Enhanced Phase Sensitivity Research Articles

Enhancing phase sensitivity by a nonlinear-feedback-assisted interferometer

Enhancing phase sensitivity by a nonlinear-feedback-assisted interferometer

Calculation of Fringe Angle with Enhanced Phase Sensitivity and 3D Reconstruction.

In the field of fringe projection profilometry, phase sensitivity is a critical factor influencing the precision of object measurements. Traditional techniques that employ basic horizontal or vertical fringe projection often do not achieve optimal levels of phase sensitivity. The identification of the fringe angle that exhibits optimal phase sensitivity has been a significant area of research. The present study introduces a novel method for determining the optimal fringe angle, facilitating 3D reconstruction without the need for equipment adjustments. Initially, the optimal fringe is derived through mathematical analysis, and the system's position within each coordinate system is standardized, leading to the determination of the optimal fringe angle in the world coordinate system. Subsequently, an optimal fringe pattern, akin to that produced by a rotating projector, is generated based on the concept of rotation around a central point, with corresponding adjustments made to the calibration parameters. Finally, the optimal fringe is projected onto the target object for 3D reconstruction, thereby validating the proposed method. The experimental results demonstrate that this approach accurately identifies the optimal fringe angle, significantly enhancing both phase sensitivity and measurement accuracy. The accuracy of the measurement is significantly greater, by an order of magnitude, compared to the traditional method, with the error being approximately 50% of that associated with the currently established improved method.

Enhanced phase sensitivity in a feedback-assisted interferometer

The topology of feedback optical parametric amplifier (FOPA) renders a number of significant advantages over the topology of traditional optical parametric amplifier (TOPA) such as a higher degree of quantum correlation, all-phase entanglement enhancement, and the robustness of the losses. Here, we propose a feedback-assisted interferometer based on the topology of FOPA for quantum metrology. We theoretically study the phase sensitivity with the method of homodyne detection and product detection. By manipulating the feedback strength of the FOPA, the phase sensitivity can be further enhanced, and approach the quantum Cramér-Rao bound. Furthermore, we demonstrate that our proposal is superior to the SU(1,1) interferometer based on the topology of TOPA.

Unbalanced beam splitters enabling enhanced phase sensitivity of a Mach-Zehnder interferometer using coherent and squeezed vacuum states

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.

Enhanced phase sensitivity in a Mach-Zehnder interferometer via photon recycling.

We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of ∼9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramér-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift ϕ while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling.

Can a terahertz metamaterial sensor be improved by ultra-strong coupling with a high-Q photonic resonator?

When a metamaterial (MM) is embedded in a one-dimensional photonic crystal (PC) cavity, the ultra-strong coupling between the MM plasmons and the photons in the PC cavity gives rise to two new polariton modes with high quality factor. Here, we investigate by simulations whether such a strongly coupled system working in the terahertz (THz) frequency range has the potential to be a better sensor than a MM (or a PC cavity) alone. Somewhat surprisingly, one finds that the shift of the resonance frequency induced by an analyte applied to the MM is smaller in the case of the dual resonator (MM and cavity) than that obtained with the MM alone. However, the phase sensitivity of the dual resonator can be larger than that of the MM alone. With the dielectric perturbation theory - well established in the microwave community - one can show that the size of the mode volume plays a decisive role for the obtainable frequency shift. The larger frequency shift of the MM alone is explained by its smaller mode volume as compared with the MM-loaded cavity. Two main conclusions can be drawn from our investigations. First, that the dielectric perturbation theory can be used to guide and optimize the designs of MM-based sensors. And second, that the enhanced phase sensitivity of the dual resonator may open a new route for the realization of improved THz sensors.

Sensitivity enhanced fiber optic hydrophone based on an extrinsic Fabry-Perot interferometer for low-frequency underwater acoustic sensing.

A miniaturized fiber optic hydrophone (FOH) based on a composite metal diaphragm with an air back cavity and a high finesse extrinsic Fabry-Perot interferometric (EFPI) scheme for low-frequency underwater acoustic sensing is proposed and experimentally demonstrated in this paper. A composite metal diaphragm is used to improve the stability of the hydrophone. A balance channel is used to equilibrate the hydrostatic pressure and maintain an air cavity, which improves the mechanical sensitivity. In addition, a white light interferometry (WLI) phase demodulation is used to demodulate the high finesse interferometer consisted of the fiber collimator end face and the diaphragm, which improves the phase sensitivity. Experimental results show that the enhanced phase sensitivity of the hydrophone is about -122.5 dB re 1 rad/µPa @ 200 Hz and the sensitivity fluctuation is below 2.5 dB between 3 Hz and 400 Hz, while the minimal detectable pressure (MDP) is 63.7 µPa/Hz1/2 @ 400 Hz. Due to its miniaturized structure and high sensitivity, the FOH may have an enormous potential in underwater target detection.

