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Vortex dynamics and applications to gaseous optical elements

Dmitri Kaganovich, B. Hafizi, Luke Johnson, and Daniel Gordon

DOI: 10.1364/JOSAB.391979 Received 04 Mar 2020; Accepted 28 May 2020; Posted 28 May 2020  View: PDF

Abstract: Experimental studies of the optical properties of compressible, viscous and rapidly-rotating gas flows (vortices) are presented. Gas vortices can function as optical elements such as lenses or waveguides. The optical properties are determined from direct interferometric phase measurements and beam propagation analysis. Output beams are analyzed in terms of Zernike polynomials for a range of gas flow parameters, including choked flow. The absolute radial gas density distribution is measured and a technique for adjusting it is demonstrated.

Goos-Hänchen shift produced by the one-dimensional photonic crystal doped with InSb

Mingyu Mao, Tao Zhang, Sijia Guo, and HaiFeng Zhang

DOI: 10.1364/JOSAB.393392 Received 23 Mar 2020; Accepted 28 May 2020; Posted 29 May 2020  View: PDF

Abstract: In this paper, a novel kind of one-dimensional (1-D) photonic crystals ( PCs) doped with the indium antimonide (InSb) is proposed, which is theoretically investigated by the transfer matrix method to create a giant lateral shift that is also called Goos-Hänchen (GH) shift. The transmittance features of the proposed PCs are ascribed to the temperature. The influences of the incident angle on the transmittance of TE and TM waves have also been studied in the theory. And for TE wave, the transmittance is also affected by magnetic field strength, due to the characteristics of the permittivity of InSb layers. Therefore, for TE wave, such PCs not only can generate huge positive and negative GH displacements but also can produce some regular changes under the effects of temperature and external magnetic field. The calculated results demonstrate that the normalized positive GH shift can reach around 55 times of the wavelength, and the normalized negative one can get to around 182 times of the wavelength. This 1-D PCs may provide a theoretical possibility for some devices that detect changes in temperature or magnetic field strength.

Parity-based, bias-free optical quantum random number generation with min-entropy estimation

Mathew Coleman, Kaylin Ingalls, John Kavulich, Sawyer Kemmerly, Nicolas Salinas, Efrain Venegas Ramirez, and Maximilian Schlosshauer

DOI: 10.1364/JOSAB.392286 Received 06 Mar 2020; Accepted 27 May 2020; Posted 28 May 2020  View: PDF

Abstract: We describe the generation of sequences of random bits from the parity of photon counts produced by polarization measurements on a polarization-entangled state. The resulting sequences are bias-free, pass the applicable tests in the NIST battery of statistical randomness tests, and are shown to be Borel normal, without the need for experimental calibration stages or postprocessing of the output. Because the photon counts are produced in the course of a measurement of the violation of the CHSH inequality, we are able to concurrently verify the nonclassical nature of the photon statistics and estimate a lower bound on the min-entropy of the bit-generating source. The rate of bit production in our experiment is around 13 bits/s.

Light interference in a hybrid aligned nematic layer with the non-ordered surface disclination lines

Alexander Parshin, Alexey Barannik, Victor Zyryanov, and Vasiliy Shabanov

DOI: 10.1364/JOSAB.395976 Received 22 Apr 2020; Accepted 26 May 2020; Posted 27 May 2020  View: PDF

Abstract: The propagation of a laser beam through a hybrid aligned nematic layer with the surface disclination line has been investigated. The model of the light interference has been developed to take into account the scattering by the structural inhomogeneities. The analytical expression that includes the factor characterizing an exponential decrease in the light scattering has been obtained. The dependence of the intensity of light transmitted through the layer on the magnetic field has been measured. The dependence has been accompanied by the interference oscillations. The theoretical expression is consistent with the experiment, that confirm the correctness of the model concepts.

Liquid crystal module for motionless generation of variable structured illumination

Loïc Tabourin and Tigran Galstian

DOI: 10.1364/JOSAB.393128 Received 18 Mar 2020; Accepted 25 May 2020; Posted 26 May 2020  View: PDF

Abstract: We present a module that can generate periodic light patterns, change their spacing, orientation and position. This is done by using liquid crystal cells without pixelation (in contrast to spatial light modulators).The absence of mechanical movements allows this module to be integrated in miniature (wearable) endomicroscopic systems to improve the image resolution by using the structured illumination method.

