Time-Modulated Hamiltonian for Interpreting Delayed-Choice Experiments via Mach-Zehnder Interferometers

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.

Simulation of distributed optical fiber disturbance detection system based on Sagnac/Mach-Zehnder interferometer and cross-correlation location

A distributed optical fiber disturbance detection system consisted of a Sagnac interferometer and a Mach-Zehnder interferometer is demonstrated. Two interferometers outputs are connected to an electric band-pass filter via a detector respectively. The central frequencies of the two filters are selected adaptively according to the disturbance frequency. The disturbance frequency is obtained by either frequency spectrum of the two interferometers outputs. An alarm is given out only when the Sagnac interferometer output is changed. A disturbance position is determined by calculating a time difference with a cross-correlation method between the filter output connected to the Sagnac interferometer and derivative of the filter output connected to the Mach-Zehnder interferometer. The frequency spectrum, derivative and cross-correlation are obtained by a signal processing system. Theory analysis and simulation results are presented. They show that the system structure and location method are effective, accurate, and immune to environmental variations.

In-Fiber Mach-Zehnder Interferometer Based on Waist-Enlarged Taper and Core-Mismatching for Strain Sensing

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.

Temperature-induced effect on refractive index of graphene based on coated in-fiber Mach-Zehnder interferometer

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.

An Improved Experiment to Determine the‘Past of a Particle’in the Nested Mach-Zehnder Interferometer

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.

Compact temperature-insensitive modulator based on a silicon microring assistant Mach-Zehnder interferometer

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.

An Ideal Experiment to Determine the ’Past of a Particle’ in the Nested Mach-Zehnder Interferometer

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.

Two-Photon Interference Constructed by Two Hong–Ou–Mandel Effects in One Mach-Zehnder Interferometer

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.

Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30°Leading Edge Using a Mach-Zehnder Interferometer

This study focuses on the experimental measurements of the heat transfer coefficient over a flat plate with a 30° leading edge. Under forced convection by a hot/cold air and flow over a cooled/heated flat plate, the thermal boundary layer and its thickness are quantitatively visualized and measured using a Mach-Zehnder interferometer. In addition, the variation in the local heat transfer coefficient is evaluated experimentally with respect to the air flow velocity and temperature. Differences within the heat transfer performance between the plates are confirmed and discussed. As a result, the average heat transfer performance is about the same for the heated plate and the cooled plate under all air velocity conditions. This contrasts with the theoretical prediction in the case of low air velocity, the reason considered was that the buoyancy at the 30° leading edge blocked air from flowing across the surface of the plate.

Theoretical Analysis and Experiment of Temperature Stability for Fiber-optic Mach-Zehnder Interferometer Filter

Fiber optic Mach Zehnder interferometer(MZI) can be used as wavelength multiplexers and demultiplexers. The △ L and △ directly influence the properties of MZI. To lengthen the △ L can demultiplex much more wavelengths, but when the △ L is longer, the temperature will influence MZI more seriously. A method to solve this problem is proposed, which enables MZI to work stably. The wavelength distance is 0.8 nm, and the extinction ratio is high.

Reflective Ladder Topology Network Based on White Light Fiber-Optic Mach-Zehnder Interferometer

In order to improve the multiplexing capability of the optical sensors based on the lower interferential optic fiber sensing technology and the white light fiber-optic Mach-Zehnder interferometer,reflective ladder topology network ( RLT) with tailored formula was proposed. The topology network consists of 6 rungs sensing elements linked by 5 couplers. Two cases with different choices of couplers were contrasted: one is equal coupling ratio,and the other is tailored coupling ratio. Through the simulation of these two cases,the detailed multiplexing capability was analyzed,and accordingly the experiments were also carried out. The simulation results showed that,the tailored formula enhances the multiplexing capability of the structure. In the first case, the maximum number of sensors which can be multiplexed is 8,and in the other case is 12 fiber optic sensors. The experimental results have a good agreement with numerical simulation results. Thus,it is considered expedient to incorporate RLT into large-scale building,grounds,bridges,dams,tunnels,highways and perimeter security.

A New Mach-Zehnder Interferometer to Measure Light Beam Dispersion and Phase Shift

A novel Mach–Zehnder(M-Z)interferometer used to measure the dispersion and phase shift of a light beam is reported.The interferometer consists of two identical beam displacing polarizers,which makes two beams of interference light pass through the same optical device and greatly improves the stability of the M-Z interferometer.The basic method of dispersion and phase measuring through the present interferometer is introduced in detail,and the actual application is demonstrated by a specific example.Because the measuring of dispersion and phase shift is the heating point in the field of optics,it is obvious that the M-Z interferometer will have important applications in aspects of optics,especially quantum optics and optical information processing.

