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Two-Photon Ghost Image and Interference-Diffraction

One of the most surprising consequences of quantum mechanics is entanglement of two or more distance particles. The two-particle entangled state was mathematically formulated by Schrodinger. Based on this unusual quantum behavior, EPR defined their 'physical reality' and then asked the question: 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?' One may not appreciate EPR's criterion of physical reality and insist that 'no elementary quantum phenomenon is a phenomenon until it is a recorded phenomenon'. Optical spontaneous parametric down conversion (SPDC) is the most effective mechanism to generate an EPR type entangled two-photon state. In SPDC, an optical beam, called the pump, is incident on a birefringent crystal. The pump is intense enough so that nonlinear effects lead to the conversion of pump photons into pairs of photons, historically called signal and idler. Technically, the SPDC is said to be type-1 or type-2, depending on whether the signal and idler beams have parallel or orthogonal polarization. The SPDC conversion efficiency is typically on the order of 10(exp -9) to 10(exp -11), depending on the SPDC nonlinear material. The signal and idler intensities are extremely low, only single photon detection devices can register them. The quantum entanglement nature of SPDC has been demonstrated in EPR-Bohm experiments and Bell's inequality measurements. The following two experiments were recently performed in our laboratory, which are more closely related to the original 1935 EPR gedankenezperiment. The first experiment is a two-photon optical imaging type experiment, which has been named 'ghost image' by the physics community. The signal and idler beams of SPDC are sent in different directions, so that the detection of the signal and idler photons can be performed by two distant photon counting detectors. An aperture object (mask) is placed in front of the signal photon detector and illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the idler beam, by scanning the idler photon detector in the transverse plane of the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal, which can be easily performed by a coincidence measurement. This effect is even more striking when we found that the object-lens-image relationship satisfies the Gaussian thin lens equation. The second experiment demonstrates two-photon 'ghost' interference-diffraction. The experimental set up is similar to the image experiment, except that rather than a lens and an aperture it is a Young's double-slit (or a single-slit) inserted into the path of the signal beam. We could not find any interference (or diffraction) pattern behind the slit. Surprisingly, an interference (or diffraction) pattern is observed when scanning the detector in the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal.

Shih, Y. H.↗

Nonclassicality of vortex Airy beams in the Wigner representation

The Wigner distribution function (WDF) of a vortex Airy beam is calculated analytically. The WDF provides intuitive pictures of the intriguing features of vorticity in phase space. The nonclassical property of the vortex Airy beam and the Airy beam is analyzed through the negative parts of the WDF. The study shows that destructive interference of certain classical waves can mimic nonclassical lights such as those due to quantum effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geometric phases in a scattering process

The study of geometric phase in quantum mechanics has so far been confined to discrete (or continuous) spectra and trace-preserving evolutions. By considering only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace-preserving process. We explore the geometric phase in the scattering process by taking only the transmission process into account. We find that the geometric phase can be calculated by the same method as in unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Overcoming the diffraction limit by multi-photon interference: a tutorial

