Many delayed-choice experiments based on Mach-Zehnder interferometers （MZI） have been considered and made to address the fundamental problem of wave-particle duality. Conventional wisdom long holds that by inserting...Many delayed-choice experiments based on Mach-Zehnder interferometers （MZI） have been considered and made to address the fundamental problem of wave-particle duality. Conventional wisdom long holds that by inserting or removing the second beam splitter （BS2） in a controllable way, microscopic particles （photons, electrons, etc.） transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ= aw ψ wave ＋ ap ψ particle. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as the BS2 is purely classical, the inserting and removing operation of the BS2 imposes a time- modulated Hamiltonian H mod （t） = a（t）Hin ＋ b（t）Hout, instead of a quantum superposition of H in and Hour as H = awHin ＋ apHout, to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as ψ mod （t） = a（t） ψ wave ＋b（t） ψ particle, instead of the stationary quantum superposition state ψ = aw ψ wave ＋ ap ψ particle. As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect that these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and the principle of complementarity.展开更多
An in-fiber Mach-Zehnder interferometer for strain measurement is proposed and experimentally demonstrated. The sensor consists of a taper followed by a short section of a multi-mode fiber （MMF） and a dispersion com...An in-fiber Mach-Zehnder interferometer for strain measurement is proposed and experimentally demonstrated. The sensor consists of a taper followed by a short section of a multi-mode fiber （MMF） and a dispersion com- pensating fiber （DCF）, which is sandwiched between two single mode fibers （SMFs）. The taper is used as a fiber coupler to excite cladding modes in the SMF, and these cladding modes transmit within the MMF and the DCF. The core mode and the cladding modes interfere in the DCF SMF fusion point to form intermodal interference. A well-defined interference spectrum is obtained in the experiment. Selected interference dips are used to measure the strain changes. The experimental results show that this device is sensitive to strain with the wavelength-referenced sensitivity of 2.6 pm/με and the power-referenced sensitivity of 0. 0027 dB/με, respectively.展开更多
The temperature-induced complex refractive index（CRI） effect of graphene is demonstrated theoretically and experimentally based on a graphene coated in-fiber MZI（Mach-Zehnder interferometer）. The relationships bet...The temperature-induced complex refractive index（CRI） effect of graphene is demonstrated theoretically and experimentally based on a graphene coated in-fiber MZI（Mach-Zehnder interferometer）. The relationships between real and imaginary parts of the graphene CRI and temperature are obtained through investigating the dip wavelength and intensity of the MZI interference spectrum changing with temperature, respectively. The temperature effect of CRI of the graphene is also analyzed theoretically. Both experimental and theoretical studies show that the real part and imaginary part of the CRI nonlinearly decrease and increase with temperature increasing, respectively. This graphene-coated in-fiber MZI structure also possesses the advantages of easy fabrication, miniaturization, low cost and robustness. It has potential applications in nanomaterial-based optic devices for communication and sensing.展开更多
On the silicon-on-insulator platform, an ultra compact temperature-insensitive modulator based on a cascaded microring assistant Mach-Zehnder interferometer is proposed and demonstrated with numerical simulation. Acco...On the silicon-on-insulator platform, an ultra compact temperature-insensitive modulator based on a cascaded microring assistant Mach-Zehnder interferometer is proposed and demonstrated with numerical simulation. According to the calculated results, the tolerated variation of ambient temperature can be as high as 134 ℃ while the footprint of such a silicon modulator is only 340 μm2.展开更多
We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 （2015）050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 （2013） 240402] does not test the past of the photon as characterized...We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 （2015）050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 （2013） 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions： （i） were the photons in A？ （ii） were the photons in B？ and （iii） were the photons in C？ the proposed experiment measures a degenerate operator answering the questions： （i） were the photons in A？ and （ii） were the photons in B and C together？ A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre- and post-selected photon, but this evidence will be in agreement with the results of Danan et al.展开更多
We present a two-photon interference experiment in a modified Mach-Zehnder （MZ） interferometer in which two Hong-Ou-Mandel effects occur in tandem and construct superposed two-photon states. The signal photons pass ...We present a two-photon interference experiment in a modified Mach-Zehnder （MZ） interferometer in which two Hong-Ou-Mandel effects occur in tandem and construct superposed two-photon states. The signal photons pass both the arms of the MZ interferometer while the idler photons pass one arm only. Interestingly, the probability of the idler photons emerging from any output port still shows a sine oscillation with the two-photon phase difference and it can be characterized only by the indistinguishability of the two-photon amplitudes. We also observe a two-photon interference pattern with a period being equal to the wavelength of the parametric photons instead of the two-photon photonie de Broglie wavelength due to the presence of two-photon phase difference, in particular, with complementary probabilities of finding the two-photon pairs in two output ports. The abundant observations can facilitate a more comprehensive understanding of the two-photon interference.展开更多
