Quantum imaging

Characterization of Defocused Coherent Imaging Systems with Periodic Objects

Recent advancements in quantum and quantum-inspired imaging techniques have enabled high-resolution 3D imaging through photon correlations. These techniques exhibit reduced degradation of image resolution for out-of-focus samples compared to conventional methods (i.e., intensity-based incoherent imaging). A key advantage of these correlation-based approaches is their independence from the system numerical aperture (NA). Interestingly, both improved resolution of defocused images and NA-independent scaling are linked to the spatial coherence of light. This suggests that while correlation measurements exploit spatial coherence, they are not essential for achieving this imaging advantage. This discovery has led to the development of optical systems that achieve similar performance by using spatially coherent illumination and relying on intensity measurements: direct 3D imaging with NA-independent resolution was recently demonstrated in a correlation-free setup using LED light. Here, we explore the physics behind the enhanced performance of defocused coherent imaging, showing that it arises from the modification of the sample's spatial harmonic content due to diffraction, unlike the blurring seen in conventional imaging. The results we present are crucial for understanding the implications of the physical differences between coherent and incoherent imaging, and are expected to pave the way for the practical application of the discovered phenomena.

A comparison between the measurement of quantum spatial correlations using qCMOS photon-number resolving and electron multiplying CCD camera technologies

Cameras with single-photon sensitivities can be used to measure the spatial correlations between the photon-pairs that are produced by parametric down-conversion. Even when pumped by a single-mode laser, the signal and idler photons are typically distributed over several thousand spatial modes yet strongly correlated with each other in their position and anti-correlated in their transverse momentum. These spatial correlations enable applications in imaging, sensing, communication, and optical processing. Here we show that, using a photon-number resolving camera, spatial correlations can be observed after only a few 10s of seconds of measurement time, thereby demonstrating comparable performance with previous single photon sensitive camera technologies but with the additional capability to resolve photon-number. Consequently, these photon-number resolving technologies are likely to find wide use in quantum, low-light, imaging systems.

Ultrafast Temporal SU(1,1) Interferometer

Interferometers are highly sensitive to phase differences and are utilized in numerous schemes. Of special interest is the quantum SU(1,1) interferometer which is able to improve the sensitivity of classical interferometers. We theoretically develop and experimentally demonstrate a temporal SU(1,1) interferometer based on two time lenses in a 4f configuration. This temporal SU(1,1) interferometer has a high temporal resolution, imposes interference on both time and spectral domains, and is sensitive to the phase derivative which is important for detecting ultrafast phase changes. Therefore, this interferometer can be utilized for temporal mode encoding, imaging, and studying the ultrafast temporal structure of quantum light.

Background-Free Near-Infrared Biphoton Emission from Single GaAs Nanowires

The generation of photon pairs from nanoscale structures with high rates is still a challenge for the integration of quantum devices, as it suffers from parasitic signals from the substrate. In this work, we report type-0 spontaneous parametric down-conversion at 1550 nm from individual bottom-up grown zinc-blende GaAs nanowires with lengths of up to 5 μm and diameters of up to 450 nm. The nanowires were deposited on a transparent ITO substrate, and we measured a background-free coincidence rate of 0.05 Hz in a Hanbury-Brown-Twiss setup. Taking into account transmission losses, the pump fluence, and the nanowire volume, we achieved a biphoton generation of 60 GHz/Wm, which is at least 3 times higher than that of previously reported single nonlinear micro- and nanostructures. We also studied the correlations between the second-harmonic generation and the spontaneous parametric down-conversion intensities with respect to the pump polarization and in different individual nanowires.

