We theoretically discuss one-photon and two-photon double-slit interferences for spontaneous and stimulated parametric down-conversions. We show that the two-photon sub-wavelength interference can exist in a general spontaneous parametric down-conversion (SPDC) for both type I and type II crystals. We propose an alternative way to observe sub-wavelength interference by a joint-intensity measurement which occurs for only type I crystal in a higher gain of SPDC. When a signal beam injects into the crystal, it may create two interference patterns by two stimulated down-converted beams, showing no sub-wavelength interference effect.
Recent work using spontaneous parametric down-conversion (SPDC) has made possible investigations of the Einstein-Podolsky-Rosen paradox in its original (position-momentum) form. We propose an experiment that uses SPDC photon pairs to measure through which slit a photon passes while simultaneously observing double-slit interference.
We study the effect of quantum interference on the structure and properties of spontaneous and stimulated transitions in a degenerate V-type three-level atom with an arbitrary total momentum of each state. Explicit expressions for the factors in the terms of the relaxation operator and stimulated transition operator with account of quantum interference effects are obtained. It has been demonstrated that the condition for the dipole transition moments to be parallel is insufficient and for conventional atoms the interference cross terms are zeros for both operators. The conditions when quantum …
In a recent paper [I.I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was shown that one can completely identify the nonclassicality of single- and two-mode Gaussian states by means of certain nonclassicality witnesses which are based on intensity moments up to the third order of optical fields, provided that an appropriate coherent displacement is applied to a given Gaussian state. Here, we utilize a mathematical equivalence between the description of the coherent displaced Gaussian states generated in the spontaneous parametric processes and the Gaussian states generated in the corresponding…
Third-order parametric down-conversion (TOPDC) describes a class of nonlinear interactions in which a pump photon is converted into a photon triplet. This process can occur spontaneously, or it can be stimulated by seeding fields. In the former case, one typically has the generation of non-Gaussian states of light. In the latter, the situation is more variegated, for stimulated TOPDC (StTOPDC) can be implemented in many ways, depending on the number and properties of the seeding fields. Here we show that StTOPDC can be exploited for the generation of quantum correlated photon pairs. We examine…
The intensity transverse profile of the light produced in the process of stimulated down-conversion is derived. A quantum-mechanical treatment is used. We show that the angular spectrum of the pump laser can be transferred to the stimulated down-converted beam, so that images can also be transferred from the pump to the down-converted beam. We also show that the transfer can occur from the stimulating beam to the down-converted one. Finally, we study the process of diffraction through an arbitrarily shaped screen. For the special case of a double-slit, the interference pattern is explicitly ob…
Spontaneous parametric down conversion has been largely exploited as a tool for absolute calibration of photon counting detectors, photomultiplier tubes or avalanche photodiodes working in Geiger regime. In this work we investigate the extension of this technique from very low photon flux of photon counting regime to the absolute calibration of analog photodetectors at higher photon flux. Moving toward higher photon rate, i.e. at high gain regime, with the spontaneous parametric down conversion shows intrinsic limitations of the method, while the stimulated parametric down conversion process, …
We report on four-wave mixing in coupled photonic crystal nano-cavities on a silicon-on-insulator platform. Three photonic wire cavities are side-coupled to obtain three modes equally separated in energy. The structure is designed to be self-filtering, and we show that the pump is rejected by almost two orders of magnitudes. We study both the stimulated and the spontaneous four-wave mixing processes: owing to the small modal volume, we find that signal and idler photons are generated with a hundred-fold increase in efficiency as compared to silicon micro-ring resonators.
We show how stimulated parametric processes can be employed in experiments on beyond the diffraction limit to overcome the problem of low visibility obtained by using spontaneous down conversion operating in the high gain regime. We further show enhancement of the count rate by several orders when stimulated parametric processes are used. Both the two photon counts and the visibility can be controlled by the phase of the stimulating coherent beam.
We report on an experiment demonstrating the conservation of orbital angular momentum in stimulated down-conversion. The orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion, but it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.
Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.
