基于关联光学的精密测量理论和方法研究
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摘要
上个世纪80年代诞生的量子信息学在最近的三十几年里得到了飞速发展，各种量子信息处理方案先后被提出，量子信息学在诸多领域不断地得到完善和发展，同时也带动各种相关的实验技术不断发展成熟。其中，以光学系统为基础的各种量子技术，较其他方法得到了更快的发展，因为光场易于传输，且相对成熟的光电技术为非经典光场的制备与检测提供了必要的实验基础。在其不断发展的过程中，光场的关联特性逐渐得到了人们越来越多的关注，并且在测量和成像等方面表现出独特的优势。
本文围绕着光场关联特性在测量上的应用的一些热点问题展开研究，主要讨论了形如(|N0+|0N)/√2的双模路径纠缠光子数态，即多光子NOON态的制备和超出散粒噪声极限的光学陀螺两方面的问题，主要内容有：
1.基于腔量子电动力学技术的多光子NOON态制备近年来，理论和实验研究发现利用处于路径纠缠的光子数态，即所谓的“NOON”态，的光场可以达到海森堡测量极限。然而，目前实验上能制备的NOON态所含的光子数比较少，无法满足实际测量的需求。如何制备含有大量光子的NOON态成为了一个亟待解决的问题。因此，本文提出了两个利用腔QED技术制备多光子NOON态的方案。
(a)利用原子与腔场之间的Bragg散射可以将原子束相干的分为两束，分别进入空间分离的两个光学腔中，从而得到在两个空间模之间的纠缠。随后，通过一个受激拉曼跃迁过程在其中一个腔中产生光子数态，由此得到两个空间模之间纠缠的光子数态。
(b)通过原子与腔场之间的相互作用，可以对双面腔的反射率和透射率进行调制。因此，利用一个阶梯型三能级原子与单模双面腔之间的相互作用，可以制备出一个两个空间模之间纠缠的光场。将这个纠缠光场用于激发分别囚禁于两个空间分离的腔中的原子系宗，使其辐射光子，从而制备出多光子NOON态。与以往工作相比，这两个方案提高了NOON态光场中的光子数目，减低了对腔寿命时间的限制，同时也降低了实际操作中的复杂度。
2.以双模压缩相干态光场为光源的光学陀螺
研究表明利用光场关联性质可以将干涉测量灵敏度由散粒噪声极限提高至海森堡极限，则以干涉为基础的传感器的测量精确度也可以进一步提高的。为此，我们就如何提高相位敏感型光学陀螺的测量精确度问题展开研究。从实际应用的角度考虑，本文采用了强度相对来说更大，制备方法较为成熟的双模压缩相干态光场。研究显示，在这种情况下，光学陀螺的测量灵敏度不仅与压缩参数有关，而且也会受到制备双模压缩光场的初始相干光场的复振幅相位影响。当陀螺光源为孪生光束时，光学陀螺的测量灵敏将会突破散粒噪声极限，在信噪比、动态范围等方面均显示出极大的优势。在灵敏度相等的情况下，相对于传统光纤陀螺，表现出更低的噪声水平和更低的对光源强度的需求。
3.噪声对超精密相位测量的影响
一般来说，在噪声环境中测量精度会降低。对于以双模压缩相干态作为光源的光学陀螺，本文分别考察了光源和光传输过程中的噪声对测量灵敏度的影响。对于光源的噪声，主要分析了光源两模强度不相等和两模相位不同步两种情况下测量灵敏度的变化。同时，从能量损耗的角度对光路中的噪声进行讨论，详细分析了光路中噪声对易和非对易两种情况下测量灵敏度的变化。结果表明，噪声将会降低陀螺测量精度，但是在一定条件下通过增大压缩参数，降低由于光源的光子噪声引起的相位涨落，以弥补传输过程中其他噪声对测量灵敏度的影响。仍然可以得到超出散粒噪声极限的测量精度。
Quantum Information Theory, born in80’s of the last century, experiencesa rapid development during the next three decades. Various schemes of quan-tum information processing has been proposed, and quantum information scienceconstantly improved and developed in many felds. These drive the relative ex-perimental techniques process. Among these quantum techniques, a variety ofquantum technology based on the optical system has been developed more fastcompared with other methods, because the light feld is easy for transport, andthe relatively mature photoelectron technology provides a necessary experimentalbasis for the preparing and testing of the non-classical light feld. In the processof its constant development, the correlation of the light feld has gradually at-tracted more and more attention, and shown unique advantages in measurementand imaging.
The dissertation focuses on some hot issues associated with the applicationof the correlation of the light feld in measurement, mainly discusses the problemsof the generation of multi-photon NOON state and the optical gyroscope beyondshot-noise limit. Our works are as follows:
1. The generation of multi-photon NOON state based on technology of cavityquantum electrodynamics Current theories and experiments have provedthat for phase measurement Heisenberg limit is the fundamental limit setby the quantum mechanics, while it can only reach the shot noise limit bythe traditional methods of measurement. And it is found that the feldin path-entangled Fock state, the so-called “NOON” state, can be appliedto achieved the Heisenberg limit measurement. However, the NOON stategenerated in present experiment condition contained a few photons, whichcan not meet the requirement of the practical measurement. How to prepare a NOON state contain large number of photons is a urgent problem to besolved. In the present thesis, two novel scheme for generating the opticalNOON state by the method of cavity QED technology have been proposed.