Quantum imaging with a photon counting camera

Classical light sources emit a randomly-timed stream of individual photons, the spatial distribution of which can be detected with a camera to form an image. Quantum light sources, based on parametric down conversion, emit photons as correlated photon-pairs. The spatial correlations between the photons enables imaging systems where the preferential selection of photon-pairs allows for enhancements in the noise performance over what is possible using classical light sources. However, until now the technical challenge of measuring, and correlating both photons has led to system complexity. Here we show that a camera capable of resolving the number of individual photons in each pixel of the detector array can be used to record an image formed from these photon-pair events and hence achieve a greater contrast than possible using a classical light source. We achieve an enhancement in the ratio of two-photon events compared to one-photon events using spatially correlated SPDC light compared to uncorrelated illumination by a LED. These results indicate the potential advantages of using photon counting cameras in quantum imaging schemes and these advantages will further increase as the technology is developed. Operating in photon sparse regimes such systems have potential applications in low-light microscopy and covert imaging.

Noise rejection through an improved quantum illumination protocol

Quantum illumination protocols can be implemented to improve imaging performance in the low photon flux regime even in the presence of both background light and sensor noise. However, the extent to which this noise can be rejected is limited by the rate of accidental correlations resulting from the detection of photon or noise events that are not quantum-correlated. Here we present an improved protocol that rejects up to [Formula: see text] of background light and sensor noise in the low photon flux regime, improving upon our previous results by an order of magnitude. This improvement, which requires no information regarding the scene or noise statistics, will enable extremely low light quantum imaging techniques to be applied in environments previously thought difficult and be an important addition to the development of covert imaging, quantum microscopes, and quantum LIDAR.

Measurement of the biphoton second-order correlation function with analog detectors

An experimental scheme and data processing approaches are proposed for measuring by analog photo detectors the normalized second-order correlation function of the biphoton field generated under spontaneous parametric down-conversion. Obtained results are especially important for quantum SPDC-based technologies in the long-wave spectral ranges, where it is difficult to use the single-photon detector at least in one of the two biphoton channels. The methods of discrimination of analog detection samples are developed to eliminate the negative influence of the detection noises and get quantitatively true values of both the correlation function and the detector quantum efficiency. The methods are demonstrated depending on whether two single-photon avalanche photo detectors are used in both SPDC channels, or at least one single-photon detector is replaced by a photo-multiplier tube which cannot operate in the photon counting mode.

Quantum frequency conversion of vacuum squeezed light to bright tunable blue squeezed light and higher-order spatial modes

Quantum frequency conversion, the process of shifting the frequency of an optical quantum state while preserving quantum coherence, can be used to produce non-classical light at otherwise unapproachable wavelengths. We present experimental results based on highly efficient sum-frequency generation (SFG) between a vacuum squeezed state at 1064 nm and a tunable pump source at 850 nm ± 50 nm for the generation of bright squeezed light at 472 nm ± 4 nm, currently limited by the phase-matching of the used nonlinear crystal. We demonstrate that the SFG process conserves part of the quantum coherence as a 4.2(±0.2) dB 1064 nm vacuum squeezed state is converted to a 1.6(±0.2) dB tunable bright blue squeezed state. We furthermore demonstrate simultaneous frequency- and spatial-mode conversion of the 1064-nm vacuum squeezed state, and measure 1.1(±0.2) dB and 0.4(±0.2) dB of squeezing in the TEM₀₁ and TEM₀₂ modes, respectively. With further development, we foresee that the source may find use within fields such as sensing, metrology, spectroscopy, and imaging.

Shaping quantum photonic states using free electrons

It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.

Entangling bosons through particle indistinguishability and spatial overlap

Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in the same system. While recent theoretical studies have shown that the spatial overlap between identical particles is necessary for nontrivial entanglement, the exact role of particle indistinguishability in the entanglement of identical particles has never been analyzed quantitatively before. Here, we theoretically and experimentally investigate the behavior of entanglement between two bosons as spatial overlap and indistinguishability simultaneously vary. The theoretical computation of entanglement for generic two bosons with pseudospins is verified experimentally in a photonic system. Our results show that the amount of entanglement is a monotonically increasing function of both quantities. We expect that our work provides an insight into deciphering the role of the entanglement in quantum networks that consist of identical particles.

