Two-mode Interferometer Research Articles

Highly sensitive liquid refractive index sensor based on a polymer two-mode ridge waveguide interferometer

In this paper, we propose and experimentally demonstrate a highly sensitive liquid refractive index (RI) sensor based on a two-mode interferometer (TMI) formed with a polymer ridge waveguide. Compared with the rectangular waveguide TMI sensor, our proposed ridge waveguide TMI sensor enables a higher waveguide sensitivity and hence device sensitivity. Our experimental results show that the fabricated ridge waveguide TMI sensor achieves a sensitivity of 6980.62 nm/RIU, indicating a significant improvement over the fabricated rectangular waveguide TMI sensor with almost identical dimensions; the latter exhibits a sensitivity of 3753.81 nm/RIU. Our proposed sensor is simple in structure but has high sensitivity and low cost.

Thermodynamic sensing of quantum nonlinear noise correlations

Abstract We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity (WC) or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the WC of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields.

Large-Momentum-Transfer Atom Interferometers with μrad-Accuracy Using Bragg Diffraction.

Large-momentum-transfer (LMT) atom interferometers using elastic Bragg scattering on light waves are among the most precise quantum sensors to date. To advance their accuracy from the mrad to the μrad regime, it is necessary to understand the rich phenomenology of the Bragg interferometer, which differs significantly from that of a standard two-mode interferometer. We develop an analytic model for the interferometer signal and demonstrate its accuracy using comprehensive numerical simulations. Our analytic treatment allows the determination of the atomic projection noise limit of a LMT Bragg interferometer and provides the means to saturate this limit. It affords accurate knowledge of the systematic phase errors as well as their suppression by 2 orders of magnitude down to a few μrad using appropriate light-pulse parameters.

Robust phase metrology with hybrid quantum interferometers against particle losses

Entanglement is an important quantum resource to achieve high sensitive quantum metrology. However, the rapid decoherence of quantum entangled states, due to the unavoidable environment noise, result in practically the unwanted sharp drop of the measurement sensitivity. To overcome such a difficulty, here we propose a spin-oscillator hybrid quantum interferometer to achieve the desirable precise estimation of the parameter encoded in the vibrations of the oscillator. Differing from the conventional two-mode quantum interferometers input by the two-mode NOON state or entangled coherent states (ECS), whose achievable sensitivities are strongly limited by the decoherence of the entangled vibrational states, we demonstrate that the present interferometer, input by a spin-dependent two-mode entangled state, possesses a manifest advantage, i.e., the measurement sensitivity of the estimated parameter is not influenced by the decoherence from the spin-oscillator entanglement. This is because that, by applying a spin-oscillator disentangled operation, the information of the estimated parameter encoded originally in the vibrational degrees can be effectively transferred into the spin degree and then can be sensitively estimated by the precise spin-state population measurements. As consequence, the proposed hybrid quantum interferometer possesses a manifest robustness against the particle losses of the vibrational modes. Interestingly, the achieved phase measurement sensitivity can still surpass the SQL obviously, even if relatively large number of particle loss occurs in one of the two modes. The potential application of the proposed spin-oscillator hybrid quantum interferometer is also discussed.

Generating two-mode squeezing with multimode measurement-induced nonlinearity

Measurement-induced nonclassical effects in a two-mode interferometer are investigated theoretically using numerical simulations and analytical results. We demonstrate that for certain parameters measurements within the interferometer lead to the occurrence of two-mode squeezing. The results strongly depend on the detection probability, the phase inside the interferometer, and the choice of the input states. The appropriate parameters for maximized squeezing are obtained. We analyze the influence of losses and confirm that the predicted effects are within reach of current experimental techniques.

