CN106289155B - A kind of hypersensitive angle detecting devices and method based on photon trajectory angular momentum - Google Patents
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Abstract
A kind of hypersensitive angle detecting devices and method based on photon trajectory angular momentum, the present invention relates to hypersensitive angle detecting devices and method based on photon trajectory angular momentum.The present invention is to cause rotation angle detection accuracy low to solve the problems, such as that the prior art is limited to classical shot noise limit.Apparatus of the present invention include single-photon source (1), transmitting modulating system (11) and reception detection system (12)；Transmitting modulating system (11) is made of quarter wave plate (2), the one 1/2 wave plate (3), the first q wave plates (4) and the 2nd 1/2 wave plate (5)；Detection system (12) is received to be made of the 3rd 1/2 wave plate (6), the 2nd q wave plates (7), polarization splitting prism (8), the first APD detectors (9) and the 2nd APD detectors (10).The present invention is applied to non-contact optical angle measurement field.
Description
Technical Field
The invention relates to an ultra-sensitive angle detection device and method based on photon orbital angular momentum.
Background
Non-contact precise angle detection is an important research topic in the field of modern optical measurement. The most convenient method at present is a measurement technique based on polarization and the Malus law. The accuracy of the method is limited by the classical shot noise limit(N is the number of photons detected cumulatively), so that the requirements of high-precision angular rotation detection cannot be met well. Therefore, an ultra-sensitive rotation angle measuring method is urgently needed.
Disclosure of Invention
The invention provides an ultra-sensitive angle detection device and method based on photon orbital angular momentum, and aims to solve the problem that the prior art is limited by the limit of classical shot noise so that the detection precision of a rotation angle is low.
An ultra-sensitive angle detection device based on photon orbital angular momentum comprises: the system comprises a single photon source, an emission modulation system and a receiving detection system;
the emission modulation system consists of a 1/4 wave plate, a first 1/2 wave plate, a first q wave plate and a second 1/2 wave plate;
the receiving detection system consists of a third 1/2 wave plate, a second q wave plate, a polarization beam splitting prism, a first APD detector and a second APD detector;
the single photon signal generated by the single photon source is modulated into linearly polarized photons in a pure polarization state through a 1/4 wave plate and a first 1/2 wave plate in sequence, the linearly polarized photons in the pure polarization state are modulated into photons with spin-orbit mixed angular momentum through a first q wave plate, the photons with the spin-orbit mixed angular momentum modulate the polarization through a second 1/2 wave plate, the photons modulated through the second 1/2 wave plate are emitted from an emission modulation system to a receiving detection system, the photons with the spin-orbit mixed angular momentum entering the receiving detection system are modulated into the linearly polarized photons in the pure polarization state again through a third 1/2 wave plate and a second q wave plate in sequence, the linearly polarized photons in the pure polarization state are subjected to polarization splitting through a polarization splitting prism and then are split into two beams of photons, wherein one beam of the photons is detected by a first APD detector, the other beam of photons is detected by a second APD detector.
The ultrasensitive angle detection method based on the photon orbital angular momentum based on the device is realized by the following steps:
the method comprises the following steps: obtaining a photon wave function of a single photon signal generated by a single photon source after being adjusted by an emission modulation system as follows:
r is a right-handed circular polarization state, and L is a left-handed circular polarization state; + -2q is orbital angular momentum quantum number;
step two: after the photons adjusted by the emission modulation system reach the receiving detection system in the first step, the photons are modulated by the third 1/2 wave plate and the second q wave plate to become linearly polarized light in a pure polarization state, and a linearly polarized light wave function in the pure polarization state is obtained according to a formula (1) and is as follows:
wherein m theta is an included angle between the polarization direction of linearly polarized light and the X-axis direction of a reference coordinate system of the detection system, m is a spin-orbit mixed angular momentum quantum number, m is 2q +1, e is an index, and i is an imaginary number unit;
step three: in the second step, the linearly polarized light adjusted by the third 1/2 wave plate and the second q wave plate is split by the polarization splitting prism and detected by the first APD detector and the second APD detector, and according to the Malus law, the probability of detecting photons by the first APD detector is as follows:
h is a horizontal linear polarization state, and the included angle theta is calculated by using a formula (3) and the actually detected probability value.