Resource Reduction for Distributed Quantum Information Processing Using Quantum Multiplexed Photons

Distributed quantum information processing is based on the transmission of quantum data over lossy channels between quantum processing nodes. These nodes may be separated by a few microns or on planetary scale distances, but transmission losses due to absorption and/or scattering in the channel are the major source of error for most distributed quantum information tasks. Of course, quantum error correction (QEC) and detection techniques can be used to mitigate such effects, but error detection approaches have severe performance limitations due to the signaling constraints between nodes, and so error correction approaches are preferable-assuming one has sufficient high quality local operations. Typically, performance comparisons between loss-mitigating codes assume one encoded qubit per photon. However, single photons can carry more than one qubit of information and so our focus in this Letter is to explore whether loss-based QEC codes utilizing quantum multiplexed photons are viable and advantageous, especially as photon loss results in more than one qubit of information being lost. We show that quantum multiplexing enables significant resource reduction, in terms of the number of single-photon sources, while at the same time maintaining (or even lowering) the number of 2-qubit gates required. Further, our multiplexing approach requires only conventional optical gates already necessary for the implementation of these codes.

Single-photon sources: Approaching the ideal through multiplexing

We review the rapid recent progress in single-photon sources based on multiplexing multiple probabilistic photon-creation events. Such multiplexing allows higher single-photon probabilities and lower contamination from higher-order photon states. We study the requirements for multiplexed sources and compare various approaches to multiplexing using different degrees of freedom.

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent pointlike emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a passive linear interferometer feeds into an array of photodetectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the special case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.

Imaging through noise with quantum illumination

The contrast of an image can be degraded by the presence of background light and sensor noise. To overcome this degradation, quantum illumination protocols have been theorized that exploit the spatial correlations between photon pairs. Here, we demonstrate the first full-field imaging system using quantum illumination by an enhanced detection protocol. With our current technology, we achieve a rejection of background and stray light of up to 5.8 and also report an image contrast improvement up to a factor of 11, which is resilient to both environmental noise and transmission losses. The quantum illumination protocol differs from usual quantum schemes in that the advantage is maintained even in the presence of noise and loss. Our approach may enable laboratory-based quantum imaging to be applied to real-world applications where the suppression of background light and noise is important, such as imaging under low photon flux and quantum LIDAR.

Generation of correlated biphoton via four-wave mixing coexisting with multi-order fluorescence processes

We investigate the parametrically amplified four-wave mixing, spontaneous parametric four-wave-mixing, second- and fourth-order fluorescence signals coming from the four-level double-Λ electromagnetically induced transparency system of a hot ⁸⁵Rb atomic vapor. The biphoton temporal correlation is obtained from spontaneous parametric four-wave-mixing and fourth-order fluorescence processes. Meanwhile, we first observed the biphoton Rabi oscillation with a background of linear Rayleigh scattering and uncorrelated second-order fluorescence. The outcomes of the investigation may contribute potentially to the applications in dense coding quantum communication systems.

Continuous-variable Quantum Phase Estimation based on Machine Learning

Making use of the general physical model of the Mach-Zehnder interferometer with photon loss which is a fundamental physical issue, we investigate the continuous-variable quantum phase estimation based on machine learning approach, and an efficient recursive Bayesian estimation algorithm for Gaussian states phase estimation has been proposed. With the proposed algorithm, the performance of the phase estimation may be improved distinguishably. For example, the physical limits (i.e., the standard quantum limit and Heisenberg limit) for the phase estimation precision may be reached in more efficient ways especially in the situation of the prior information being employed, the range for the estimated phase parameter can be extended from [0, π/2] to [0, 2π] compared with the conventional approach, and influences of the photon losses on the output parameter estimation precision may be suppressed dramatically in terms of saturating the lossy bound. In addition, the proposed algorithm can be extended to the time-variable or multi-parameter estimation framework.

Retrieving Ideal Precision in Noisy Quantum Optical Metrology

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.

Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions

We propose a quantum critical detector (QCD) to amplify weak input signals. Our detector exploits a first-order discontinuous quantum-phase-transition and exhibits giant sensitivity (χ ∝ N²) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.