The general expressions for the time development of the ensemble averages of E^- and E^-E^+ are found for N two level molecules (TLMs) interacting with a single mode electromagnetic field. The TLMs are assumed to be at equivalent mode positions in the field. In the main body of the paper, the general results are then simplified by assuming that all TLMs are in the up state at time 0. Examples of spontaneous emission behavior including both Super Radiant behavior and emission suppression are shown in Appendix E while stimulated emission with all TLMs initially in the lower state is examined in …
Nanoscale semiconductor lasers have been developed recently using either metal, metallo-dielectric or photonic crystal nanocavities. While the technology of nanolasers is steadily being deployed, their expected performance for on-chip optical interconnects is still largely unknown due to a limited understanding of some of their key features. Specifically, as the cavity size is reduced with respect to the emission wavelength, the stimulated and the spontaneous emission rates are modified, which is known as the Purcell effect in the context of cavity quantum electrodynamics. This effect is expec…
Do the wavepacket-size of free-electron wavefunction and its history have physical effect in its interaction with light? Here we answer this problem by analyzing a QED model, considering both spontaneous and stimulated emission of quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission/absorption of photons has a dependence on wavepacket size that decays when it exceeds the interacting radiation wavelength, consistently and complementarily with Schrodinger equation analysis of wavepacket acceleration in classical electromagnetic field. Furthermore…
Single-photon stimulated four wave mixing (StFWM) processes have great potential for photonic quantum information processing, compatible with optical communication technologies and integrated optoelectronics. In this paper, we demonstrate single-photon StFWM process in a piece of optical fiber, with seeded photons generated by spontaneous four wave mixing process (SpFWM). The effect of the single-photon StFWM is confirmed by time-resolved four-photon coincidence measurement and variation of four-photon coincidence counts under different seed-pump delays. According to the experiment results, th…
Spontaneous parametric down conversion (SPDC) has been largely exploited as a tool for absolute calibration of photon-counting detectors, i.e detectors registering very small photon fluxes. In [J. Opt. Soc. Am. B 23, 2185 (2006)] we derived a method for absolute calibration of analog detectors using SPDC emission at higher photon fluxes, where the beam is seen as a continuum by the detector. Nevertheless intrinsic limitations appear when high-gain regime of SPDC is required to reach even larger photon fluxes. Here we show that stimulated parametric down conversion allow one to avoid this limit…
Scattering of a short (much shorter then the spontaneous lifetime) laser pulse has been considered in a dense resonant medium subject to local field effects. The system was studied in the limit of Hartree-Fock approximation for Bogolubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations for reduced density operators. A closed set of equations for atomic and field density operators was derived to describe stimulated scattering of radiation. Numerically as well as theoretically the capability of multicomponent spectrum with maximums multiple to Rabi frequency has been demonstrated. Relativ…
Using a neutron double-slit setup, we construct a quantum bit commitment scheme in which time development of quantum states plays an essential role. Our scheme evades the widely accepted no-go theorem by the fact that it is neither possible to stop the time evolution of spreading wave packets, nor is it possible to evolve them backward in time. Moreover, for unstable particles such as neutrons, one cannot delay detecting their positions indefinitely, or they would disintegrate spontaneously and escape detection. We find that using non-stationary states instead of stationary ones, unconditional…
We propose the use of stimulated Raman adiabatic passage (STIRAP) to offer a fast high fidelity method of performing SU(2) rotations on spinor Bose Einstein condensates (BEC). Past demonstrations of BEC optical control suffer from difficulties arising from collective enhancement of spontaneous emission and inefficient two-photon transitions originating from selection rules. We present here a novel scheme which allows for arbitrary coherent rotations of two-component BECs while overcoming these issues. Numerical tests of the method show that for BECs of \ce{^{87}Rb} with up to $ 10^4 $ atoms an…
In spontaneous emission an atom in an excited state undergoes a transition to the ground state and emits a single photon. Associated with the emission is a change of the atomic momentum due to photon recoil. Photon emission can be modified close to surfaces and in cavities. For an ion, localized in front of a mirror, coherence of the emitted resonance fluorescence has been reported. In free space experiments demonstrated that spontaneous emission destroys motional coherence. Here we report on motional coherence created by a single spontaneous emission event close to a mirror surface. The coher…