The invention has the following effects:
the invention uses the spin-orbit angular momentum mixed state with the total angular momentum quantum number of m generated by the q wave plate as the optical gear, can amplify the mechanical rotation theta of the to-be-detected machine by the current polarization direction rotation angle of the m-fold, namely, the method can achieve the detection precision of other quantum detection strategies when detecting by using m photons by using single photons, and is slightly influenced by the photon dissipation. Then according to the Malus law, the probability that an APD detector arranged behind the polarization beam splitter prism detects photons is used for calculating theta. The invention can stably improve the original detection sensitivity by two orders of magnitude and improve the angle measurement sensitivity to 10 in terms of the maximum m which can be reached at present being 101-6And (4) degree.
Drawings
FIG. 1 is a schematic diagram of a detection method according to the present invention;
FIG. 2 is a reference frame diagram of a transmitting and receiving system;
FIG. 3 is a diagram showing the result of detection;
fig. 4 is a diagram of the detection result after enlargement.
Detailed Description
The first embodiment is as follows: as shown in fig. 1, an ultra-sensitive angle detection device based on photon orbital angular momentum includes: the system comprises a single photon source 1, an emission modulation system 11 and a receiving detection system 12;
the emission modulation system 11 is composed of a 1/4 wave plate 2, a first 1/2 wave plate 3, a first q wave plate 4 and a second 1/2 wave plate 5;
the receiving detection system 12 is composed of a third 1/2 wave plate 6, a second q wave plate 7, a polarization splitting prism 8, a first APD detector 9 and a second APD detector 10;
the single photon signal generated by the single photon source 1 is modulated into linearly polarized photons with a pure polarization state (only spin angular momentum) by the 1/4 wave plate 2 and the first 1/2 wave plate 3 in turn, the polarization direction of the linearly polarized photons with the pure polarization state is controllable, the linearly polarized photons with the pure polarization state are modulated into photons with spin-orbit mixed angular momentum (state) by the first q wave plate 4, the photons with the spin-orbit mixed angular momentum are modulated into polarization by the second 1/2 wave plate 5 (the total angular momentum quantum number m of the photons is maximized and is emitted), the photons modulated by the second 1/2 wave plate 5 are emitted from the emission modulation system 11 to the receiving detection system 12, the photons with the spin-orbit mixed angular momentum entering the receiving detection system 12 are demodulated into the linearly polarized photons with the pure polarization state again by the third 1/2 wave plate 6 and the second q wave plate 7 in turn, the linearly polarized light beam in the pure polarization state is subjected to polarization splitting through the polarization splitting prism 8 and then is split into two beams of photons, wherein one beam of photons is detected (responded) by the first APD detector 9, and the other beam of photons is detected (responded) by the second APD detector 10.
After the photons reach the receiving detection system 12, because the reference coordinate system changes, from the view of the receiving system, the photons equivalently carry the angle difference information between the transmitting system and the receiving system, after the photons are demodulated by the third 1/2 wave plate 6 and the second q wave plate 7 which are symmetrical to the transmitting system, the spin-orbit angular momentum mixed state is changed into linearly polarized light in a pure polarization state again, the angle difference information is specifically expressed on the rotation of the polarization direction, and the rotation angle of the polarization direction is only m times of the angle theta to be measured. At the moment, the photons are subjected to polarization beam splitting through the polarization beam splitting prism 8 and are detected and responded by the two APD detectors, and the angle theta to be measured can be calculated by utilizing the Malus law according to the probability that the photons are responded at the two APDs.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the reference coordinate systems of the transmission modulation system 11 and the receiving detection system 12 form an included angle θ, as shown in fig. 2.
The emission modulation system 11 and the receiving detection system 12 are fixed on two different optical benches and the optical axes are coincident. Their reference coordinate systems all have the optical axis direction as the Z-axis, the direction perpendicular to the optical axis and parallel to the respective optical bench plane as the X-axis, and the direction perpendicular to the optical axis and the respective optical bench plane as the Y-axis. Since the transmitting system can be rotated by an arbitrary angle θ along the optical axis with respect to the receiving system, the reference coordinate systems of the two will also have an angle θ.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the ultrasensitive angle detection method based on the photon orbital angular momentum comprises the following steps:
the method comprises the following steps: the photon wave function of the single photon signal generated by the single photon source 1 after being adjusted by the emission modulation system 10 is obtained as follows:
where | n>xA state with n photons in the x-mode, x ═ H, R or L, H, R and L represent horizontal linearly-biased, right-handed and left-handed circularly-biased modes, respectively; r is a right-handed circular polarization state, L is a left-handed circular polarization state, and H is a horizontal linear polarization state; + -2q is orbital angular momentum quantum number;
step two: in the first step, after the photons adjusted by the emission modulation system 10 reach the receiving detection system 11, the photons are modulated by the third 1/2 wave plate 6 and the second q wave plate 7 to become linearly polarized light in a pure polarization state, and a linearly polarized light wave function in the pure polarization state is obtained according to a formula (1) and is:
wherein m theta is an included angle between the polarization direction of linearly polarized light and the X-axis direction of a reference coordinate system of the detection system, m is a spin-orbit mixed angular momentum quantum number, m is 2q +1, e is an index, and i is an imaginary number unit;
the included angle between the polarization direction of the linearly polarized light and the horizontal direction of the detection system is m theta. This is the "optical gear" effect, and can magnify the mechanical rotation θ to be measured by m times and reflect it on the rotation of the polarization direction. The probability that the photon is detected by the APD placed at the horizontal transmission port can be known as formula (3) according to the Malus law only by splitting through the polarization splitting prism.