The nature of light, extending from the optical to the x-ray regime, is reviewed from a diffraction point of view by comparing field-based statistical optics and photon-based quantum optics approaches. The topic is introduced by comparing historical diffraction concepts based on wave interference, Dirac’s notion of photon self-interference, Feynman’s interference of space–time photon probability amplitudes, and Glauber’s formulation of coherence functions based on photon detection. The concepts are elucidated by a review of how the semiclassical combination of the disparate photon and wave concepts have been used to describe light creation, diffraction, and detection. The origin of the fundamental diffraction limit is then discussed in both wave and photon pictures. By use of Feynman’s concept of probability amplitudes associated with independent photons, we show that quantum electrodynamics, the complete theory of light, reduces in lowest order to the conventional wave formalism of diffraction. As an introduction to multi-photon effects, we then review fundamental one- and two-photon experiments and detection schemes, in particular the seminal Hanbury Brown–Twiss experiment. The formal discourse of the paper starts with a treatment of first-order coherence theory. In first order, the statistical optics and quantum optics formulations of coherence are shown to be equivalent. This is elucidated by a discussion of Zernike’s powerful theorem of partial coherence propagation, a cornerstone of statistical optics, followed by its quantum derivation based on the interference of single-photon probability amplitudes. The treatment is then extended to second-order coherence theory, where the equivalence of wave and particle descriptions is shown to break down. This is illustrated by considering two photons whose space–time probability amplitudes are correlated through nonlinear birth processes, resulting in entanglement or cloning. In both cases, the two-photon diffraction patterns are shown to exhibit resolution below the conventional diffraction limit, defined by the one-photon diffraction patterns. The origin of the reduction is shown to arise from the interference of two-photon probability amplitudes. By comparing first- and second-order diffraction, it is shown that the conventional first-order concept of partial coherence with its limits of chaoticity and first-order coherence has the second-order analogue of partial entanglement, with its limits corresponding to two entangled photons (“entangled biphotons”) and two cloned photons (“cloned biphotons”), the latter being second-order coherent. The concept of cloned biphotons is extended to the case of $n$ cloned photons, resulting in a $1/n$ reduction of the diffraction limit. In the limit of $n$th-order collective state are shown to propagate on particle like trajectories, reproducing the 0th-order ray-optics picture. These results are discussed in terms of the linearity of quantum mechanics and Heisenberg’s space–momentum uncertainty principle. Finally, a general concept of coherence based on photon density is developed that in first order is equivalent to the conventional wave-based picture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interference of biphotons upon parametric down-conversion in the field of biharmonic pumping

We report theoretical investigation of interference of biphotons emitted upon type-II collinear parametric down-conversion in the case of biharmonic pumping. Interference occurs when an optical or electronic shutter is used as an amplitude modulator in the experimental scheme. The phase of the interference is shown to depend on the time interval between the instant the shutter is opened and the instant corresponding to the maximum pump intensity. The main parameter affecting the visibility of the interference pattern is a time interval during which the shutter is open. (nonlinear optical phenomena)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-Hermitian Gyroscopes: Can Exceptional Points Increase Sensor Precision

We show that exceptional points in conservatively coupled systems can increase the quantum-limited precision of laser gyroscopes as a result of gain saturation, but that this requires recovery of the beat note by interference with an auxiliary mode, with consequences for the quantum and classical noise that depend on the particular recovery scheme.

David D Smith↗

Quantum Key Distribution with Temporal Coding of Time-Bin Qubits

In this study, we demonstrate the possibility of realizing the quantum key distribution system by temporal coding of time-bin qubits that are prepared and measured using unbalanced Mach-Zehnder interferometers. We also show that, to exclude a clear a priori identification of time-bin qubits with equal bases, their encoding with the symbols 0 and 1 can be accomplished by delaying one of them by half the clock interval. The uniqueness of measurements of qutrits in this algorithm is shown to be based on the ability of quantum particles in β-states to interfere with the probability amplitudes at the ports of the system interferometers, as well as the absence of collisions of signaling states of the qutrits in adjacent clock intervals. We describe a method for controlling such collisions, including those that are based on qubits prepared from quasi-one-photon coherent laser states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum complementarity of cavity photons coupled to a three-level system

Recently a device enabling the ultrafast all-optical control of the wave-particle duality of light was proposed [Ridolfo et al., Phys. Rev. Lett. 106, 013601 (2011)]. It is constituted by a three-level quantum emitter strongly coupled to a microcavity and can be realized by exploiting a great variety of systems ranging from atomic physics and semiconductor quantum dots to intersubband polaritons and Cooper pair boxes. Control pulses with specific arrival times, performing which-path and quantum-eraser operations, are able to destroy and recover interference almost instantaneously. Here we show that the coherence sudden death implies the sudden birth of a higher order correlation function storing coherence. Such storing enables coherence rebirth after the arrival of an additional suitable control pulse. We derive analytical calculations describing the all-optical control of the wave-particle duality and the entanglement-induced switch-off of the strong coupling regime. We also present analytical calculations describing a homodynelike method exploiting pairs of phase locked pulses with precise arrival times to probe the optical control of wave-particle duality of this system. Within such a method the optical control of wave-particle duality can be directly probed by just detecting the photons escaping the microcavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sample-Efficient Adaptive Calibration of Quantum Networks Using Bayesian Optimization

