We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N= 10^5 particles generated by a quantum-injected optical parametric amplifier (QI-OPA), seeded by a single-photon belonging to an EPR entangled pair, is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize a Macroscopic Quantum Superposition (MQS) involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in space-like separated distant places.
Density matrices of pure multiphoton Fock polarization states and of arising from them reduced density matrices of mixed states are expressed in similar ways in terms of matrices of correlators defined as averaged products of equal numbers of creation and annihilation operators. Degree of entanglement of considered states is evaluated for various combinations of parameters of states and character of their reduction.
In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement.
We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different models of inefficient detection: a beam splitter of a small reflectivity located in front of a perfect detector and a Weierstrass transform applied to the unperturbed measurement outcomes. We explicitly give an operator which describes the coherent action of the filters in the realistic experimental conditions. The filtered states may find applications in qua…
Multiphoton heralding generates large-amplitude squeezed Schrödinger cat states and parity-selective Fock superpositions from squeezed vacuum via an OPA
In this paper we discuss the quantum properties for superposition of squeezed displaced number states against multiphoton Jaynes-Cummings model (JCM). In particular, we investigate atomic inversion, photon-number distribution, purity, quadrature squeezing, Mandel $Q$ parameter and Wigner function. We show that the quadrature squeezing for three-photon absorption case can exhibit revivals and collapses typical to those occurring in the atomic inversion for one-photon absorption case. Also we prove that for odd number absorption parameter there is a connection between the evolution of the atomic…
Nonlinear dynamics of establishment of electron-hole coherent superpositions states in graphene by multiphoton resonant excitation of interband transitions in laser fields is considered. The single-particle time dependent density matrix for such a quantized system is calculated in the multiphoton resonant approximation. The dependence of Rabi oscillations of Fermi-Dirac sea in graphene on the time, momentum, and photon number at multiphoton laser-excitation is analyzed.
A theory of electron detachment from atoms or negative ions by a superposition of a static and a laser (or, more generally, ac) fields, parallel to each other, is developed in the case when the photon energy and the field amplitude are much less than the detachment energy and intra-ion field, respectively. Simple analytical results together with their validity conditions are obtained. Several qualitatively different regimes of detachment have been identified. Applications of the present theory to electron emission from metal and semiconductor surfaces and from photosynthetic bio-complexes are …
The coherent control of electron beams and ultrafast electron wave packets dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Bot…
We derive a generalized master equation for multiphoton pulses interacting with multiple emitters in a waveguide-quantum electrodynamics system where the emitter frequency can be modulated and the effects of non-guided modes can also be considered. Based on this theory, we can calculate the real-time dynamics of an array of interacting emitters driven by an incident photon pulse which can be vacuum, a coherent state, a Fock state or their superpositions. Moreover, we also derive generalized input-output relations to calculate the reflectivity and transmissivity of this system. We can also calc…
It has been shown that there are not only transverse but also longitudinal couplings between microwave fields and a superconducting qubit with broken inversion symmetry of the potential energy. Using multiphoton processes induced by longitudinal coupling fields and frequency matching conditions, we design a universal algorithm to produce arbitrary superpositions of two-mode photon states of microwave fields in two separated transmission line resonators, which are coupled to a superconducting qubit. Based on our algorithm, we analyze the generation of evenly-populated states and NOON states. Co…
We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, w…
The multiphoton quantum superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The effect can be greatly enhanced if the mirror is part of a cavity structure or is used within an optical interferometer. The overall process will realize an Entangled Macroscopic Quantum Superposition involving a ''microscopic'' singe-photon state of polarization and the coherent ''macroscopic'' displacement of the BEC structure acting in space-l…
Based on heralded interference on a six-port Mach-Zehnder interferometer, we propose protocols to generate a series of multiphoton states in primary output port, by injecting a coherent state in primary input port and two Fock states in two ancillary input ports, and measuring two Fock states in two ancillary output ports. Only manipulating at the single-photon level (i.e, |0> or |1>) in all ancillary ports, we generate sixteen types (six categories) of multiphoton nonclassical states, whose state vectors are unified as superposition of a new coherent state, a single-photon added coherent stat…
The interference of quanta lies at the heart of quantum physics. The multipartite generalization of single-quanta interference creates entanglement, the coherent superposition of states shared by several quanta. Entanglement allows non-local correlations between many quanta and hence is a key resource for quantum information technology. Entanglement is typically considered to be essential for creating non-local correlations, manifested by multipartite interference. Here, we show that this is not the case and demonstrate multiphoton non-local quantum interference without entanglement of any int…
With the Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition, and researched the effect of initial state superposition coefficient $C_{1}$, the transition photon number $N$, the quantum discord $δ$ and the nonlinear coefficient $χ$ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, and obtained some results, which should have been used in quantum computing and quantum information.
Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric set-up to simultaneously measure the…
The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an $N$-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of the cavity mode involving the vacuum and an $M$-Fock state, with $M<N$. Besides, driving the cavity mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {$|0\rangle,|1\rangle,..., |N-1\rangle$} can be populated, i.e., we show how to implement a Fock state …
This Letter demonstrates control over multiphoton absorption processes in driven two-level systems, which include for example superconducting qubits or laser-irradiated graphene, through spectral shaping of the driving pulse. Starting from calculations based on Floquet theory, we use differential evolution, a general purpose optimization algorithm, to find the Fourier coefficients of the driving function that suppress a given multiphoton resonance in the strong field-regime. We show that the suppression of the transition probability is due to the coherent superposition of high-order Fourier ha…
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more genera…
"Schrodinger's cat" is a gedankenexperiment intended to highlight conceptual difficulties in the interpretation of quantum mechanics. The generation of 'cat-like' states is central to numerous quantum information protocols. In particular, much attention has been drawn by states containing N photons in a superposition of all being in one of two designated modes. These maximally path entangled states, known as 'NOON' states, exhibit enhanced phase sensitivity and allow reaching the fundamental quantum limit of precision measurement. Such states could also be used for obtaining 'super-resolution'…
As typically implemented, single photon sources cannot be made to produce single photons with high probability, while simultaneously suppressing the probability of yielding two or more photons. Because of this, single photon sources cannot really produce single photons on demand. We describe a multiplexed system that allows the probabilities of producing one and more photons to be adjusted independently, enabling a much better approximation of a source of single photons on demand.
We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quit…
Multiphoton quantum simulation of the generalized Hopfield memory model
Università degli Studi di Salerno（萨莱诺大学）；Institute of Nanotechnology of the National Research Council of Italy, CNR-NANOTEC, Rome Unit（意大利国家研究委员会纳米技术研究所罗马分部）；INFN, Sezione di Napoli, Gruppo Collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所）；Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所混合量子网络中心）；Department of Physics, Sapienza University of Rome（罗马大学物理系）；Quantum Lab, Boehringer Ingelheim（勃林格殷格翰量子实验室）；Institute of Nanotechnology of the National Research Council of Italy, CNR-NANOTEC, Lecce Central Unit（意大利国家研究委员会纳米技术研究所莱切中央分部）；Center for Life Nano- & Neuro-Science, Italian Institute of Technology, IIT, Rome（意大利理工学院生命纳米与神经科学中心）
Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states'', we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing non degenerate and degenerate multiphoton processes. We determine the coherent…
We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be expressed by the classical Gegenbauer polynomials. This new …
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED has been reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modif…
We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schrödinger cat states, defined as orthonormalized eigenstates of $k$-th powers of nonlinear $f$-oscillator annihilation operators, with $f$ of hypergeometric type. These "$k$-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states $|z_l\rangle, l=0,1,\dots,k-1$, with $z_l=z e^{2πi l/k}$ a $k$-th root of $z^k$, and they interpolate between number and coherent states. This fact motiva…
Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these cla…
Thermal states of light are widely used in quantum optics for various quantum phenomena testing. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states become of much significance. Therefore, in this work we present a technique for statistical parameter estimation of multimode multiphoton subtracted thermal states of light, which can be used for multimode photon annihilation test.