Step three: in the second step, the linearly polarized light adjusted by the third 1/2 wave plate 6 and the second q wave plate 7 is split by the polarization splitting prism 8, and then detected by the first APD detector 9 and the second APD detector 10, according to malus law, where the probability that the first APD detector 9 detects a photon is (the sum of the probabilities detected by the first APD detector 9 and the second APD detector 10 is equal to 1):
h is a horizontal linear polarization state, and the included angle theta can be calculated by using a formula (3) and the actually detected probability value.
The angle between the reference coordinate systems of the two systems results from the transmission modulation system being rotated along the optical axis by an angle theta, which is the detection object of the present invention.
To detect the probability value, if n photons are detected each time, and the detection is repeated v times, the statistical error of θ is formula (4).
Emission system preparation of photon states with spin-orbit mixed angular momentumAs an "optical gear", the transmission ratio of the "optical gear" is the total angular momentum m of the state. The receiving system demodulates the state, and the m-times body of the angle theta to be measured can be amplified on the rotation of the polarization direction. Then, according to Malus' theorem, the probability of detecting photons by APD (avalanche photo diode) placed at the horizontal transmission port of the polarization splitting prism is cos2m theta. And calculating the angle theta to be measured according to the expression and the probability of detecting the photons by the port actually.
The emission modulation system is utilized to firstly add orbital angular momentum of 2q to pure polarized photons only with spin angular momentum by adopting a special liquid crystal device q-wave plate. Then the direction of the spin angular momentum is modulated by the 1/2 wave plate to be consistent with the orbital angular momentum, so that the quantum number of the photon angular momentum reaches the maximum value m which is 2q + 1. The demodulation process and the modulation process are symmetrical, photons reach the receiving detection system and then sequentially pass through the 1/2 wave plate and the q wave plate to be converted into pure linear polarized light, and the polarization direction rotates by an angle of m theta.
The fourth concrete implementation mode: the third difference between the present embodiment and the specific embodiment is that: the specific process of obtaining the photon wave function of the single photon signal generated by the single photon source 1 and adjusted by the emission modulation system 10 in the step one is as follows:
the single photon signal generated by the single photon source 1 is modulated into linearly polarized photons through the 1/4 wave plate 2 and the first 1/2 wave plate 3, and the wave function is as follows:
linearly polarized light is passed through the first q-wave plate 4The mode is switched over, and the mode is switched over,subscripts 0 and ± q represent orbital angular momentum quantum numbers for the generator of photons with spin and orbital angular momentum; wherein, respectively, a right-handed photon without orbital angular momentum, a right-handed photon with angular momentum quantum number of-2 q, a left-handed photon without orbital angular momentum, and a left-handed photon with angular momentum quantum number of 2 q. After passing through the first q-wave plate 4, the wave function becomesAnd then carrying out polarization modulation on the single photon signal by the second 1/2 wave plate 5 to obtain a photon wave function of the single photon signal generated by the single photon source 1 after the single photon signal is adjusted by the emission modulation system 10.
The single photon state is a superposition state of two angular momentum eigenstates, the angular momentum quantum numbers of the two angular momentum eigenstates are both m 2q +1, and the directions are opposite. If the 1/2 wave plate is not added, m is 2 q-1.
Other steps and parameters are the same as those in the third embodiment.