All physical systems employed for quantum information tasks must act as unbiased carriers of encoded quantum states. Ensuring such indistinguishability of information carriers is a major challenge in many quantum information applications, including advanced quantum communication protocols. For photons, the workhorses of quantum communication networks, it is difficult to obtain and maintain their indistinguishability because of environment-induced transformations and loss imparted by communication channels, especially in noisy scenarios. Conventional strategies to mitigate these transformations often require hardware or software overhead that is restrictive (e.g., adding noise), infeasible (e.g., on a satellite), or time-consuming for deployed networks. In this work we propose and develop resource-efficient Bayesian optimization techniques to rapidly and adaptively calibrate the indistinguishability of individual photons for quantum networks using only information derived from their measurement. To experimentally validate our approach, we demonstrate the optimization of Hong-Ou-Mandel interference between two photons-a central task in quantum networking- finding rapid, efficient, and reliable convergence towards maximal photon indistinguishability in the presence of high loss and shot noise. We expect our resource-optimized and experimentally friendly methodology will allow fast and reliable calibration of indistinguishable quanta, a necessary task in distributed quantum computing, communications, and sensing, as well as for fundamental investigations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Deeper Look at the Fundamentals of Heterodyne Detection Requirements

We generally accept the experimentally observed criteria for heterodyne detections that the two waves that are mixed must (i) be collinear, (ii) have matched wave fronts and (iii) cannot be orthogonally polarized. We have not found in the literature adequate physical explanations for these requirements. The purpose of this paper is to find deeper physical understanding of the coherent heterodyne detection processes that could lead to better coherent laser radar system designs1. We find that there are a number of unresolved paradoxes in classical and quantum optics regarding the definitions and understanding of the "interference" and "coherence" properties of light, which are attributed as essentially due to inherent properties of the EM waves. A deeper exploration indicates that it is the various quantum mechanical properties of the detecting material dipoles that make light detectable (visible, or measurable) to us. Accordingly, all the properties that we generally attribute to only light, are in reality manifestations of collective properties of dipole-light interactions. "Interference" and "coherence" can be better understood in terms of this mutual interaction, followed by energy absorption by the dipoles from EM wave fields, manifesting in some measurable transformation of the detecting dipoles. Light beams do not interfere by themselves. The superposition effects due to light beams become manifest through the response characteristics of the detecting dipoles. In this paper, we will show some preliminary expe rimental results that clearly demonstrate that the heterodyning wave fronts have quantitative degradation in signal generation as the angle between them deviates from perfect collinearity. Subsequently, we will propose a hypothesis for this behavior. We will present experimental data establishing that the so called incoherent light can be detected through heterodyne mixing as long as the pulse length contained in the "incoherent" light is longer than the response time of the detector. We will also present a correspondingly better interpretation of two distinguishable coherence properties, temporal coherence and spectral coherence. Our investigation provides a deeper insight into how to rela x various system requirements for heterodyne detection and accordingly develop systems that are simpler, more reliable and lower in cost. Also, we believe that engineering of detector architecture by appropriately modifying dipole behavior using emerging nanotechnology to optimize heterodyne efficiency will be advantageous.

Roychoudhuri, Chandrasekhar↗

Chromatic dispersion effects in ultra-low coherence interferometry

We consider the properties of an interference signal shift from zero-path-difference position in the presence of an uncompensated dispersive layer in one of the interferometer arms. It is experimentally shown that in using an ultra-low coherence light source, the formation of the interference signal is also determined by the group velocity dispersion, which results in a nonlinear dependence of the position of the interference signal on the geometrical thickness of the dispersive layer. The discrepancy in the dispersive layer and compensator refractive indices in the third decimal place is experimentally shown to lead to an interference signal shift that is an order of magnitude greater than the pulse width. (interferometry)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum calculations of the carrier mobility: Methodology, Matthiessen's rule, and comparison with semi-classical approaches

We discuss carrier mobilities in the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a method for the extraction of the mobility that is free from contact resistance contamination and with minimal needs for ensemble averages. We focus on silicon thin films as an illustration, although the method can be applied to various materials such as semiconductor nanowires or carbon nanostructures. We then introduce a new paradigm for the definition of the partial mobility μ{sub M} associated with a given elastic scattering mechanism “M,” taking phonons (PH) as a reference (μ{sub M}{sup −1}=μ{sub PH+M}{sup −1}−μ{sub PH}{sup −1}). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [e.g., surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We discuss the reasons for these discrepancies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Heterodyne coherent anti-Stokes Raman scattering by the phase control of its intrinsic background