Quantum state tomography (QST) is a universal tool for the design and optimization of entangled-photon sources. It typically requires single-photon detectors and coincidence measurements. Recently, it was suggested that the information provided by the QST of photon pairs generated by spontaneous parametric down-conversion could be obtained by exploiting the stimulated version of this process, namely difference frequency generation. In this protocol, so-called "stimulated-emission tomography" (SET), a seed field is injected along with the pump pulse, and the resulting stimulated emission is mea…
Here we present a semiclassical analysis of spontaneous and stimulated radiative emission from unmodulated and optically-modulated electron quantum wavepackets. We show that the radiative emission/absorption and corresponding deceleration/acceleration of the wavepackets depend on the controllable 'history-dependent' wavepacket size. The characteristics of the radiative interaction when a wavepacket of size (duration) is short relative to the radiation wavelength, are close to the predictions of the classical point-particle modeling. On the other hand, in the long-sized wavepacket limit, the in…
Vacuum-stimulated Raman scattering in strongly coupled atom-cavity systems allows one to generate free-running single photon pulses on demand. Most properties of the emitted photons are well defined, provided spontaneous emission processes do not contribute. Therefore, electronic excitation of the atom must not occur, which is assured for a system adiabatically following a dark state during the photon-generation process. We experimentally investigate the conditions that must be met for adiabatic following in a time-of-flight driven system, with atoms passing through a cavity and a pump beam or…
We present a new method for the spectral characterization of pulsed twin beam sources in the high gain regime, using cascaded stimulated emission. We show an implementation of this method for a ppKTP spontaneous parametric down-conversion source generating up to 60 photon pairs per pulse, and demonstrate excellent agreement between our experiments and our theory. This work enables the complete and accurate experimental characterization of high gain effects in parametric down conversion, including self and cross-phase modulation. Moreover, our theory allows the exploration of designs with the g…
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of stimulated Raman adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heati…
Stimulated Raman interaction of a classically pumped single three-level $Λ$-type atom in a resonator cavity featuring both radiative and unwanted losses is studied. It is shown that in the regime of stimulated adiabatic Raman passage the excited outgoing wave packet of the cavity-assisted electromagnetic field can be prepared in a one-photon Fock state with high efficiency. In this regime, the spatio-temporal shape of the wave packet does not depend on the interaction shape of the pump field, provided that the interaction of the atom with the pump is time-delayed with respect to the interactio…
We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interf…
The existence of higher order entanglement in the stimulated and spontaneous Raman processes is established using the perturbative solutions of the Heisenberg equations of motion for various field modes that are obtained using the Sen-Mandal technique and a fully quantum mechanical Hamiltonian that describes the stimulated and spontaneous Raman processes. Specifically, the perturbative Sen-Mandal solutions are exploited here to show the signature of the higher order two-mode and multi-mode entanglement. In some special cases, we have also observed higher order entanglement in the partially spo…
We discuss an experimental setup where two laser-driven atoms spontaneously emit photons and every photon causes a ``click'' at a point on a screen. By deriving the probability density for an emission into a certain direction from basic quantum mechanical principles we predict a spatial interference pattern. Similarities and differences with the classical double-slit experiment are discussed.
We consider ultracold atoms in a far detuned optical lattice orientated across a high-Q optical resonator. Applying an external driving laser to the atoms, which is red detuned from the cavity mode by one vibrational quantum, induces cavity-enhanced sideband cooling. For a dense and cold enough atomic ensemble we predict an oscillation threshold for optical Raman sideband lasing concurrent with coherent matter-wave amplification. Above this oscillation threshold photons and atoms in the lowest band are dominantly created pairwise via stimulated emission with a strong suppression of competing s…
A detailed analysis of the stimulated parametric down-conversion (PDC) process is performed to investigate the effects of the spatiotemporal degrees of freedom. The analysis provides information that would be useful for PDC-based metrology applications. Using a Wigner functional approach, we obtain the parametric down-converted state as the Bogoliubov transformed input state, in terms of Bogoliubov kernel functions. The result is used to consider the case for a coherent state seeding stimulated PDC. We also compute the background which is obtained from spontaneous PDC.