Topology optimization of photonics devices: Fluctuations-Trend Analysis concept. Random initial conditions with Gaussian and Durden-Vesecky power density bandlimited spectrums


DOI: 10.1364/JOSAB.396594 Received 30 Apr 2020; Accepted 21 May 2020; Posted 26 May 2020  View: PDF

Abstract: We present a topology optimization method for a 1D dielectric metasurface, based on a new concept: Fluctuations and Trend Analysis for initial random conditions. The key point of the proposed optimization method is that the procedure initially generates a couple of device distributions termed Fluctuation/mother and Trends/father, with specific spectra, that efficiently sample, not the local minimum of the objective function but basins of optimal solutions in the design space. Studying a 1D dielectric metagrating deflecting a normal incident TE polarized wave onto a range of angles, we show that a suited choice of a specific power density spectrum for this initial couple, highly increases the probability to reach a basin of high-performance devices.We guess, initial geometries holding the physical properties of the desired final device, allows to target accurately these high-performance devices basins in the design space. To include desired physical properties in the initial geometry model, we introduce a formalism allowing to generate random process with particular power density or correlation function. Thanks to a suited definition of the trend function, we identify an ultimate power density bandlimited spectrum for the fluctuation functions allowing a very high probability, leading to a rapid descent to favorable basins of optimal solutions, consequently to reach high-performance final structure in the design space.

Spectral singularities and tunable slab laserswith 2D material coating

Hamed Ghaemi-Dizicheh, Ali Mostafazadeh, and Mustafa Sarisaman

DOI: 10.1364/JOSAB.392009 Received 03 Mar 2020; Accepted 21 May 2020; Posted 26 May 2020  View: PDF

Abstract: We investigate linear and nonlinear spectral singularities in the transverse electric and transverse magnetic modes of a slab laser consisting of an active planar slab sandwiched between a pair of Graphene or Weyl semimetal thin sheets. The requirement of the presence of linear spectral singularities gives the laser threshold condition while the existence of nonlinear spectral singularities due to an induced weak Kerr nonlinearity allows for computing the laser output intensity in the vicinity of the threshold. The presence of the Graphene and Weyl semimetal sheets introduces additional physical parameters that we can use to tune the output intensity of the laser. We provide a comprehensive study of this phenomenon and report peculiarities of lasing in the TM modes of the slab withWeyl semimetal coatings. In particular, we reveal the existence of a critical angle such that no lasing seems possible forTMmodes of the slab with smaller emission angle. Our results suggest that for TM modes with emission angle slightly exceedingthe critical angle, the laser output intensity becomes highly sensitive to the physical parameters of the coating.

Sudden Death and Rebirth of Entanglement in Classical Optics: an Analogy with Quantum Optics

Firat Yasar and Shahram Dehdashti

DOI: 10.1364/JOSAB.386100 Received 17 Dec 2019; Accepted 21 May 2020; Posted 26 May 2020  View: PDF

Abstract: In this paper, we study the possibility of realization of a classical system with quantum characters on the level of classical optics. Indeed, we first use the formalism of quantum optics to consider the propagation of two coherent states in the Kerr medium while the interaction between two states is described by the Cross-Kerr interaction. Then, we draw an analogy between the dynamical process of this structure and Gaussian wave propagation in a quadratic gradient-index medium. We demonstrate that by using this structure, we can generate a sudden death and rebirth of an entangled state of su(2)-coherent state in the level of the classical optics.

Performance Analysis of Efficient and Stable Perovskite Solar Cell and Comparative Study of Incorporating Metal Oxide Transport Layers

Arnob Ghosh, Shahriyar Safat, Sk Saud, Nazmus Saqib, and Arnob Saha

DOI: 10.1364/JOSAB.391817 Received 03 Mar 2020; Accepted 18 May 2020; Posted 18 May 2020  View: PDF

Abstract: As poor stability is the primary constraint for the commercialization of perovskite solar cells, improving stabilityhas been the primary focus of recent researches in perovskite solar cells. Different metal oxide transport layers are being used with the aim offabricating stable perovskite solar cells. A stable and efficient solar cell with both metal oxide transport layers (ZnO and NiOx) and perovskite (methyl ammonium lead iodide) absorber layer is simulated in this work and a comparison of performance parameters is made with other transport layers from literature. The issue of optimizationregarding thethickness of absorber layer andthe doping concentration in absorber and transport layers has been addressed, and the effect of defect concentration at the interface investigated. Optimum performance isachievedwith an 800 nm thick absorber layer. Linear grading is also introduced in the absorber layer by varying the concentration of different halides, which increases the efficiency by approximately 8% owing to the increase in short circuit current density.