An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer （MZI） by using standard quantum mechanics with quantum non-demolition measurements. We find that when the...An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer （MZI） by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI. When it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics contradicts the statement based on two-state vector formulism, ＇the photon did not enter the （inner） interferometer, the photon never left the interferometer, but it was there＇. Therefore, the statement and also the overlapping claim are incorrect.展开更多
By designing and fabricating a series of dual-interferometer coupled silicon microrings, the coupling condition of the pump, signal, and idler beams can be engineered independently and then we carried out both the con...By designing and fabricating a series of dual-interferometer coupled silicon microrings, the coupling condition of the pump, signal, and idler beams can be engineered independently and then we carried out both the continuous-wave and pulse pumped four-wave mixing experiments to verify the dependence of conversion efficiency on the coupling conditions of the four interacting beams, respectively. Under the continuous-wave pump, the four-wave mixing efficiency gets maximized when both the pump and signal/idler beams are closely operated at the critical coupling point, while for the pulse pump case, the efficiency can be enhanced greatly when the pump and converted idler beams are all overcoupled. These experiment results agree well with our theoretical calculations. Our design provides a platform for explicitly characterizing the four-wave mixing under different pumping conditions, and offers a method to optimize the four-wave mixing, which will facilitate the development of on-chip all-optical signal processing with a higher efficiency or reduced pump power.展开更多
We study the fringe visibility and the which-path information(WPI) of a general Mach-Zehnder interferometer with an asymmetric beam splitter(BS). A minimum error measurement in the detector is used to extract the WPI....We study the fringe visibility and the which-path information(WPI) of a general Mach-Zehnder interferometer with an asymmetric beam splitter(BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI I_(path) are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship V^2 + I_(path)~2 ≤ 1 is found, and the conditions for equality are also presented.展开更多
We study the wave–particle duality in a general Mach–Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory.The correlations(including the classical correlation and ...We study the wave–particle duality in a general Mach–Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory.The correlations(including the classical correlation and the quantum correlation)between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach–Zehnder interferometer.It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle.The complementary relations between the fringe visibility and the correlations are also presented.展开更多
We propose a method to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By manipulating the coupling strength between two involved internal states of ...We propose a method to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By manipulating the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination with NOON states. Using current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.展开更多
This paper theoretically explores the effect of PM2.5 air pollution on the phase precision of a Mach-Zehnder inter- ferometer. With the increasing of PM2.5 concentration, phase precision for inputs of coherent state ...This paper theoretically explores the effect of PM2.5 air pollution on the phase precision of a Mach-Zehnder inter- ferometer. With the increasing of PM2.5 concentration, phase precision for inputs of coherent state ＆ vacuum state and inputs of coherent state ＆ squeezed vacuum state will gradually decrease and be lower than the standard quantum limit. When the value of relative humidity is increasing, the precision of two input cases is decreasing much faster. We also find that the precision for inputs of coherent state ＆ squeezed state is better than that of coherent state ＆ vacuum state when PM2.5 concentration is lower. As PM2.5 concentration increases, the precision for inputs of coherent state ＆ squeezed state decreases faster, and then the two precisions tend to be the same while the concentration is higher.展开更多
Quantum interferometric strategy with input two-mode squeezed vacuum [Phys. Rev. Lett. 104 103602] is reexamined for both parity and S^z2 measurements. Unlike the previous scheme, we find that phase sensitivity obtain...Quantum interferometric strategy with input two-mode squeezed vacuum [Phys. Rev. Lett. 104 103602] is reexamined for both parity and S^z2 measurements. Unlike the previous scheme, we find that phase sensitivity obtained with the S^z2 measurement is minimized at phase origin, which may be useful to estimate a small phase shift at high precision. For the phase deviated from zero, the sensitivity increases more slowly than that of the parity detection.展开更多