We propose experimental measurements of the logarithmic negativity, which quantifies quantum correlations using Gouy phase measurements in an asymmetric double-slit interference experiment for twin photons. This is possible because both quantities have analogous dependence with the spatial confinement by the slits and enables one to manipulate the portion of entanglement by the Gouy phase. In order to obtain those measurements, we need to work in a regime where the position correlations between particles are strong, therefore we investigate such correlations for biphotons. Since we would like …
Working in the limit in which the localization length scale is large compared to other relevant length scales we examine three experimental situations with the continuous spontaneous localization (CSL) model---a well-motivated alternative to standard quantum theory. These are the two-slit experiment; scattering from a potential barrier; and the release of two non-interacting particles simultaneously from a potential trap. In each case we calculate the diagonal part of the time evolved density matrix giving a probability density function over final measured states. The case of the two-slit expe…
We report an experimental implementation of the minimal Deutsch algorithm in an optical setting. In this version, a redundancy is removed from the most famous form of the algorithm. The original version involves manipulation of two qubits, while in its minimal version, only one qubit is used. Our qubit is encoded in the transversal spatial modes of a spontaneous parametric down-converted signal photon, with the aid of a double slit, with the idler photon playing a crucial role in creating a heralded single photon source. A spatial light modulator (SLM) is programmed to physically generate one-…
We probe the principle of complementarity by performing a double-slit experiment based on entangled photons created by spontaneous parametric down-conversion from a pump mode in a TEM01-mode. Our setup brings out the need for a careful selection of the signal-idler photon pairs for our study of visibility and distinguishability. Indeed, when the signal photons interfering at the double-slit belong to this double-hump mode we obtain almost perfect visibility of the interference fringes and no "which-slit" information is available. However, when we break the symmetry between the two maxima of th…
Warm rubidium vapours are known to be a versatile medium for a variety of experiments in atomic physics and quantum optics. Here we present experimental results on producing the frequency converted light for quantum applications based on spontaneous and stimulated processes in rubidium vapours. In particular, we study the efficiency of spontaneously initiated stimulated Raman scattering in the Λ-level configuration and conditions of generating the coherent blue light assisted by multi-photon transitions in the diamond-level configuration. Our results will be helpful in search for new types of …
We present a quantum optics approach for describing stimulated parametric down conversion in the two type-I crystal "sandwich" configuration, which allows for parametric interaction of vector vortex beams. We analyze the conditions for which phase conjugation of the seed vector beam occurs. We then use two strategies for defining generalized Stokes parameters to describe phase conjugation of vector vortex beams. These allow for geometrical representations, such as higher-order Poincaré spheres. Our results are useful for description and design of stimulated and spontaneous parametric down conv…
We investigate the performance of a certain nonclassicality identifier, expressed via integrated second-order intensity moments of optical fields, in revealing bipartite entanglement of quantum-optical frequency combs (QOFCs), which are generated in both spontaneous and stimulated parametric down-conversion processes. We show that, by utilizing that nonclassicality identifier, one can well identify the entanglement of the QOFC directly from the experimentally measured intensity moments without invoking any state reconstruction techniques or homodyne detection. Moreover, we demonstrate that the…
We compute the output of multimode cavity-enhanced spontaneous parametric down-conversion (SPDC) for sub-threshold, but otherwise arbitrary, gain. We find analytic Bogoliubov transformations that allow us to calculate arbitrary field correlation functions, including the second-order intensity correlation function $G^{(2)}(T)$. The results show evidence of increased coherence due to stimulated SPDC. We extend an earlier model [Lu and Ou, Phys. Rev. A, 62, 033804 (2000)] to arbitrary gain and finesse, and show the extension gives accurate results in most scenarios. The results will allow simple,…
It is known that photon pairs generated from pulse-pumped spontaneous parametric processes can be described by independent temporal modes and form a multi-temporal mode entangled state. However, the exact form of the temporal modes is not known even though the joint spectral intensity of photon pairs can be measured by the method of stimulated emission tomography. In this paper, we describe a feedback-iteration method which, combined with the stimulated emission method, can give rise to the exact forms of the independent temporal modes for the temporally entangled photon pairs.