Sensitivity comparison of free-space and waveguide Raman for bulk sensing

Jerome Michon, Derek Kita, and Juejun Hu

DOI: 10.1364/JOSAB.394973 Received 20 Apr 2020; Accepted 18 May 2020; Posted 18 May 2020  View: PDF

Abstract: The sensitivity advantage of waveguide-enhanced Raman spectroscopy (WERS) over free-space Raman is well established for thin molecular layer sensing, which traditionally relies on confocal Raman setups. However, for bulk liquid or gas samples, WERS needs to be benchmarked against non-confocal Raman configurations. We use ray tracing to calculate the power collection efficiency of several model free-space systems, such as microscopes and probes, encompassing both single-objective and dual-lens systems. It is shown that considering only the focal volume of the pump beam or the confocal volume of the microscope significantly underestimates the collected power from free-space Raman systems. We show that waveguide-based systems can still outperform the best free-space systems in terms of both signal collection efficiency and signal-to-noise ratio.

Light splitting, stopping and their combination via controllable Bloch oscillation in a lattice

Lei Du and Yan Zhang

DOI: 10.1364/JOSAB.384001 Received 25 Nov 2019; Accepted 18 May 2020; Posted 19 May 2020  View: PDF

Abstract: We study controllable Bloch oscillation and its potential applications in a one-dimensional lattice with partly phase-modulated hopping rates. Under proper conditions, such a system can be built by using a quasi-one-dimensional sawtooth lattice with Peierls phases induced by a synthetic magnetic field. The amplitude of the Bloch oscillation can be adjusted precisely and continuously by adjusting the phase, and hence we realize tunable light splitting in the presence of a V-type potential. Moreover, we construct two distinct sandwich structures to realize tunable light stopping and delayed splitting, respectively, of which the stopping and delay durations are tunable. Our proposal may imply exciting opportunities for potential applications in optical communications and photonic device fabrication involving unconventional light transports.

Calculation of the Disentropy of the Wigner Function using the Lambert-Tsallis Wq Function with non-Integer q Values

Jose Leonardo da Silva and Rubens Ramos

DOI: 10.1364/JOSAB.390323 Received 12 Feb 2020; Accepted 18 May 2020; Posted 19 May 2020  View: PDF

Abstract: The Wigner function is a mathematical tool that provides important information about a quantum light state, like entanglement and quantumness. For example, in a recent work it was shown the disentropy of the Wigner function using the Lambert-Tsallis Wq function with q = 2 can be used as a measure of quantumness. When the value of q is non-integer, the disentropy and the Wq function have fractional powers and, hence, a negative value of the Wigner function can result in a complex value for the disentropy. This prohibits the use of those functions in the calculation of the disentropy of the Wigner function of highly interesting states, like Schrödinger cats. In order to overcome this problem, we propose a new disentropy equation inspired in the Rényi entropy. The advantages and disadvantages of this new disentropy are discussed and numerical examples are shown.

Enhanced principle component method for fringe removal in cold atom images

Colin Parker, Feng Xiong, and Yun Long

DOI: 10.1364/JOSAB.391297 Received 25 Feb 2020; Accepted 18 May 2020; Posted 19 May 2020  View: PDF

Abstract: Many powerful imaging techniques for cold atoms are based on determining the optical density by comparing a beam image having passed through the atom cloud to a reference image taken under similar conditions with no atoms. In practice the beam profile typically contains interference fringes whose phase is not stable between camera exposures. To reduce the error of these fringes in the computed optical density, an algorithm based on principle component analysis (PCA) is often employed. However, PCA is general purpose and not tailored to the specific case of interference fringes. Here we demonstrate an algorithm that takes advantage of the Fourier-space structure of interference fringes to further reduce the residual fringe signatures in the optical density.