Criticality in two-mode interferometers

To achieve the optimal phase sensitivity in two-mode interferometers, one key problem is how to distribute photons between the two input ports, given a fixed total average photon number. In both the $\text{SU}(2)$ and $\text{SU}(1,1)$ interferometers with a product of coherent and Fock states as inputs, we find there exists a critical value of the total photon number, below which the optimal phase sensitivity can be achieved with the second port being the vacuum state. The critical points can be analytically fixed. We further consider a more general input state as a product of coherent and squeezed Fock states. Then we analytically identify three regions in the parameter space, similar to a phase diagram, and find that critical phenomena occur in two regions. If the total average input photon number is less than the critical value, the optimal distribution tends to minimize the average photon number in the second port. Our finding indicates that, in order to get interferometers with high sensitivity, one must carefully choose the photon number distribution according to the value of the input total average photon number. This central result will be useful in theoretical studies in the field of quantum parameter estimation.

Stable multiwavelength semiconductor optical amplifier‐based fiber laser using a 2‐mode interferometer

AbstractA multiwavelength semiconductor optical amplifier (SOA) fiber laser based on all‐fiber two‐mode interferometer (TMI) structure is demonstrated. The TMI generates in a comb‐like spectrum with a 1‐nm wavelength spacing and extinction ratio of 5.7 dB. By incorporating a TMI in the laser cavity, stable multiwavelength operation is obtained with 30 output channels from 1570.8 to 1600.8 nm with peak powers of at least 10 dB from the highest peak. The output comb spectrum and the overall stability of the multiwavelength are also enhanced with by inducing the four‐wave‐mixing effect in the cavity. The multiwavelength SOA fiber laser shows high operational stability with peak power fluctuations exceeding 1 dB observed only at the 1st, 23rd, 26th, and 30th peaks, which are at the ends of the multiwavelength spectrum.

Heisenberg-limited single-mode quantum metrology in a superconducting circuit

Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form left( {left| 0 rightrangle + left| N rightrangle } right)/sqrt 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.

Efficient two-mode interferometers with spinor Bose-Einstein condensates

We consider general three-mode interferometers using a spin-1 atomic Bose-Einstein condensate with macroscopic magnetization. We show that these interferometers, combined with the measurement of the number of particles in each output port, provide an ultrahigh phase sensitivity. We construct effective two-mode interferometers which involve two Zeeman modes showing that they also provide an ultrahigh phase sensitivity but of a bit reduced factor in the corresponding Fisher information. A special case of zero magnetization is shown to persist the efficiency of the two-mode interferometry.

Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

Phase-sensitivity bounds for two-mode interferometers

We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of state with different total number of particles, particle entanglement is necessary but not sufficient to overcome the shot noise limit. The highest possible phase estimation sensitivity, the Heisenberg limit, is established under general unbiased properties of the estimator. When coherences can be created, manipulated and detected, a phase sensitivity bound can only be set in the central limit, with a sufficiently large repetition of the interferometric measurement.

Ultrasensitive Two-Mode Interferometry with Single-Mode Number Squeezing

A major challenge of the phase estimation problem is the engineering of high-intensity entangled probe states. The goal is to significantly enhance above the shot-noise limit the sensitivity of two-mode interferometers. Here we show that this can be achieved by squeezing in input, and then measuring in output, the population fluctuations of a single mode. The second input mode can be left as an arbitrary nonvacuum (e.g., a bright coherent) state. This two-mode state belongs to a novel class of particle-entangled states which are not spin squeezed. Already a 2.4db gain above shot noise can be obtained when just a single-particle Fock state is injected into the empty input port of a classical interferometer configuration. Higher gains, up to the Heisenberg limit, can be reached with squeezed states of a larger number of particles. We finally study the robustness of this protocol with respect to detection noise.

Fisher information and multiparticle entanglement

The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\overline{F}$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\overline{F}$ is able to detect certain bound entangled states.

Silicon Oxynitride Optical Waveguide Ring Resonator Utilizing a Two-Mode Interferometer Structure

Silicon oxynitride (SiOxNy, SiON) optical waveguide ring resonator, in which a two-mode interferometer is used to replace the directional coupler in a conventional ring resonator, has been designed and fabricated. Preliminary results exhibit the same of free spectral range of 100 GHz but different quality factors of 3700 and 3900 at 1550 nm for transverse electric (TE) and transverse magnetic (TM) mode, respectively. The extinction ratio is more than 18 dB over the entire C-band, and the insertion loss is lower than 9.5 dB for TE and TM mode.