We analyze the error in trapped-ion, hyperfine qubit, quantum gates due to spontaneous scattering of photons from the gate laser beams. We investigate single-qubit rotations that are based on stimulated Raman transitions and two-qubit entangling phase-gates that are based on spin-dependent optical dipole forces. This error is compared between different ion species currently being investigated as possible quantum information carriers. For both gate types we show that with realistic laser powers the scattering error can be reduced to below current estimates of the fault-tolerance error threshold…
We characterise the spontaneous emission time and direction from small numbers of dipole-coupled two-level atoms (2LAs) in the presence of incident fields. We show how to use adiabatic passage to admit population transfer between states in the one-quantum subspace for two and three 2LAs. Our method is a multi-atom generalisation of stimulated-Raman-adiabatic-passage (STIRAP) for a single multi-level atom. We use numerical results to justify an ansatz that enables us to give analytical expressions for the directional emission which depends on the incident fields. Our results admit a characteris…
We have measured antinormally ordered Hanbury-Brown--Twiss correlations for coherent states of electromagnetic field by using stimulated parametric down-conversion process. Photons were detected by stimulated emission, rather than by absorption, so that the detection responded not only to actual photons but also to zero-point fluctuations via spontaneous emission. The observed correlations were distinct from normally ordered ones as they showed excess positive correlations, i.e., photon bunching effects, which arose from the thermal nature of zero-point fluctuations.
We show that the two-photon transition rates of quantum dots coupled to nanocavities are enhanced by up to 8 orders of magnitude relative to quantum dots in bulk host. We then propose how to take advantage of this enhancement to implement coherent quantum dot excitation by two-photon absorption, entangled photon pair generation by two-photon spontaneous emission, and single-photon generation at telecommunication wavelengths by two-photon stimulated and spontaneous emission.
We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: $\frac{d}{dt} ρ_{ij} =-\frac{i}{\hbar}[H,ρ]_{ij}-ρ_{ij}/τ_{ij}$. Different from other collapse models, the collapsing scale $τ_{ij}$ here does not contain a universal parameter, but is specified by the two states $| i\rangle $ and $ | j\rangle$: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then $τ_{ij}$ is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\…
We study two-photon excitation of Rydberg states of atoms under stimulated adiabatic passage with delayed laser pulses. We find that the combination of strong interaction between the atoms in Rydberg state and the spontaneous decay of the intermediate exited atomic state leads to the Rydberg excitation of precisely one atom within the atomic ensemble. The quantum Zeno effect offers a lucid interpretation of this result: the Rydberg blocked atoms repetitively scattering photons effectively monitor a randomly excited atom which therefore remains in the Rydberg state. This system can be used for …
We study the process of seeded, or stimulated, third-order parametric down-conversion, as an extension of our previous work on spontaneous parametric downconversion (TOSPDC). We present general expressions for the spectra and throughputs expected for the cases where the seed field or fields overlap either only one or two of the TOSPDC modes, and also allow for both pump and seed to be either monochromatic or pulsed. We present a numerical study for a particular source design, showing that doubly-overlapped seeding can lead to a considerably greater generated flux as compared with singly-overla…
Compact silicon integrated devices, such as micro-ring resonators, have recently been demonstrated as efficient sources of quantum correlated photon pairs. The mass production of integrated devices demands the implementation of fast and reliable techniques to monitor the device performances. In the case of time-energy correlations, this is particularly challenging, as it requires high spectral resolution that is not currently achievable in coincidence measurements. Here we reconstruct the joint spectral density of photons pairs generated by spontaneous four-wave mixing in a silicon ring resona…
Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy phase shifts (D. Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)) allowing for a non-destructive manipulation of photonic quantum states. In this work we exploit the relation between phase space correlations of biphotons produced by spontaneously parametric down conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double slit setup. Using an analytical approach based on a double-gaussian approximation for type-I SP…
We find an interference effect for electron-phonon interactions in coupled semiconductor quantum dots that can dominate the nonlinear transport properties even for temperatures close to zero. The intradot electron tunnel process leads to a `shake up' of the phonon system and is dominated by a double-slit-like interference effect of spontaneously emitted phonons. The effect is closely related to subradiance of photons (Dicke effect) in a laser-trapped two-ion system and explains the oscillations in the nonlinear current-voltage characteristics of coupled dots observed recently.