Quantum Enhanced Phase Sensitivity with Bright Entangled Twin and Coherent Beams Based on the Mach-Zehnder Interferometer

Quantum Enhanced Phase Sensitivity with Bright Entangled Twin and Coherent Beams Based on the Mach-Zehnder Interferometer

A Switchable Biomimetic Antenna Array

Biomimetic antenna arrays inspired by the fly Ormia ochracea showed a promising improvement of the angle estimation capabilities of radar sensors. So far, there is usually a loss of output power associated with this improvement decreasing the detectability of weak radar targets. In this paper, an electronically switchable two-element biomimetic antenna array is presented for the first time. This array provides the possibility to switch between a biomimetic antenna mode with enhanced phase sensitivity and a conventional antenna mode with better SNR. Circuit requirements are discussed, the design process is described, and a realization in the 77-GHz range using PIN diodes as switching elements is presented. Radar measurements verify the concept. By switching, the phase sensitivity of the realized array can be enhanced by a factor of 3 with a relative power loss of maximum 14 dB.

Enhanced phase sensitivity with a nonconventional interferometer and nonlinear phase shifter

We propose a theoretical scheme of an enhanced phase sensitivity by introducing a nonlinear phase shifter to the nonconventional interferometer consisting of a balanced beam splitter (BBS) and an optical parameter amplifier (OPA), a modified nonlinear interferometer (MNI). Then we use coherent state and even coherent state as inputs and homodyne detection at one output port of the MNI for phase sensitivity, both without and with photon losses. We find that the nonlinear phase shifter can not only improve phase sensitivity, but also significantly resist the decoherence from photon losses. In comparison to both the BBS+OPA scheme with linear phase shifter and the traditional Mach–Zehnder interferometer with nonlinear one, the phase sensitivity of the MNI scheme shows the best performance. It is interesting that the nonlinear phase shifter can stimulate potential of the OPA, although there is no improvement in signal-to-noise ratio beyond standard quantum limit for the BBS+OPA scheme with a linear phase shifter.

Enhancing Phase Sensitivity in Mach–Zehnder Interferometers for Arbitrary Input StatesSupported by the National Natural Science Foundation of China (Grant Nos. 11875231 and 11935012), the National Key Research and Development Program of China (Grant Nos. 2017YFA0304202 and 2017YFA0205700), and the Fundamental Research Funds for the Central Universities (Grant No. 2018FZA3005).

To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.

Enhancing phase sensitivity with number state filtered coherent states

Number state filtered coherent states are a class of nonclassical states obtained by removing one or more number states from a coherent state. Phase sensitivity of an interferometer is enhanced if these nonclassical states are used as input states. The optimal phase sensitivity, which is related to the quantum Cramer-Rao bound (QCRB) for the input state, improves beyond the standard quantum limit. It is argued that removal of more than one suitable number state leads to better phase sensitivity. As an important limiting case in this context, the even and odd coherent states, where the odd and even number states are filtered from coherent state respectively, are considered. The optimal phase sensitivity for these limiting cases equals that of the squeezed vacuum. It is observed that the improvement in phase sensitivity is not in direct proportion to the nonclassicality of the input states.

A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry.

The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F = 1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of |F = 1, m = ±1〉 atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1%.

Design principles for enhancing phase sensitivity and suppressing phase fluctuations simultaneously in biochemical oscillatory systems

Biological systems need to function accurately in the presence of strong noise and at the same time respond sensitively to subtle external cues. Here we study design principles in biochemical oscillatory circuits to achieve these two seemingly incompatible goals. We show that energy dissipation can enhance phase sensitivity linearly by driving the phase-amplitude coupling and increase timing accuracy by suppressing phase diffusion. Two general design principles in the key underlying reaction loop formed by two antiparallel pathways are found to optimize oscillation performance with a given energy budget: balancing the forward-to-backward flux ratio between the two pathways to reduce phase diffusion and maximizing the net flux of the phase-advancing pathway relative to that of the phase-retreating pathway to enhance phase sensitivity. Experimental evidences consistent with these design principles are found in the circadian clock of cyanobacteria. Future experiments to test the predicted dependence of phase sensitivity on energy dissipation are proposed.

Terahertz artificial material based on integrated metal-rod-array for phase sensitive fluid detection.

A terahertz artificial material composed of metal rod array is experimentally investigated on its transmission spectral property and successfully incorporated into microfluidics as a miniaturized terahertz waveguide with an extended optical-path-length for label-free fluidic sensing. Theoretical and experimental characterizations of terahertz transmission spectra show that the wave guidance along the metal rod array originates from the resonance of transverse-electric-polarized waves within the metal rod slits. The extended optical path length along three layers of metal-rod-array enables terahertz waves sufficiently overlapping the fluid molecules embedded among the rods, leading to strongly enhanced phase change by approximately one order of magnitude compared with the blank metal-parallel-plate waveguide. Based on the enhanced phase sensitivity, three kinds of colorless liquid analytes, namely, acetone, methanol, and ethanol, with different dipole moments are identified in situ using the metal-rod-array-based microfluidic sensor. The detection limit in molecular amounts of a liquid analyte is experimentally demonstrated to be less than 0.1 mmol, corresponding to 2.7 μmol/mm2. The phase sensitive terahertz metal-rod-array-based sensor potentially has good adaptability in lab-chip technology for various practical applications, such as industrial toxic fluid detection and medical breath inspection.