Not all pure entangled states are useful for sub-shot-noise interferometry

We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.

An accurate analysis for two-mode interferometer based Mach–Zehnder interferometers interleaver

By using a more accurate analysis, we investigate the effect of the mode coupling and radiation loss of a two-mode interferometer (TMI) which is employed in the design of Mach–Zehnder interferometer interleaver by considering different branching angles and index contrasts. Based on our study, we find that the transmission characteristics of a TMI in the interleaver design cannot always be treated as a simple zero gap directional coupler (DC), called pure model. Under certain conditions, its characteristics should be treated as a zero gap DC combined with two variable gap DCs, and correspondently called integrated model. The conditions under which a TMI is treated as pure model or integrated model are defined in terms of branching angle and index contrast. Our findings are confirmed with the experimental results.

Modeling and Compensation of Periodic Nonlinearity in Two-mode Interferometer Using Neural Networks

The periodic nonlinearity in nano-metrology systems based on heterodyne interferometers is the most important limitation to the accuracy of displacement measurement. It is mainly produced due to the polarization-mixing and frequency-mixing. In this paper, a new approach based on an ensemble of neural networks for modeling and compensation of nonlinearity in a high-resolution laser heterodyne interferometer is presented. We model the periodic nonlinearity arising from elliptical polarization and non-orthogonality of the laser polarized light based on the neural network approaches, including the multi-layer perceptrons and radial basis function as single neural networks and stacked generalization method as ensemble of neural networks. It is also shown that by using the stacked generalization method, the primary periodic nonlinearity of 1.3 nm is significantly compensated by a factor of 168.

Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system

The effects of periodic nonlinearity, intermodulation distortion, phase detection uncertainty and electrical cross-talk in a three-longitudinal-mode laser heterodyne Doppler interferometer (TLMI) displacement measurement system are presented. A frequency-path model consisting of three frequency components and two paths is also designed. As a result, there will be six frequency-path elements and 21 distinct interference terms. The periodic nonlinearity in the TLMI is mathematically modelled and simulated. Simulation results are compared with the typical two-mode heterodyne interferometer to confirm the designed model performance. The authors demonstrate that the nonlinearity of TLMI can be greatly reduced using the same compensation method as used in a two-frequency interferometer proposed by Hou et al.

A novel two-mode fiber-optic interferometer based on HE11–TE01 modal interference utilizing a liquid-crystal-clad fiber modal filter

A novel scheme of two-mode fiber-optic interferometer based on interference between HE11 and TE01 modes of a circular symmetric fiber is reported. This interferometer exploits a modal filter made of a piece of liquid-crystal-clad fiber, to select one of the second-order modes TE01 and filter the other TM01 and HE21 modes. Thus, two spatial modes, fundamental mode HE11 and second-order mode TE01, serve as the two arms of the interferometer to exhibit their phase modulation produced within a sensing region, on the output intensity pattern. A polarizer (analyzer) is employed at the output end of the fiber to achieve a two-lobe radiation pattern. Theoretical and experimental studies on the operating characteristics of such a two-mode fiber-optic interferometer are presented. The variation of the two-lobe pattern has a predictable dependence on the phase retardation between the two modes and can easily obtain an optimized visibility by rotating the polarizer (analyzer). The application of this interferometer for temperature sensing between 20 and 100°C is demonstrated. The measurement results show a phase shift sensitivity of 0.9rad/m°C, comparable to that of the existing two-mode fiber interferometer using an elliptical-core fiber.

Optimizing PCFs for two-mode interference

Three criterions are presented for optical fibers to construct two-mode fiber interferometers. Polarization maintaining two-mode photonic crystal fiber (PMTMPCF) is preferred because it can be designed and fabricated to satisfy the criterions. A 3-step process is proposed for designing a PMTMPCF. An optimized PCF and its two-mode interference properties are reported.