We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton "tail" are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee…
We propose a scheme for generation of arbitrary coherent superposition of vortex states in Bose-Einstein condensates (BEC) using the orbital angular momentum (OAM) states of light. We devise a scheme to generate coherent superpositions of two counter-rotating OAM states of light using known experimental techniques. We show that a specially designed Raman scheme allows transfer of the optical vortex superposition state onto an initially non-rotating BEC. This creates an arbitrary and coherent superposition of a vortex and anti-vortex pair in the BEC. The ideas presented here could be extended t…
We recently proposed a scheme for the creation of coherent superpositions of vortex states in Bose-Einstein condensates (BEC) using orbital angular momentum (OAM) states of light [Phys. Rev. Lett. 95, 173601 (2005)]. Here we discuss further technical details of the proposal, provide alternative, time-reversal-symmetric scheme for transfer of a superposition of OAM states of light to the BEC via a procedure analogous to the traditional STimulated Raman Adiabatic Passage (STIRAP) technique, and discuss an alternative trap configuration conducive for sustaining large charge vortices. Superpositio…
We experimentally demonstrate storage and on-demand release of phase-sensitive, photon-number superposition states of the form $α|0\rangle + βe^{iθ} |1\rangle$ for an optical quantized oscillator mode. For this purpose, we introduce a phase-probing mechanism to a storage system composed of two concatenated optical cavities, which was previously employed for storage of phase-insensitive single-photon states [Phys. Rev. X 3, 041028 (2013)]. This is the first demonstration of all-optically storing highly nonclassical and phase-sensitive quantum states of light. The strong nonclassicality of the s…
The measurement of the tunneling time in attosecond experiments, termed attoclock, triggered a hot debate about the tunneling time, the role of time in quantum mechanics, where the interaction with the laser pulse involves two regimes of a different character, the multiphoton and the tunneling (field-) ionization. In the adiabatic field calibration, one of us (O. K.) developed in earlier works a real tunneling time model and showed that the model fits well to the experimental data of Landsmann et al. (Optica {\bf 1}, 343 2014). In the present work, it is shown that the model explains the exper…
In the framework of the non-secular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions have been obtained beyond the rotating wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong…
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfections such as partial distinguishability of interfering photons. Here we introduce a method where appropriate design of the modal structure of input photons can alleviate deleterious effects caused by another, experimentally inaccessible degree of freedom. This result is accompanie…
Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer, and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show the first quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by in…
In this paper we investigate the quantum phase properties for the coherent superposition states (Schrödinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner ($W$) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the $W$ function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore…
A method for generating a mesoscopic superposition state of the collective spin variable of a gas of atoms is proposed. The state consists of a superposition of the atomic spins pointing in two slightly different directions. It is obtained by using off resonant light to carry out Quantum Non Demolition Measurements of the spins. The relevant experimental conditions, which require very dense atomic samples, can be realized with presently available techniques. Long-lived atomic superposition states may become useful as an off-line resource for quantum computing with otherwise linear operations.
Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal correlations between incoherently mixed local states of the two subsystems. Thus, even if one subsystem happens to be macroscopic as in the entangled "Schrodinger's cat" state resulting from an ideal measurement, this state is not the paradoxical macroscopic superposition it is generally presumed to be. It is, instead, a "macroscopic correlation," a coherent quantum…
We investigate prospects of using counter-rotating vortex superposition states in non-equilibrium exciton-polariton Bose-Einstein condensates for the purposes of Sagnac interferometry. We first investigate the stability of vortex-antivortex superposition states, and show that they survive at steady-state in a variety of configurations. Counter-rotating vortex superpositions are of potential interest to gyroscope and seismometer applications for detecting rotations. Methods of improving the sensitivity are investigated by targeting high momentum states via metastable condensation, and the appli…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is…
We use a fiber based double slit Young interferometer for studying the far-field spatial distribution of the two-photon coincidence rate (coincidence pattern) for various quantum states with different degree of spatial entanglement. The realized experimental approach allows to characterize coincidence patterns for different states without any modifications of the setup. Measurements were carried out with path-entangled and separable states. The dependence of the coincidence pattern on the phase of the interferometer for superposition and separable states was studied. The results have implicati…