Enhanced Phase Sensitivity in Plasmonic Refractive Index Sensor Based on Slow Light

Fano spectrum exhibits an intriguing feature of narrow asymmetrical resonance profile, which can be used in designing an ultra sensitive refractive index sensor. Here, in this letter, an ultra compact surface plasmon sensor is investigated. The sensor is based on Metal-Dielectric-Metal (MDM) waveguide geometry and connected to a pair of stub resonators. The distance between resonators is adjusted in such a manner that their increased coupling leads to an asymmetrical profile resonance, which is known as Fano resonance. The Fano resonance is very sensitive to any change in refractive index of the material. To measure the sensitivity of the device, stubs are filled with liquid/gaseous material under test. The structure is numerically simulated by the Finite difference time-domain method and the value of sensitivity is obtained as high as S = 510 nm/refractive index unit with a narrow line width of 19 nm and large quality factor Q ≈ 80. Fano resonance is generally accompanied with sharp dispersion, which leads to the generation of slow light. To account an effect of slow light in the waveguide phase, sensitivity is also analyzed as a function of a group delay. The large value of phase sensitivity is reported, which is equal to S O = 41.9 rad for per unit change in refractive index unit. The phase sensitivity rises linearly with the increasing value of group delay or decreasing value of group velocity. Thus, the device is well suited for designing on-chip optical sensors, optical buffers, switches, modulators, and so on.

Loss-tolerant state engineering for quantum-enhanced metrology via the reverse Hong-Ou-Mandel effect.

Highly entangled quantum states, shared by remote parties, are vital for quantum communications and metrology. Particularly promising are the N00N states—entangled N-photon wavepackets delocalized between two different locations—which outperform coherent states in measurement sensitivity. However, these states are notoriously vulnerable to losses, making them difficult to both share them between remote locations and recombine in order to exploit interference effects. Here we address this challenge by utilizing the reverse Hong–Ou–Mandel effect to prepare a high-fidelity two-photon N00N state shared between two parties connected by a lossy optical medium. We measure the prepared state by two-mode homodyne tomography, thereby demonstrating that the enhanced phase sensitivity can be exploited without recombining the two parts of the N00N state. Finally, we demonstrate the application of our method to remotely prepare superpositions of coherent states, known as Schrödinger's cat states.

Enhanced phase sensitivity of an SU(1,1) interferometer with displaced squeezed vacuum light

We study the phase sensitivity of an SU(1,1) interferometer with two input beams in the displaced squeezed vacuum state and the coherent state, respectively. We find that there exists an optimal squeezing fraction of the displaced squeezed vacuum state that optimizes the phase sensitivity. We also examine the effects of some factors, including the loss, mean photon number of the input beams and amplitude gain of the optical parameter amplifiers, on the optimal squeezing fraction so that we can choose the optimal values to enhance the phase sensitivity.

Enhanced phase sensitivity of metamaterial absorbers near the point of darkness

Plasmonic resonances are accompanied by abrupt phase changes. Utilization of this phase signal and lower phase noises can improve the refractive index resolution of plasmonic sensors. It is shown that the maximal phase change in the frequency domain is achieved at the point of the minimal reflection—the point of darkness. Since the metamaterial absorbers have near zero reflection at their resonance by definition, their phase can be used for sensing purpose. Considered metamaterial absorbers consist of parallel gold strips separated by a dielectric spacer from a thick metallic plate. By the optimization of the spacer thickness and strip widths, and by the adjustment of the angle of incidence, the phase sensitivity above 104 deg/RIU can be achieved in the dynamic range of 2×10−2 RIU.

Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination

We developed an off-axis quantitative phase microscopy that works for a light source with an extremely short spatial coherence length in order to reduce the diffraction noise and enhance the spatial resolution. A dynamic speckle wave whose coherence length is 440 nm was used as an illumination source. To implement an off-axis interferometry for a source of low spatial coherence, a diffraction grating was inserted in the reference beam path. In doing so, an oblique illumination was generated without rotation of the wavefront, which leads to a full-field and single-shot phase recording with improved phase sensitivity of more than a factor of 10 in comparison with coherent illumination. The spatial resolution, both laterally and axially, and the depth selectivity are significantly enhanced due to the wide angular spectrum of the speckle wave. We applied our method to image the dynamics of small intracellular particles in live biological cells. With enhanced phase sensitivity and speed, the proposed method will serve as a useful tool to study the dynamics of biological specimens.