A simple technique for producing an asymmetric grating

Sorakrai Srisuphaphon, Sitti Buathong, and Sarayut Deachapunya

DOI: 10.1364/JOSAB.387688 Received 07 Jan 2020; Accepted 16 May 2020; Posted 18 May 2020  View: PDF

Abstract: The interference contrast in a near-field diffraction pattern can be improved using an asymmetric grating with a small grating window. However, commercial asymmetrically shaped gratings are not available. Here, we report a method that overlaps two gratings to produce an arbitrary open fraction in the combination grating. Both theoretical simulation and experimental observations of the near-field Talbot effect are provided to validate this concept. A characterization of optical vortices is also used as demonstration of potential applications. This method is simple and can improve the resolution in metrology with optical sensors.

Precise phase theory for accuracy improvement in fiber probe interferometer for nanometric sensing, taking into account fiber coupling

Toshihiko Yoshino

DOI: 10.1364/JOSAB.390836 Received 19 Feb 2020; Accepted 15 May 2020; Posted 18 May 2020  View: PDF

Abstract: In a single-mode fiber probe type of interferometer, the effect of fiber coupling on the sensing performance is theoretically comprehensively investigated in order to analyze and improve the achievable sensing accuracy for nanometric sensing. In both direct and via-lens coupling schemes for the interferometer, the scale factors to deduce optical path length change from measured phase are analytically and numerically examined in terms of deviation from the plane wave assumption of conventional use. It is manifested that the scale factor deviation is of considerable magnitude in the case of direct coupling, but, by the incorporation of suitable collimating optics for coupling, the degree of deviation can be drastically reduced to as small as typically 10^(-8), supporting to achieve ultra-high accuracy such as pm in displacement sensing. The effect of reflector tilting is also addressed.

Robust Design Method for Metasurface High-Sensitivity Sensors and Absorbers

Amin Rastgordani and Zahra Ghattan Kashani

DOI: 10.1364/JOSAB.386320 Received 18 Dec 2019; Accepted 15 May 2020; Posted 15 May 2020  View: PDF

Abstract: In this study, we propose and investigate a generalized circuit model for metasurface high-sensitivity sensors and broadband absorbers. Firstly, we propose a Terahertz (THz) tunable and polarization-independent high-sensitivity sensor based on a bulk Dirac semimetal (BDS) metasurface. We compare the results of the proposed circuit model with those of full-wavesimulation. In addition, we have achieved the spectra of the sensor absorption for healthy and cancer cells. Moreover, since for most practical applications, the absorption bandwidth is one of the most substantial metrics, we propose a broadband absorber in the wavelength range between600 to 800nm. Because of verifying our proposed model, we compare the results of the circuit model with those of the experimental data. Additionally, a good agreement is observed between the results of the circuit model, those of the full-wave simulations, and the experimental data. The proposed circuit model is general. It provides a physical insight into the design and the operation of various sub-wavelength structures in the broad frequency range. In addition, the proposed sensor can be used as a platform for the design of the sensors needed in various chemical andbiomedical systems.

Analysis of the features of a multifunctional device based on the regulation of magnetic field in one-dimensional photonic crystals only containing the plasma with a novel quasi-periodic structure

Sijia Guo, Caixing Hu, and HaiFeng Zhang

DOI: 10.1364/JOSAB.392047 Received 03 Mar 2020; Accepted 14 May 2020; Posted 14 May 2020  View: PDF

Abstract: In this paper, the features of a multifunctional device which is realized by one-dimensional (1-D) magnetized plasma photonic crystals (MPPCs) only containing the plasma regulated by the external magnetic field in an innovative quasi-periodic arrangement are studied by the transfer matrix method (TMM), which possess the characteristics of the omnidirectional band gap (OBG), nonreciprocity (NR) and the polarization separation (PS). The manipulated effects of the magnetic field and other physical parameters including the plasma frequency and incident angle on those three properties are illustrated, respectively. The computed results demonstrate that, with the gradually increasing magnetic field, the performances of OBG and NR are deteriorated apparently while the PS region expands ideally. Meanwhile, the greater functions of PS and OBG can be gotten with the proper rise of the plasma frequency. Nevertheless, the larger the plasma frequency is, the worse quality of NR will be observed. Furthermore, an appropriate incident angle also plays a crucial part in the display of NR and PS for the proposed devices and those properties can be enhanced well with the larger incident angle. This new kind of MPPCs will have the potential value in designing the tunable and multifunctional optical instruments.