(a) By using the atomic Bragg scattering with the cavity feld, a beamof atoms can be split coherently, and fy into two spatially separatedcavities, so that the entanglement between two spatial modes can beestablished. And then, through a stimulated Raman transition a op-tical Fock state is generated in either one of the two cavities. Conse-quently, the entangled optical Fock state between two spatial modesis obtained.
(b) The refectance and the transmittance of a two-sided cavity will bemodulated by the interaction between the atom and the cavity. There-fore, a entangled light feld between two spatial modes can be preparedby using the interaction between a ladder-type three-level atom anda single-mode two-sided optical cavity. Then, the entangled feld isapplied to induce two atomic ensembles trapped in two spatially sep-arated cavities to emit photons, so that a multi-photon NOON stateis generated.
2. Optical gyroscope with the light feld in two-mode squeezed coherent stateas light source
It has been proved by plenty theoretical and experimental studies that themeasurement limit of interferometry can be improved from the shot-noiselimit to Heisenberg limit, which means that the accuracy of the sensorsbased on interferometry can be further improved. For this reason, we in-vestigate the problem about how to improve the measurement accuracy ofthe phase-sensitive sensors, especially that of the phase-sensitive opticalgyroscope. From the perspective of the practical application, the light feldin the two-mode coherent state, which is rather strong in power and easy inpreparation, is adapted in our work. While, the method for measurementis still frst-order interferometry by measuring the intensity diference. Itshows that in this condition the sensitivity of the optical gyroscope not onlyis relative to the squeezing parameters, but also depends on phase of the amplitude of the initial coherent light feld used to prepare the two-modesqueezed light feld. Specifcally, when the light source is so-called twinbeam the sensitivity of the optical gyroscope will beyond the shot-noiseand shows great advantage in the signal-to-noise rate, the dynamic range,and so on. Compared with the classical optical gyroscope, the noise level isreduced greatly and the demand on the light source intensity is decreasedas well.
3. Infuence of the noise
In addition, we investigate the infuence of the noise in the source and in theprocess of optical transmission. On the one hand, we discuss the infuence ofthe intensity-diference and phase-diference of the two-mode squeezed lightfeld using as the source of the gyroscope. On the other hand, the infuenceof the noise in the light path, both commutative and non-commutative, isanalyzed in detail from the perspective of the energy loss.It shows that ina given condition, though the noise will cause a decrease in the sensitivityof the gyroscope the phase sensitivity below the shot-noise limit can still beachieved by increasing the squeezing parameter which decreases the photonstatistical noise, and then compensates the loss caused by other noise.
本文围绕着光场关联特性在测量上的应用的一些热点问题展开研究，主要讨论了形如(|N0+|0N)/√2的双模路径纠缠光子数态，即多光子NOON态的制备和超出散粒噪声极限的光学陀螺两方面的问题，主要内容有：
1.基于腔量子电动力学技术的多光子NOON态制备近年来，理论和实验研究发现利用处于路径纠缠的光子数态，即所谓的“NOON”态，的光场可以达到海森堡测量极限。然而，目前实验上能制备的NOON态所含的光子数比较少，无法满足实际测量的需求。如何制备含有大量光子的NOON态成为了一个亟待解决的问题。因此，本文提出了两个利用腔QED技术制备多光子NOON态的方案。
(a)利用原子与腔场之间的Bragg散射可以将原子束相干的分为两束，分别进入空间分离的两个光学腔中，从而得到在两个空间模之间的纠缠。随后，通过一个受激拉曼跃迁过程在其中一个腔中产生光子数态，由此得到两个空间模之间纠缠的光子数态。
(b)通过原子与腔场之间的相互作用，可以对双面腔的反射率和透射率进行调制。因此，利用一个阶梯型三能级原子与单模双面腔之间的相互作用，可以制备出一个两个空间模之间纠缠的光场。将这个纠缠光场用于激发分别囚禁于两个空间分离的腔中的原子系宗，使其辐射光子，从而制备出多光子NOON态。与以往工作相比，这两个方案提高了NOON态光场中的光子数目，减低了对腔寿命时间的限制，同时也降低了实际操作中的复杂度。
2.以双模压缩相干态光场为光源的光学陀螺
研究表明利用光场关联性质可以将干涉测量灵敏度由散粒噪声极限提高至海森堡极限，则以干涉为基础的传感器的测量精确度也可以进一步提高的。为此，我们就如何提高相位敏感型光学陀螺的测量精确度问题展开研究。从实际应用的角度考虑，本文采用了强度相对来说更大，制备方法较为成熟的双模压缩相干态光场。研究显示，在这种情况下，光学陀螺的测量灵敏度不仅与压缩参数有关，而且也会受到制备双模压缩光场的初始相干光场的复振幅相位影响。当陀螺光源为孪生光束时，光学陀螺的测量灵敏将会突破散粒噪声极限，在信噪比、动态范围等方面均显示出极大的优势。在灵敏度相等的情况下，相对于传统光纤陀螺，表现出更低的噪声水平和更低的对光源强度的需求。
3.噪声对超精密相位测量的影响
一般来说，在噪声环境中测量精度会降低。对于以双模压缩相干态作为光源的光学陀螺，本文分别考察了光源和光传输过程中的噪声对测量灵敏度的影响。对于光源的噪声，主要分析了光源两模强度不相等和两模相位不同步两种情况下测量灵敏度的变化。同时，从能量损耗的角度对光路中的噪声进行讨论，详细分析了光路中噪声对易和非对易两种情况下测量灵敏度的变化。结果表明，噪声将会降低陀螺测量精度，但是在一定条件下通过增大压缩参数，降低由于光源的光子噪声引起的相位涨落，以弥补传输过程中其他噪声对测量灵敏度的影响。仍然可以得到超出散粒噪声极限的测量精度。