We propose a novel all fiber Mach-Zehnder interferometer（MZI） based on photonic crystal fiber（PCF） filled with liquid crystal（LC）. The interference between the core mode and the cladding modes of a PCF is utiliz...We propose a novel all fiber Mach-Zehnder interferometer（MZI） based on photonic crystal fiber（PCF） filled with liquid crystal（LC）. The interference between the core mode and the cladding modes of a PCF is utilized.To excite the cladding modes, a region is formed using fiber fusion splicer. Due to the fact that varying effective index difference between the core region and the LC-filled cladding region can cause different transmission spectra,we mainly study the MZIs with different LC-filled structures and different lengths of LC filling. The measured results demonstrate that quite clear interference spectra can be obtained. Through analysis spatial frequency spectrum and temperature spectrum of two MZIs with different LC-filled structures, we can obtain that the MZI with adjacent two LC-filled holes has clearer interference spectrum and higher temperature sensitivity. Thus we choose this MZI to measure the temperature sensitivity with different lengths of LC filling. When the length of LC filling is 2 cm, the temperature sensitivities can be enlarged to 1.59 nm/C. The interferometer shows a good temperature tunability and sensitivity, which can be a good candidate for a highly tunable optical filtering and temperature sensing applications.展开更多
基金Supported by the National Basic Research Program of China under Grant No 2013CB632704the National Natural Science Foundation of China under Grant No 11434017
文摘Many delayed-choice experiments based on Mach-Zehnder interferometers （MZI） have been considered and made to address the fundamental problem of wave-particle duality. Conventional wisdom long holds that by inserting or removing the second beam splitter （BS2） in a controllable way, microscopic particles （photons, electrons, etc.） transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ= aw ψ wave ＋ ap ψ particle. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as the BS2 is purely classical, the inserting and removing operation of the BS2 imposes a time- modulated Hamiltonian H mod （t） = a（t）Hin ＋ b（t）Hout, instead of a quantum superposition of H in and Hour as H = awHin ＋ apHout, to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as ψ mod （t） = a（t） ψ wave ＋b（t） ψ particle, instead of the stationary quantum superposition state ψ = aw ψ wave ＋ ap ψ particle. As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect that these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and the principle of complementarity.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61077006,60727004,and 61077060the China National Petroleum Corporation Science and Technology Development Projects under Grant No 2014B-4012the Science Research Plan Projects of Shaanxi Education Department under Grant No 14JK1580
文摘An in-fiber Mach-Zehnder interferometer for strain measurement is proposed and experimentally demonstrated. The sensor consists of a taper followed by a short section of a multi-mode fiber （MMF） and a dispersion com- pensating fiber （DCF）, which is sandwiched between two single mode fibers （SMFs）. The taper is used as a fiber coupler to excite cladding modes in the SMF, and these cladding modes transmit within the MMF and the DCF. The core mode and the cladding modes interfere in the DCF SMF fusion point to form intermodal interference. A well-defined interference spectrum is obtained in the experiment. Selected interference dips are used to measure the strain changes. The experimental results show that this device is sensitive to strain with the wavelength-referenced sensitivity of 2.6 pm/με and the power-referenced sensitivity of 0. 0027 dB/με, respectively.
基金Project supported by the Shandong Provincial Natural Science Foundation of China(Grant Nos.ZR2009AM017 and ZR2013FM019)the National Postdoctoral Project of China(Grant Nos.200902574 and 20080441150)+2 种基金the Shandong Provincial Education Department Foundation of China(Grant No.J06P14)the Opening Foundation of State Key Lab of Minning Disaster Prevention and Control Co-founded by Shandong Provincethe Ministry of Science and Technology of China(Grant No.MDPC201602)
文摘The temperature-induced complex refractive index（CRI） effect of graphene is demonstrated theoretically and experimentally based on a graphene coated in-fiber MZI（Mach-Zehnder interferometer）. The relationships between real and imaginary parts of the graphene CRI and temperature are obtained through investigating the dip wavelength and intensity of the MZI interference spectrum changing with temperature, respectively. The temperature effect of CRI of the graphene is also analyzed theoretically. Both experimental and theoretical studies show that the real part and imaginary part of the CRI nonlinearly decrease and increase with temperature increasing, respectively. This graphene-coated in-fiber MZI structure also possesses the advantages of easy fabrication, miniaturization, low cost and robustness. It has potential applications in nanomaterial-based optic devices for communication and sensing.