The fifth concrete implementation mode: this embodiment is different from the third or fourth embodiment in that: the specific process of obtaining the linearly polarized light wave function in the pure polarization state in the second step is as follows:
after the photons reach the receiving detection system 12, because the emission modulation system (11) and the reference coordinate system of the receiving detection system (12) have an included angle θ, the wave function under the reference coordinate system of the receiving detection system 12 is obtained by a geometric rotation operator acting on the wave function of formula (1):
the linearly polarized light which is converted into a pure polarization state through the modulation of the third 1/2 wave plate 6 and the second q wave plate 7 (which is symmetrical to the modulation process) is obtained, and a wave function shown in a formula (2) is obtained.
Other steps and parameters are the same as those of the third or fourth embodiment.
The sixth specific implementation mode: the difference between this embodiment and one of the third to fifth embodiments is: the statistical error of the included angle theta in the third step is as follows:
wherein n is the number of photons participating in the detection and v is the number of repeated measurements.
The m of the denominator in the formula (4) shows that the angle amplification effect of the optical gear provided by the invention can reduce the measurement error to 1/m of the condition without amplification and improve the detection sensitivity. As shown in fig. 3 and 4, the probability of detecting photons at two detectors changes periodically as the angle θ to be measured changes, fig. 3 shows the non-amplified measurement result, and fig. 3 shows the amplified measurement result using the "optical gear". It can be seen that the period of probability change is much smaller when the measurement is magnified than when it is not magnified, so that the magnified measurement can resolve smaller angle changes.
For device reasons, the q parameter of the current q-wave plate can reach 50 at most, and m is 101. Therefore, if the optical gear amplification effect provided by the invention and the existing polarization-based angle measurement method are combined, the angle detection sensitivity can be stably improved by 2 orders of magnitude.
Other steps and parameters are the same as those in one of the third to fifth embodiments.
In the field of existing optical angle measurement, because the minimum angle change which can be resolved by a detection system depends on the angle detection uncertainty of the system, the uncertainty of angle detection is an important index for measuring the angle detection sensitivity, and the detection uncertainty can also be directly called as the detection sensitivity. The angular detection uncertainty of the conventional malus law based scheme satisfies the following inequality
Wherein N is the number of photons participating in the detection. For a detection system with fixed light source power and detection program, the minimum angle detection uncertainty which can be achieved is determined by the formula (5), so that the angle detection sensitivity of the traditional optical angle measurement system isThe uncertainty of angle detection in the scheme of the invention is given by the formula (4), so that the sensitivity of angle detection isCompared with the traditional detection system, the sensitivity is improved2m times, so compared with the prior detection technology, the method has the ultra-sensitive characteristic.
The first embodiment is as follows:
in the implementation process of the invention, the modulation transmitting system is fixed, and the receiving and detecting system is driven by the motor to deflect along the direction of the optical axis. The q-wave plate is a liquid crystal device, and is driven by a driving circuit to ensure that liquid crystal molecules are arranged according to a certain rule and have different q values. The higher q the higher the spatial frequency of the liquid crystal arrangement and the higher the requirements on the drive circuit. Single photon source at a certain frequencyAnd emitting single photon signals, and solving the probability of the photons exiting from the horizontal or vertical transmission port according to APD photon counting information in a fixed time interval tau to finish one-time measurement. The average value was found v times in each angle. The detection results are shown in fig. 3 and 4, which are also compared with the probability variation curve of the unamplified measurement (classical malus-law detection method) shown in fig. 3. It can be seen that the method can realize the angle measurement with ultrahigh resolution and ultrahigh sensitivity along with the increase of the number of m-angular momentum quanta.
The 1/4 wave plate and the 1/2 wave plate are products of Thorlabs company with the models of WPQ10ME-532 and WPH10ME-532 respectively.
The q wave plate is a liquid crystal film with the thickness of 5-10 mu m in principle, wherein liquid crystal molecules are distributed in a certain mode to form the q wave plate with different q values, and the actual experiment can be realized by adopting a liquid crystal on silicon spatial light modulator with the model number of X10468-04 produced by the Japan Hamamatsu company.