Dynamically tunable coherent perfect absorption based on bulk Dirac semi-metal

Xiang Zhai, Ting Zhou, Yong Li, Hai-Yu Meng, Lingling Wang, Hongjian Li, Panpan Fang, and Shihao Ban

DOI: 10.1364/JOSAB.392986 Received 16 Mar 2020; Accepted 13 May 2020; Posted 13 May 2020  View: PDF

Abstract: Coherent perfect absorption (CPA) is realized in metasurfaces composed of crossed vertical bulk Dirac semi-metal (BDS) stripes and SiO₂. Under the illumination of two counter-propagating coherent beams, the coherent absorption is continuously tuned from almost 0 (approximately 6.2 × 10¯⁵) to 99.97% by controlling their relative phase, which gives a modulation depth of about 1.6 × 10⁴. Furthermore, the coherent absorption can be tuned substantially by varying the relative intensity, the Fermi energy of BDS, and the thickness of metasurfaces. Further research shows that the metasurface has broadband angular selectivity: CPA frequency splits into TE and TM polarization bands under oblique incidence. Our results provide an effective way to manipulate the interaction of light and BDS, and there may be potential applications in coherent detectors and optical modulators.

Research on terahertz transmission characteristics of non-polar liquid based on frequency-domain spectroscopy


DOI: 10.1364/JOSAB.392333 Received 23 Mar 2020; Accepted 11 May 2020; Posted 11 May 2020  View: PDF

Abstract: In our research, the terahertz frequency-domain spectroscopy based on the continuous-wave and coherent detection which offers advantages of frequency selectivity and much higher frequency resolution, is used to acquire the optical parameter of non-polar liquid samples in a Poly tetra fluoroethylene (PTFE) rectangle cell. The transfer matrix method is raised to remove the oscillation generated by the Fabry–Pérot interferometer caused of the cell wall, thereby dielectric constants of liquids can be extracted successfully. The refractive index of the non-polar liquid samples cyclohexane (C6H12) and n-Hexane (C6H14) are obtained within the frequency range of 400-1600 GHz. The processed results of cyclohexane and n-Hexane in our method are basically stable with the refractive index of about 1.42 and 1.37, respectively, which agree well with the experimental results using other method before.

Highly Sensitive Temperature Sensor Based on Cascaded HiBi-FLMs With Vernier Effect

Zhichao Ding, Zhongwei Tan, Piaokun Zhang, and Liwei Zhang

DOI: 10.1364/JOSAB.394236 Received 02 Apr 2020; Accepted 10 May 2020; Posted 11 May 2020  View: PDF

Abstract: Abstract: We propose and experimentally demonstrate a highly sensitive temperature sensor based on cascaded high birefringence fiber loop mirrors (HiBi-FLMs) with Vernier effect. The working principle of the proposed sensor is analogous to a Vernier-scale, one of the two cascaded HiBi-FLMs is for sensing and the other acts as a filter. The two HiBi-FLMs have almost the same free spectrum range (FSR) which can be regard as two scales with different period of an optical Vernier-scale, and act as the fixed part and the sliding part, respectively. A Gauss fitting algorithm is introduced to fit the Vernier envelope to accurately trace the wavelength shift of the envelope peak. The temperature sensitivity and temperature resolution of the Vernier spectra for the cascade configuration is much larger than that of the transmission spectrum for single HiBi-FLM due to the Vernier effect. Experimental result shows that the temperature sensitivity of the proposed sensor can be improved from −1.7 nm/℃ (single HiBi-FLM) to −43 nm/℃ (cascaded configuration) by employing the Vernier effect, and the temperature resolution is enhanced from 0.0291 ℃ to 0.0012 ℃. The amplification factor of temperature sensitivity and temperature resolution are both 24.96, which shows good agreement with the theoretical prediction. The proposed sensor with huge temperature sensitivity, high resolution, simple configuration and good repeatability may be a promising candidate for some applications that need precise temperature control.