Structured-Pump-Enabled Quantum Pattern Recognition

We report a new scheme of ghost imaging by using a spatially structured pump in the Fourier domain of spontaneous parametric down-conversion for quantum-correlation-based pattern recognition. We exploit the mathematical feature of Laguerre-Gaussian mode's Fourier transform to describe the pump-modulated formation of a ghost image. Of particular interest is the experimental demonstration of a quantum equivalence of a Vander Lugt filter, based on which the nonlocal spiral phase contrast for vortex mapping and quantum-correlation-based human face recognition are implemented successfully. The photons used for probing a test object, scanning the database, and producing a correlation signal can belong to three different light beams, which suggests some security applications where low-light-level illumination and covert operation are desired.

Twin-beam intensity-difference squeezing below 10 Hz

We report the generation of strong, bright-beam intensity-difference squeezing down to measurement frequencies below 10 Hz. We generate two-mode squeezing in a four-wave mixing (4WM) process in Rb vapor, where the single-pass-gain nonlinear process does not require cavity locking and only relies on passive stability. We use diode laser technology and several techniques, including dual seeding, to remove the noise introduced by seeding the 4WM process as well as the background noise. Twin-beam intensity-difference squeezing down to frequencies limited only by the mechanical and atmospheric stability of the lab is achieved. These results should enable important low-frequency applications such as direct intensity-difference imaging with bright beams on integrating detectors.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T² time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T⁴ in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Quantum metrology investigates the improvement given to precision measurements by exploiting quantum mechanics, but it has been mostly limited to systems with static Hamiltonians. Here the authors study it in the general case of time-varying Hamiltonians, showing that optimizing the quantum Fisher information via quantum control provides an advantage.

Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array

We demonstrate coincidence measurements of spatially entangled photons by means of a multi-pixel based detection array. The sensor, originally developed for positron emission tomography applications, is a fully digital 8×16 silicon photomultiplier array allowing not only photon counting but also per-pixel time stamping of the arrived photons with an effective resolution of 265 ps. Together with a frame rate of 500 kfps, this property exceeds the capabilities of conventional charge-coupled device cameras which have become of growing interest for the detection of transversely correlated photon pairs. The sensor is used to measure a second-order correlation function for various non-collinear configurations of entangled photons generated by spontaneous parametric down-conversion. The experimental results are compared to theory.

Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cramér-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does not mandate any loss of precision in estimating even deep sub-Rayleigh separations. We propose two coherent measurement techniques, easily implementable using current linear-optics technology, that approach the quantum limit over an arbitrarily large range of separations. Our bound is valid for arbitrary source strengths, all regions of the electromagnetic spectrum, and for any imaging system with an inversion-symmetric point-spread function. The measurement schemes can be applied to microscopy, optical sensing, and astrometry at all wavelengths.

Efficient photon triplet generation in integrated nanophotonic waveguides

Generation of entangled photons in nonlinear media constitutes a basic building block of modern photonic quantum technology. Current optical materials are severely limited in their ability to produce three or more entangled photons in a single event due to weak nonlinearities and challenges achieving phase-matching. We use integrated nanophotonics to enhance nonlinear interactions and develop protocols to design multimode waveguides that enable sustained phase-matching for third-order spontaneous parametric down-conversion (TOSPDC). We predict a generation efficiency of 0.13 triplets/s/mW of pump power in TiO₂-based integrated waveguides, an order of magnitude higher than previous theoretical and experimental demonstrations. We experimentally verify our device design methods in TiO₂ waveguides using third-harmonic generation (THG), the reverse process of TOSPDC that is subject to the same phase-matching constraints. We finally discuss the effect of finite detector bandwidth and photon losses on the energy-time coherence properties of the expected TOSPDC source.

Dissipative Quantum Control of a Spin Chain

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

Probing limits on spatial resolution using nonlinear optical effects and nonclassical light

Using a simple optical setup to detect and characterize transmission gratings in the far field, we demonstrate that going beyond the diffraction limit is not possible using linear interaction of nonclassical illumination with the target grating. We also confirm that nonlinear optical interactions with the target grating, or with the optical medium around it, do allow improvement in resolution.