Quantum Information Theory, born in80’s of the last century, experiencesa rapid development during the next three decades. Various schemes of quan-tum information processing has been proposed, and quantum information scienceconstantly improved and developed in many felds. These drive the relative ex-perimental techniques process. Among these quantum techniques, a variety ofquantum technology based on the optical system has been developed more fastcompared with other methods, because the light feld is easy for transport, andthe relatively mature photoelectron technology provides a necessary experimentalbasis for the preparing and testing of the non-classical light feld. In the processof its constant development, the correlation of the light feld has gradually at-tracted more and more attention, and shown unique advantages in measurementand imaging.
The dissertation focuses on some hot issues associated with the applicationof the correlation of the light feld in measurement, mainly discusses the problemsof the generation of multi-photon NOON state and the optical gyroscope beyondshot-noise limit. Our works are as follows:
1. The generation of multi-photon NOON state based on technology of cavityquantum electrodynamics Current theories and experiments have provedthat for phase measurement Heisenberg limit is the fundamental limit setby the quantum mechanics, while it can only reach the shot noise limit bythe traditional methods of measurement. And it is found that the feldin path-entangled Fock state, the so-called “NOON” state, can be appliedto achieved the Heisenberg limit measurement. However, the NOON stategenerated in present experiment condition contained a few photons, whichcan not meet the requirement of the practical measurement. How to prepare a NOON state contain large number of photons is a urgent problem to besolved. In the present thesis, two novel scheme for generating the opticalNOON state by the method of cavity QED technology have been proposed.
(a) By using the atomic Bragg scattering with the cavity feld, a beamof atoms can be split coherently, and fy into two spatially separatedcavities, so that the entanglement between two spatial modes can beestablished. And then, through a stimulated Raman transition a op-tical Fock state is generated in either one of the two cavities. Conse-quently, the entangled optical Fock state between two spatial modesis obtained.
(b) The refectance and the transmittance of a two-sided cavity will bemodulated by the interaction between the atom and the cavity. There-fore, a entangled light feld between two spatial modes can be preparedby using the interaction between a ladder-type three-level atom anda single-mode two-sided optical cavity. Then, the entangled feld isapplied to induce two atomic ensembles trapped in two spatially sep-arated cavities to emit photons, so that a multi-photon NOON stateis generated.
2. Optical gyroscope with the light feld in two-mode squeezed coherent stateas light source
It has been proved by plenty theoretical and experimental studies that themeasurement limit of interferometry can be improved from the shot-noiselimit to Heisenberg limit, which means that the accuracy of the sensorsbased on interferometry can be further improved. For this reason, we in-vestigate the problem about how to improve the measurement accuracy ofthe phase-sensitive sensors, especially that of the phase-sensitive opticalgyroscope. From the perspective of the practical application, the light feldin the two-mode coherent state, which is rather strong in power and easy inpreparation, is adapted in our work. While, the method for measurementis still frst-order interferometry by measuring the intensity diference. Itshows that in this condition the sensitivity of the optical gyroscope not onlyis relative to the squeezing parameters, but also depends on phase of the amplitude of the initial coherent light feld used to prepare the two-modesqueezed light feld. Specifcally, when the light source is so-called twinbeam the sensitivity of the optical gyroscope will beyond the shot-noiseand shows great advantage in the signal-to-noise rate, the dynamic range,and so on. Compared with the classical optical gyroscope, the noise level isreduced greatly and the demand on the light source intensity is decreasedas well.
3. Infuence of the noise
In addition, we investigate the infuence of the noise in the source and in theprocess of optical transmission. On the one hand, we discuss the infuence ofthe intensity-diference and phase-diference of the two-mode squeezed lightfeld using as the source of the gyroscope. On the other hand, the infuenceof the noise in the light path, both commutative and non-commutative, isanalyzed in detail from the perspective of the energy loss.It shows that ina given condition, though the noise will cause a decrease in the sensitivityof the gyroscope the phase sensitivity below the shot-noise limit can still beachieved by increasing the squeezing parameter which decreases the photonstatistical noise, and then compensates the loss caused by other noise.
引文
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