Mid-infrared tunable triple-band cross polarization converter based on periodic ellipse graphene patch with slit

Lanlan Zhang, Ping Li, and XiaoWei Song

DOI: 10.1364/JOSAB.392916 Received 23 Mar 2020; Accepted 09 May 2020; Posted 11 May 2020  View: PDF

Abstract: A novel triple-band, tunable, high-efficiency, mid-infrared reflected cross polarization converter based on graphene metasurface is proposed and studied, which comprised a periodic ellipse graphene patch with slit, a dielectric spacer, and a metal gold substrate. Numerical simulations indicate that the proposed converter can convert a linearly polarized wave to its cross-polarized wave at three resonance frequencies due to the superimposition of the two reflected components with a near 180°or 0° phase difference. The polarization conversion ratios of the three bands are 98.29%, 98.42% and 97.64%, respectively. The polarization converter can be dynamically tuned by changing the Fermi energy or electron scattering time. Our proposed tunable polarization converter has great potential in the application of electromagnetic polarization control.

The ability of gas modulation to reduce the pick-up of fluctuations in refractometry

Ove Axner, Isak Silander, Clayton Forssen, Johan Zakrisson, and Martin Zelan

DOI: 10.1364/JOSAB.387902 Received 09 Jan 2020; Accepted 09 May 2020; Posted 11 May 2020  View: PDF

Abstract: Gas modulation refractometry (GAMOR) is a technique for assessment of gas refractivity, density, and pressure that, by a rapid modulation of the gas, provides a means to significantly reduce the pick-up of fluctuations. Although its unique feature has previously been demonstrated, no detailed explication or analysis of this ability has yet been given. This work provides a theoretical explanation, in terms of the length of the modulation cycle, to which extent gas modulation can reduce the pick-up of fluctuations. It is indicated that a rapid modulation can reduce significantly the influence of fluctuations with Fourier frequencies lower than the inverse of the modulation cycle length, which often are those that dominate. The predictions are confirmed experimentally.

A study of the highly-sensitive refractive index sensor designed by a subwavelength grating

Xufeng Li, zhao yali, xueying Zhou, and Peng Wei

DOI: 10.1364/JOSAB.391110 Received 20 Feb 2020; Accepted 09 May 2020; Posted 11 May 2020  View: PDF

Abstract: This paper puts forward a subwavelength grating for highly-sensitive refractive index (RI) sensing. The light-coupling condition of the grating covered by the liquid to be detected is sensitive to changes in RI of the liquid. The influence of the change in grating period and thickness on the coupling is studied at the large incident angle, in this case, it is found that the effective RI of the grating slab is varied with the incident angle, and then the coupling based on the guided-mode resonance(GMR) affected by the variation is revealed. With scanning the angle of wave incidence at a wavelength of 6 .8nm, the calculated results indicate the sensor sensitivity is mainly depended on the period, while the resolution by calculating the full width at half maximum(FWHM) of the coupling angle is controlled by the thickness. After the period and thickness have been optimized in sequence, a sensitivity of ~2900/RIU( ~240O/RIU) and a resolution ranged from 0.10 to 0.30 are obtained, which of the grating sensor are better than that of the surface plasmon resonance (SPR) sensor.

Polarization ray tracing in thermally loaded solid-state laser crystals

Phillip Lino Rall and Christoph Pflaum

DOI: 10.1364/JOSAB.391216 Received 21 Feb 2020; Accepted 06 May 2020; Posted 07 May 2020  View: PDF

Abstract: A new ray tracing method for the propagation of electrical fields in inhomogeneous and weakly anisotropic media is presented. With this method, we could efficiently simulate the propagation of laser beams in solid-state laser amplifiers, which suffer from high thermal loads. As a result of this method, we could find optical compensation setups which significantly reduce the depolarization losses in high power solid-state amplifiers. To the best of our knowledge, we theoretically demonstrated for the first time, that [100]-cut YAG crystal reduce the depolarization by more than a magnitude in comparison to [111]-cut crystals while achieving an overall better beam quality at the same time.

Enhancing Sensitivity of an Atom Interferometer to the Heisenberg Limit using Increased Quantum Noise

Renpeng Fang, Resham Sarkar, and Selim Shahriar

DOI: 10.1364/JOSAB.396358 Received 29 Apr 2020; Accepted 06 May 2020; Posted 14 May 2020  View: PDF

Abstract: In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1/root-N. Under usual spin-squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged, while producing phase amplification. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N, while increasing the quantum noise by root-N, and amplifying the phase by a factor of N. Because of the enhancement in quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schroedinger Cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N. Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of root-2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme, via one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed, because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.

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