We demonstrate the use of femtosecond laser pulse shaping for precise control of the interference between the coherent anti-Stokes Raman scattering (CARS) signal and the coherent nonresonant background generated within the same sample volume. Our technique is similar to heterodyne detection with the coherent background playing the role of the local oscillator field. In our experiment, we first apply two ultrashort (near-transform-limited) femtosecond pump and Stokes laser pulses to excite coherent molecular oscillations within a sample. After a short and controllable delay, we then apply a laser pulse that scatters off of these oscillations to produce the CARS signal. By making fine adjustments to the probe field spectral profile, we vary the relative phase between the Raman-resonant signal and the nonresonant background, and we observe a varying spectral interference pattern. These controlled variations of the measured pattern reveal the phase information within the Raman spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ultrafast laser control of backward superfluorescence towards standoff sensing

We study infrared backward cooperative emission in a rubidium vapor induced by ultrafast two-photon optical excitations. The laser coherent control of the backward emission is demonstrated by using a pair of 100 fs pulses with a variable time delay. The temporal variation (quantum beat) of the backward beam intensity due to interference of atomic transitions in the rubidium atomic level system 5S-5P-5D is produced and controlled. Based on the obtained experimental results, we discuss possible applications of the developed approach for creation of an effective “guide star” in the sodium atomic layer in the upper atmosphere (mesosphere)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Method of Blind Detection of Ultrawideband Chaotic Radio Pulses on the Background of Interpulse Interference

The problem of blind detection of ultrawideband (UWB) microwave chaotic radio pulses transmitted via a multipath propagation channel has been considered. Based on the results of measurements of the UWB chaotic radio pulse propagation in a real wireless channel, a method of their detection not subject to the influence of interpulse interference is proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interference effects in the formation of the light bullet spectrum under axicon focusing

Specific features of the anti-Stokes band of the light bullet supercontinuum spectrum under filamentation of 1900-nm femtosecond pulses, focused by an axicon in fused silica and calcium fluoride, have been experimentally, numerically, and analytically investigated. It is found that the formation of two or more light bullets in a filament leads to modulation of spectral components’ intensity. The oscillation period of spectral components, defined as the wavelength interval between adjacent intensity minima, decreases with decreasing their wavelength. On a logarithmic scale, the relative change in the oscillation period in the spectrum is proportional to the spectral component wavelength and is independent of the pulse energy and the position of the light bullet formation region in the filament. It is established that the modulation in the spectrum is due to the interference of the broadband supercontinuum emitted by light bullets, and its period decreases with increasing interval between them. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamics of ionisation and entanglement in the 'atom + quantum electromagnetic field' system

The dynamics of a model Rydberg atom in a strong nonclassical electromagnetic field is investigated. The field-induced transitions to the continuum involving different numbers of photons (with intermediate states in the discrete spectrum) are taken into account and the specific features of ionisation in 'squeezed' field states are considered in comparison with the case of classical light. A significant decrease in the ionisation rate is found, which is caused by the interference stabilisation of the atomic system. The entanglement of the atomic and field subsystems, the temporal dynamics of the correlations found, and the possibility of measuring them are analysed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Optical Extinction-Based 3D Nano-Imaging of WS 2 on Gold

Broad band nano-extinction images recorded in the tip-enhanced optical spectroscopy geometry track the 3D topography of a single layer of WS 2 on Au substrate. The described nano-optical method is complementary to conventional AFM and offers additional information about the buried material-metal interface that is not accessible using conventional topographic imaging. Beyond 3D optical imaging, we observe large variations in the junction plasmon resonance on the nanoscale. The latter is important to understand and account for in tip-enhanced Raman and photoluminescence studies that target low-dimensional materials specifically. Further, our observations and (coherent) optical scattering-based method are also relevant to emerging efforts aimed at exploring strong coupling and Fano interferences in hybrid plasmonic-low dimensional quantum material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