基金Project supported by the National Basic Research Program of China(Grant Nos.2011CBA00608,2011CBA00303,2011CB301803, and 2010CB327405)the National Natural Science Foundation of China(Grant Nos.61036011 and 61036010)the Project of Science and Technology from the Communication Information Security Control Laboratory
文摘On the silicon-on-insulator platform, an ultra compact temperature-insensitive modulator based on a cascaded microring assistant Mach-Zehnder interferometer is proposed and demonstrated with numerical simulation. According to the calculated results, the tolerated variation of ambient temperature can be as high as 134 ℃ while the footprint of such a silicon modulator is only 340 μm2.
基金Supported by the German-Israeli Foundation for Scientific Research and Development under Grant No I-1275-303.14
文摘We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 （2015）050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 （2013） 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions： （i） were the photons in A？ （ii） were the photons in B？ and （iii） were the photons in C？ the proposed experiment measures a degenerate operator answering the questions： （i） were the photons in A？ and （ii） were the photons in B and C together？ A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre- and post-selected photon, but this evidence will be in agreement with the results of Danan et al.
基金Supported by the National Key R&D Program of China under Grant Nos 2017YFA0303800 and 2017YFA0303700the National Natural Science Foundation of China under Grant Nos 11534006,11774183 and 11674184+1 种基金the Natural Science Foundation of Tianjin under Grant No 16JCZDJC31300the Collaborative Innovation Center of Extreme Optics
文摘We present a two-photon interference experiment in a modified Mach-Zehnder （MZ） interferometer in which two Hong-Ou-Mandel effects occur in tandem and construct superposed two-photon states. The signal photons pass both the arms of the MZ interferometer while the idler photons pass one arm only. Interestingly, the probability of the idler photons emerging from any output port still shows a sine oscillation with the two-photon phase difference and it can be characterized only by the indistinguishability of the two-photon amplitudes. We also observe a two-photon interference pattern with a period being equal to the wavelength of the parametric photons instead of the two-photon photonie de Broglie wavelength due to the presence of two-photon phase difference, in particular, with complementary probabilities of finding the two-photon pairs in two output ports. The abundant observations can facilitate a more comprehensive understanding of the two-photon interference.
基金Supported by the National Basic Research Program of China under Grant Nos 2011CB922203 and 2012CB921603the National Natural Science Foundation of China under Grant Nos 1174026 and U1330203
文摘An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer （MZI） by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI. When it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics contradicts the statement based on two-state vector formulism, ＇the photon did not enter the （inner） interferometer, the photon never left the interferometer, but it was there＇. Therefore, the statement and also the overlapping claim are incorrect.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0303700)the National Natural Science Foundation of China(Grant Nos.61632021,11627810,11690031,and 11621091)Open Funds from the State Key Laboratory of High Performance Computing of China(HPCL,National University of Defense Technology)
文摘By designing and fabricating a series of dual-interferometer coupled silicon microrings, the coupling condition of the pump, signal, and idler beams can be engineered independently and then we carried out both the continuous-wave and pulse pumped four-wave mixing experiments to verify the dependence of conversion efficiency on the coupling conditions of the four interacting beams, respectively. Under the continuous-wave pump, the four-wave mixing efficiency gets maximized when both the pump and signal/idler beams are closely operated at the critical coupling point, while for the pulse pump case, the efficiency can be enhanced greatly when the pump and converted idler beams are all overcoupled. These experiment results agree well with our theoretical calculations. Our design provides a platform for explicitly characterizing the four-wave mixing under different pumping conditions, and offers a method to optimize the four-wave mixing, which will facilitate the development of on-chip all-optical signal processing with a higher efficiency or reduced pump power.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11434011 and 11575058
文摘We study the fringe visibility and the which-path information(WPI) of a general Mach-Zehnder interferometer with an asymmetric beam splitter(BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI I_(path) are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship V^2 + I_(path)~2 ≤ 1 is found, and the conditions for equality are also presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975095)the Natural Science Foundation of Hebei Province,China(Grant No.A2022106001)Shijiazhuang University Doctoral Scientific Research Startup Fund Project(Grant No.20BS023)。
文摘We study the wave–particle duality in a general Mach–Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory.The correlations(including the classical correlation and the quantum correlation)between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach–Zehnder interferometer.It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle.The complementary relations between the fringe visibility and the correlations are also presented.