Claims (6)
1. An ultrasensitive angle detecting device based on photon orbital angular momentum, the ultrasensitive angle detecting device comprising: a single photon source (1), an emission modulation system (11) and a receiving detection system (12);
the emission modulation system (11) is composed of a 1/4 wave plate (2), a first 1/2 wave plate (3), a first q wave plate (4) and a second 1/2 wave plate (5);
the receiving detection system (12) is composed of a third 1/2 wave plate (6), a second q wave plate (7), a polarization splitting prism (8), a first APD detector (9) and a second APD detector (10);
single photon signals generated by a single photon source (1) are modulated into linearly polarized photons in a pure polarization state sequentially through a 1/4 wave plate (2) and a first 1/2 wave plate (3), the linearly polarized photons in the pure polarization state are modulated into photons with spin-orbit mixed angular momentum through a first q wave plate (4), the photons with the spin-orbit mixed angular momentum are modulated in a polarization mode through a second 1/2 wave plate (5), the photons modulated through the second 1/2 wave plate (5) are emitted out of an emission modulation system (11) to a receiving detection system (12), the photons with the spin-orbit mixed angular momentum entering the receiving detection system (12) are modulated into the linearly polarized photons in the pure polarization state again through a third 1/2 wave plate (6) and a second q wave plate (7), the linearly polarized photons in the pure polarization state are divided into two photons after being subjected to polarization splitting through a polarization splitting prism (8), one of the photons is detected by a first APD detector (9) and the other photon is detected by a second APD detector (10).
2. The ultrasensitive angular detector based on photonic orbital angular momentum according to claim 1, wherein the reference coordinate systems of the emission modulation system (11) and the receiving detection system (12) form an included angle θ;
the emission modulation system (11) and the receiving detection system (12) are fixed on two different optical benches, optical axes of the two reference coordinate systems coincide, the direction of the optical axis is taken as a Z axis, the direction perpendicular to the optical axis and parallel to the plane of each optical bench is taken as an X axis, and the direction perpendicular to the optical axis and the plane of each optical bench is taken as a Y axis.
3. An ultrasensitive angle detection method based on photon orbital angular momentum based on the device of claim 1 or 2, wherein the detection method comprises the following steps:
the method comprises the following steps: obtaining a photon wave function of a single photon signal generated by a single photon source (1) after being adjusted by an emission modulation system (11) as follows:
r is a right-handed circular polarization state, and L is a left-handed circular polarization state; + -2q is orbital angular momentum quantum number;
step two: after the photons adjusted by the emission modulation system (11) reach the receiving detection system (12), the photons are modulated by the third 1/2 wave plate (6) and the second q wave plate (7) to become linearly polarized light in a pure polarization state, and the linearly polarized light wave function in the pure polarization state is obtained according to a formula (1):
wherein m theta is an included angle between the polarization direction of linearly polarized light and the X-axis direction of a reference coordinate system of the detection system, m is a spin-orbit mixed angular momentum quantum number, m is 2q +1, e is an index, and i is an imaginary number;
step three: linearly polarized light adjusted by the third 1/2 wave plate (6) and the second q wave plate (7) in the second step is split by the polarization splitting prism (8) and then detected by the first APD detector (9) and the second APD detector (10), and according to the Malus law, the probability that the first APD detector (9) detects photons is as follows:
h is a horizontal linear polarization state, and the included angle theta is calculated by using a formula (3) and the actually detected probability value.
4. The method for detecting the ultrasensitive angle based on the photon orbital angular momentum according to claim 3, wherein the specific process for obtaining the photon wave function of the single photon signal generated by the single photon source (1) after the single photon signal is adjusted by the emission modulation system (11) in the step one is as follows:
the single photon signal generated by the single photon source (1) is modulated into a linearly polarized photon through the 1/4 wave plate (2) and the first 1/2 wave plate (3), and the wave function is as follows:
linearly polarized light photons go through a first q wave plate (4)A mode change-over, wherein, respectively generating operators of right-handed photons without orbital angular momentum, right-handed photons with angular momentum quantum number of-2 q, left-handed photons without orbital angular momentum and left-handed photons with angular momentum quantum number of 2 q; after passing through the first q wave plate (4), the wave function becomesAnd then carrying out polarization modulation on the single photon signal by the second 1/2 wave plate (5) to obtain a photon wave function of the single photon signal generated by the single photon source (1) after the single photon signal is adjusted by the emission modulation system (10).
5. The ultrasensitive angle detection method based on photon orbital angular momentum according to claim 4, wherein the specific process of obtaining the linearly polarized light wave function in the pure polarization state in the second step is as follows:
after the photons reach the receiving detection system (12), the wave function under the reference coordinate system of the receiving detection system (12) is obtained by a geometric rotation operator acting on the wave function of the formula (1):
the linear polarized light of the pure polarization state is changed through the modulation of the third 1/2 wave plate (6) and the second q wave plate (7), and a wave function shown in a formula (2) is obtained.
6. The ultrasensitive angle detection method based on photon orbital angular momentum according to claim 5, wherein the statistical error of the included angle θ in the three steps is as follows:
wherein n is the number of photons participating in detection at a single time, and v is the number of repeated measurements.
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