signal light path input LG -l, 0pattern.In signal light path, first gray-scale values different for object is encoded into different angle seam angle θ, and being loaded in signal light path with the form of fan-shaped phase place, in literary composition, the present invention selects 0 to this interval of π (0 to π interval corresponding coincidence counting and angle seam angle θ are a monotonic quantity).If the gray shade scale of imaging object is M, i.e. value 0,1, ..., M-2, M-1, then corresponding angle seam angle θ is 0, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1) and π, evenly be divided into M part by 0 to π interval, M angle seam θ value is corresponding with M gray-scale value.Have general applicability in order to illustrate to different gray scale, the present invention uses " NUPT " of 128 × 128 respectively, and " LENA " of 4 gray scales " LENA " and 8 gray scales carries out simulating, verifying.
3) signal light path and idle light path are carried out coincidence measurement, obtain coincidence counting.By formula known, coincidence counting value and angle seam θ are monotonic quantitys in [0, π] interval, as shown in Figure 3.
4) due to the object to be imaged gray-scale value with load angle seam θ and there is one-to-one relationship, the corresponding relation between the gray-scale value that can be obtained coincidence counting value and the object to be imaged by step 2 further.Receiving end, according to the gray-scale value of each pixel of the coincidence counting value determination object to be imaged, recovers imaging object.
In order to verify the validity of this method, the present invention respectively to 128 × 128 " NUPT " 2 gray scale object, " LENA " object of 4 gray scales " LENA " object and 8 gray scales carries out numerical simulation.As shown in Figure 4, wherein Fig. 4 (a) is 2 gray scales " NUPT " former figure, Fig. 4 (b) is its recovery figure to result, and the PSNR value after imaging is 78.0744.Fig. 4 (c) be 4 gray scales " LENA " former figure, Fig. 4 (d) its be recovery figure, the PSNR after imaging is 14.1949.Fig. 4 (e) is 8 gray scales " LENA " former figure, Fig. 4 (f) be its recovery figure, the PSNR after imaging is 13.9295.As can be seen here, the present invention can obtain the information of the object to be imaged effectively in reference path.No matter be 2 gray scales, 4 gray scales or image the method for 8 gray scales can carry out imaging clearly.
The present invention tests noise resisting ability of the present invention further.Fig. 5 be 8 gray scales " LENA " figure after adding different noise (signal to noise ratio (S/N ratio)), rebuild the change curve of image Y-PSNR after imaging.As seen from the figure, there is monotonic increasing function relation in SNR and PSNR, and SNR value is larger, and after obtaining imaging, image Y-PSNR PSNR is also larger, and represent that in imaging object, noise is larger, the quality of imaging is poorer.

Claims (6)

1., based on the relevance imaging method that Angle Position tangles, described method comprises the steps:
Step one: a branch of Gauss's pump light is through Ι type degenerate non-linear phase matcher crystal, and it is right to be tangled for a pair by parametric down conversion generation, and the photon entanglement of generation is to being expressed as wherein s and i representation signal light path and idle light path; | l> represents that exponent number is the eigenstate of the orbital angular momentum of l; | c l| 2it is the probability under exponent number is respectively l and-l pattern;
Step 2: set up the Quantum Correlation formation method tangled based on Angle Position and realize schematic diagram, the idle light path of order is |+l> pattern, signal light path is |-l> pattern;
Step 3: first the gray-coded of the object to be imaged is become different angle seam θ in signal light path, and be loaded into signal light path with the form of fan-shaped phase place; The value of angle seam angle is selected to be 0 to π, if the gray shade scale of object is M, the then gray-scale value of imaging object correspondence 0 respectively, π/(M-1), 2 π/(M-1) ..., (M-2) π/(M-1), with the M such as π different angle seam θ, different gray-scale value is encoded into different angle seam θ;
Step 4: by the information of the object to be imaged, namely different angle seam angle θ is loaded in signal light path, and carries out coincidence measurement to signal light path and idle light path, obtains coincidence counting; There is single-valued relationship in the angle theta of the fan-shaped phase place that signal light path loads and coincidence counting value, c lall constant with A; The angle seam θ size loaded is obtained by coincidence counting value;
Step 5: the coding corresponding relation of the gray-scale value produced by step 3 and angle seam, recovers the gray-scale value of each pixel in idle light path, obtains object to be imaged information.
2. a kind of Quantum Correlation formation method tangled based on Angle Position according to claim 1, is characterized in that: described method tangles a kind of relevance imaging method based on theory by the Angle Position of entangled photon pairs; Exist premised on single-valued relationship between the fan-shaped angle seam phase place of carrying added by coincidence counting value and signal light path.
3. a kind of Quantum Correlation formation method tangled based on Angle Position according to claim 1, is characterized in that: described method is applicable to the relevance imaging of many gray scales object to be imaged.
4. a kind of Quantum Correlation formation method tangled based on Angle Position according to claim 1, is characterized in that: there is strictly monotone relation between described method coincidence counting value and the added fan-shaped angle seam phase place of carrying of signal light path.
5. a kind of Quantum Correlation formation method tangled based on Angle Position according to claim 1, is characterized in that: change under Gauss's pump light of described method carries out parameter by bbo crystal, produce an entangled photon pairs; If signal light path is LG -l, 0pattern, then idle light path will be LG + l, 0pattern; The different information of object to be imaged are encoded into the angle seam θ of different angles, and different angle seams is loaded in the phase place of signal beams; Owing to there is dull funtcional relationship between coincidence counting and angle seam θ, by arranging specific region, obtain the one-to-one relationship between coincidence counting and object information; The information of object can be obtained in reference path according to coincidence counting, obtain the imaging of object.
6. a kind of Quantum Correlation formation method tangled based on Angle Position according to claim 1, is characterized in that: Angle Position tangles and is applied in relevance imaging technology by described method.
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CN109347566B (en) * 2018-11-15 2021-10-01 上海理工大学 Communication method based on quaternary coding mode and time-correlated imaging
CN109814318A (en) * 2019-03-20 2019-05-28 南开大学 A kind of quantum spiral imaging system
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