Mach-Zehnder Interferometers with Asymmetric Modulation Arms in Applications of High Speed Silicon-on-Insulator Based Optical Switches

有不同宽度的调整手臂被介绍给 Mach-Zehnderinterferometers (MZI ) 获得改进性能。理论分析和数字模拟看了那二只手臂的宽度什么时候适当地被设计完成固有的 m pi/2 (m 是一个奇怪的整数) 手臂之间的光阶段差别，不对称的 MZI 介绍更高的调整速度。而且，搬运人吸收导致了基于的插入损失 insilicon-on-insulator (SOI ) 的分叉 MZI 光开关能显然被改进。

A novel 2×2 wavelength selective cross-connect based on Mach-Zehnder interferometer

A novel 2×2 wavelength selective cross-connect (WSXC) module, which is composed of a Bragg-grating-based Mach- Zehnder interferometer (MZI), a pair of optical waveguides, a pair of 1×2 optical switches (OSWs) and a pair of Y-model combiners is proposed. The mathematical description of the proposed 2×2 WSXC module is given and explained. Multi- channel multi-wavelength selective cross-connect can be fabricated with the proposed 2×2 WSXC module, together with multistage interconnection networks (MINs). A four-wavelength 4×4 WSXC is demonstrated by simulation to validate the flexibility of the proposed WSXC.

Strain and Temperature Discrimination Based on a Mach-Zehnder Interferometer With Cascaded Single Mode Fibers

An in-fiber Mach-Zehnder interferometer is proposed for the discrimination of strain and temperature.The sensor is based on two cascaded standard single mode fibers using three peanut tapers fabricated by simple splicing.The cascaded structure excites more frequency components,which induce four sets of interference dips in the transmission spectrum.One set of the spectrum dips have different sensitivities to temperature and strain from those of the other three.The sensor can discriminate strain and temperature by monitoring the wavelength shifts of two spectrum dips.Repeated experiments are taken both for strain and temperature increasing and decreasing scenarios.Experimental results show that Dip 1 has an average strain sensitivity of-0.911 pm/με and an average temperature sensitivity of 49.98pm/℃.The strain sensitivity for Dip 2 is negligible and its average temperature sensitivity is 60.52pm/℃.The strain and temperature resolutions are±3.82με and±0.33℃.

Accurate measurement of aerosol optical properties using the multilongitudinal mode high-spectral-resolution lidar with self-tuning Mach-Zehnder interferometer

The multilongitudinal mode[MLM]high-spectral-resolution lidar[HSRL]based on the Mach±Zehnder interferometer[MZI]is constructed in Xi’an for accurate measurements of aerosol optical properties.The critical requirement of the optimal match between the free spectral range of MZI and the longitudinal mode interval of the MLM laser is influenced by the laboratory temperature,pressure,and vibration.To realize the optimal separation of aerosol Mie scattering signals and molecular Rayleigh scattering signals excited by the MLM laser,a self-tuning technique to dynamically adjust the optical path difference[OPD]of the MZI is proposed,which utilizes the maximum ratio between the received power of the Mie channel and Rayleigh channel as the criterion of the OPD displacement.The preliminary experiments show the feasibility of the MLM-HSRL with self-tuning MZI and the stable performance in the separation of aerosol Mie scattering signals and molecular Rayleigh scattering signals.

Properties of sandwich-structure based Mach-Zehnder interferometer cascaded with FBG response to dual-parameter sensing

An all-fiber temperature and curvature sensor based on Mach-Zehnder interferometer(MZI)was proposed.The MZI was a sandwich structure which is composed of ring-core fiber(RCF),no-core fiber(NCF)and single-mode fiber(SMF).The temperature and curvature can be demodulated by the wavelength shift and the intensity variation of the dips respectively in the transmission spectrum.The measurement results show that the sensitivity of curvature is−7.88 dBm/m^(−1)in the range from 3.0 m^(−1)to 4.2 m^(−1)and the sensitivity of temperature is 53.5 pm/°C in the range from 60°C to 200°C.In addition,the cascaded FBG in the proposed structure,also sensitive to temperature,was used to monitor the fluctuation of temperature.The compact structure,the real-time temperature and the high curvature sensitivity make the sensor have the potential in the field of construction health monitoring and mining safety production.

Wavelength-tunable mode-locked fiber laser based on an all-fiber Mach-Zehnder interferometer filter

Wavelength-tunable dissipative solitons and amplifier similaritons have been obtained by inserting all-fiber Mach-Zehnder interferometer(MZI) filters with different free spectral ranges(FSRs) in a Yb-doped mode-locked fiber laser.The MZI filter is fabricated by splicing one segment of seven-core fiber(SCF) between two segments of single-mode fibers.The bandwidth of the filter depends on the FSR of the modulated interference curve and consequently depends on the tapered fiber diameter.Inserting MZI filters with bandwidths in a fiber laser and applying a tensile strain on the tapered SCF,both wavelengthtunable dissipative solitons and amplifier similaritons have been obtained.

Simultaneous Curvature and Temperature Sensing Based on a Novel Mach-Zehnder Interferometer

A novel fiber inline Mach-Zehnder interferometer(MZI)is proposed for simultaneous measurement of curvature and temperature.The sensor composes of single mode-multimode-dispersion compensation-multimode-single mode fiber(MMF-DCF-MMF)structure,using the direct fusion technology.The experimental results show curvature sensitivities of−12.82 nm/m^(−1) and−14.42 nm/m^(−1) in the range of 0−0.65 m^(−1) for two resonant dips,as well as temperature sensitivities of 57.6 pm/and 74.3℃pm/within the range of 20℃℃−150.In addition,℃the sensor has unique advantages of easy fabrication,low cost,high fringe visibility of 24 dB,and high sensitivity,which shows a good application prospect in dual-parameters of sensing of curvature and temperature.