Nonlinearity in single photon detection: modeling and quantum tomography

Single Photon Detectors are integral to quantum optics and quantum information. Superconducting Nanowire based detectors exhibit new levels of performance, but have no accepted quantum optical model that is valid for multiple input photons. By performing Detector Tomography, we improve the recently proposed model [M.K. Akhlaghi and A.H. Majedi, IEEE Trans. Appl. Supercond. 19, 361 (2009)] and also investigate the manner in which these detectors respond nonlinearly to light, a valuable feature for some applications. We develop a device independent model for Single Photon Detectors that incorporates this nonlinearity.

Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ∼(N-N(max))(½) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.

High-flux and broadband biphoton sources with controlled frequency entanglement

We report the high-flux and broadband generation of biphotons with controlled frequency entanglement. For the generation of the entangled state consisting of frequency-anticorrelated photons, we use PPMgSLT pumped by a continuous-wave (cw) laser. Meanwhile, the state consisting of frequency-correlated photons is produced from PPKTP under the extended phase-matching condition. Both states exhibited interference patterns with over 90% visibilities in two-photon interference experiments.

A gain criterion for the improvement of detection tasks with sub-Poissonian light

Based on a standard binomial model of sub-Poissonian photocounting statistics, we analyze the discrimination performance between the two possibilities that light has been potentially absorbed or not. For that purpose, we study with numerical simulations the behavior of different information-theory-based measures of the contrast and show that the Chernoff measure allows one to obtain a useful contrast characterization that has simple physical interpretation and that helps in analyzing the benefit of using sub-Poissonian light to improve detection tasks.

Full characterization of Gaussian bipartite entangled states by a single homodyne detector

We present the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement, and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of optical parametric oscillator signals and represent a tool for quantum technology based on continuous variable entanglement.

Broadband frequency mode entanglement in waveguided parametric downconversion

We report the observation of beatings of the coincidence event rate in a Hong-Ou-Mandel interference (HOMI) between signal and idler photons from a parametric downconversion (PDC) process inside a multimode KTP waveguide. As an explanation we introduce biphotonic states entangled in their broadband frequency modes generated by waveguide mode triples and propose a suitable entanglement detection scheme.

Tools for multimode quantum information: modulation, detection, and spatial quantum correlations

We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear chi(2) material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.

Spatial quantum correlations in multiple scattered light

We predict a new spatial quantum correlation in light propagating through a multiple scattering random medium. The correlation depends on the quantum state of the light illuminating the medium, is infinite in range, and dominates over classical mesoscopic intensity correlations. The spatial quantum correlation is revealed in the quantum fluctuations of the total transmission or reflection through the sample and should be readily observable experimentally.

Universality of quantum critical dynamics in a planar optical parametric oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the "quantum image" critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.

Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion

Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.

Quantum-Enhanced Measurements: Beating the Standard Quantum Limit

Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ "quantum tricks" such as squeezing and entanglement.

Incoherent coincidence imaging and its applicability in X-ray diffraction

Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the coincidence rate of these two photons. From a classical perspective, the image is proportional to the fourth-order correlation function of the wave field. Using classical statistical optics, we study a particular aspect of coincidence imaging with incoherent sources. As an application, we give a proposal to realize lensless Fourier-transform imaging, and discuss its applicability in x-ray diffraction.

A quantum laser pointer

The measurement sensitivity of the pointing direction of a laser beam is ultimately limited by the quantum nature of light. To reduce this limit, we have experimentally produced a quantum laser pointer, a beam of light whose direction is measured with a precision greater than that possible for a usual laser beam. The laser pointer is generated by combining three different beams in three orthogonal transverse modes, two of them in a squeezed-vacuum state and one in an intense coherent field. The result provides a demonstration of multichannel spatial squeezing, along with its application to the improvement of beam positioning sensitivity and, more generally, to imaging.

Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm

We formulate a theory for entangled imaging, which includes also the case of a large number of photons in the two entangled beams. We show that the results for imaging and for the wave-particle duality features, which have been demonstrated in the microscopic case, persist in the macroscopic domain. We show that the quantum character of the imaging phenomena is guaranteed by the simultaneous spatial entanglement in the near and in the far field.