基金Project supported by the Special Foundation for Theoretical Physics Research Program of China(Grant No.11347152)the Startup Funds for Scientific Research of Civil Aviation University of China(Grant No.2012QD13X)+3 种基金the Special Funds of the National Natural Science Foundation of China(Grant No.11247006)the National Natural Science Foundation of China(Grant Nos.11075223 and 11004226)the National Basic Research Program of China(Grants Nos.2012CB821305 and 2012CB922102)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No.NCET-10-0850)
文摘We propose a method to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By manipulating the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination with NOON states. Using current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.
基金Project supported by the National Natural Science Foundation of China(Grant No.61306131)the Science Foundation of Shaanxi Provincial Department of Education,China(Grant No.14JK1682)
文摘This paper theoretically explores the effect of PM2.5 air pollution on the phase precision of a Mach-Zehnder inter- ferometer. With the increasing of PM2.5 concentration, phase precision for inputs of coherent state ＆ vacuum state and inputs of coherent state ＆ squeezed vacuum state will gradually decrease and be lower than the standard quantum limit. When the value of relative humidity is increasing, the precision of two input cases is decreasing much faster. We also find that the precision for inputs of coherent state ＆ squeezed state is better than that of coherent state ＆ vacuum state when PM2.5 concentration is lower. As PM2.5 concentration increases, the precision for inputs of coherent state ＆ squeezed state decreases faster, and then the two precisions tend to be the same while the concentration is higher.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174028)the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Crant Nos.2011JBZ013 and 2012YJS117)+1 种基金the Program for New Century Excellent Talents in University of Ministry of Education of China(Crant No.NCET-11-0564)the National Innovation Experiment Program for University Students,China(Grant Nos.1270021 and 1270037)
文摘Quantum interferometric strategy with input two-mode squeezed vacuum [Phys. Rev. Lett. 104 103602] is reexamined for both parity and S^z2 measurements. Unlike the previous scheme, we find that phase sensitivity obtained with the S^z2 measurement is minimized at phase origin, which may be useful to estimate a small phase shift at high precision. For the phase deviated from zero, the sensitivity increases more slowly than that of the parity detection.
基金Supported by the National Natural Science Foundation of China under Grant Nos U1531102,61107059,61308052 and U1331114the 111 Project to the Harbin Engineering University under Grant No B13015the Fundamental Research Funds for the Central Universities
文摘We propose a novel all fiber Mach-Zehnder interferometer（MZI） based on photonic crystal fiber（PCF） filled with liquid crystal（LC）. The interference between the core mode and the cladding modes of a PCF is utilized.To excite the cladding modes, a region is formed using fiber fusion splicer. Due to the fact that varying effective index difference between the core region and the LC-filled cladding region can cause different transmission spectra,we mainly study the MZIs with different LC-filled structures and different lengths of LC filling. The measured results demonstrate that quite clear interference spectra can be obtained. Through analysis spatial frequency spectrum and temperature spectrum of two MZIs with different LC-filled structures, we can obtain that the MZI with adjacent two LC-filled holes has clearer interference spectrum and higher temperature sensitivity. Thus we choose this MZI to measure the temperature sensitivity with different lengths of LC filling. When the length of LC filling is 2 cm, the temperature sensitivities can be enlarged to 1.59 nm/C. The interferometer shows a good temperature tunability and sensitivity, which can be a good candidate for a highly tunable optical filtering and temperature sensing applications.
