We propose to experimentally test the nonclassicality of quantum states through homodyne tomography. For single-mode states we check violations of inequalities involving the photon-number probability. For two-mode states we test the nonclassicality by reconstructing some suitable number-operator functions. The test can be performed with available quantum efficiency of homodyne detection, by measuring the pertaining quantities on the corresponding noisy states.
It is demonstrated that thermal radiation of small occupation number is strongly nonclassical. This includes most forms of naturally occurring radiation. Nonclassicality can be observed as a negative weak value of a positive observable. It is related to negative values of the Margenau-Hill quasi-probability distribution.
A full characterization of nonclassical space-time dependent correlations of radiation is formulated in terms of normally and time-ordered field correlation functions. It describes not only the properties of initially prepared multimode radiation fields, but also the dynamics of radiation sources. Some of these correlation effects occur in the resonance fluorescence of a single two-level atom.
We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicalilty indicators could give further evidence of …
We report the experimental realization and tomographic analysis of novel quantum light states obtained by exciting a classical thermal field by a single photon. Such states, although completely incoherent, possess a tunable degree of quantumness which is here exploited to put to a stringent experimental test some of the criteria proposed for the proof and the measurement of state non-classicality. The quantum character of the states is also given in quantum information terms by evaluating the amount of entanglement that they can produce.
Based on a microscopic derivation of the emission spectra of a bulk semiconductor we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.
We describe the creation of nonclassical states of microwave radiation via ideal dichotomic single photon detection, i.e., a detector that only indicates presence or absence of photons. Ideally, such a detector has a back action in the form of the subtraction operator. Using the non-linearity of this back action, it is possible to create a large family of nonclassical states of microwave radiation, including squeezed and multi-component cat states, starting from a coherent state. We discuss the applicability of this protocol to current experimental designs of Josephson Photomultipliers (JPMs).
Polya states of single mode radiation field are proposed and their algebraic characterization and nonclassical properties are investigated. They degenerate to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1) coherent) states in two different limits and further to the number, the ordinary coherent and Susskind-Glogower phase states. The algebra involved turn out to be a two-parameter deformation of both su(2) and su(1,1). Nonclassical properties are investigated in detail.
We propose a legitimate and easily computable nonclassicality indicator for the states of electromagnetic fields based on the standard deviation in the measurement of the homodyne rotated quadrature operator. The proposed nonclassicality indicator is the nonclassical area projected by the optical tomogram of the quantum state of light on the optical tomographic plane. If the nonclassical area projected by the optical tomogram of a quantum state is greater than zero, the state is nonclassical, and the area is zero for the pure classical state. It is also noted that the nonclassical area of a qu…
Intermediate states interpolating coherent states and Pegg-Barnett phase states are investigated using the ladder operator approach. These states reduce to coherent and Pegg-Barnett phase states in two different limits. Statistical and squeezing properties are studied in detail.
In quantum optics, nonclassical properties of various quantum states of radiation field are frequently studied. Some of those states are finite dimensional and referred to as qudits. These states are important because of their potential applications in quantum information processing. Further, nonclassical states are those which do not have any classical counterpart. Consequently, to establish quantum supremacy, we always require nonclassical state. Recently, Sivakumar and Meher have studied the nonclassical properties of the number state filtered coherent state, and shown that the number state…
The nonclassical feature of photons in the open finite-size Dicke model is investigated via the two-photon correlation function. The quantum dressed master equation combined with the extended coherent photonic states is applied to analyze the dissipative dynamics of both the photons and qubits. The anti-bunching to bunching transition of photons is clearly observed by tuning the qubit-photon coupling strength. The optimal qubits number is unraveled to enhance the two-photon correlation function. Moreover, the temperature bias of thermal baths induces significant two-photon bunching signature w…
The quantum properties of the fluorescence light emitted by diamond nanocrystals containing a single nitrogen-vacancy (NV) colored center is investigated. We have observed photon antibunching with very low background light. This system is therefore a very good candidate for the production of single photon on demand. In addition, we have measured larger NV center lifetime in nanocrystals than in the bulk, in good agreement with a simple quantum electrodynamical model.
We demonstrate the existence of new nonclassical correlations in the radiation of two atoms, which are coherently driven by a continuous laser source. The photon-photon-correlations of the fluorescence light show a spatial interferene pattern not present in a classical treatment. A feature of the new phenomenon is, that bunched and antibunched light is emitted in different spatial directions. The calculations are performed analytically. It is pointed out, that the correlations are induced by state reduction due to the measurement process when the detection of the photons does not distinguish b…
Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner. For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon b…
We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative phase-space functions of quantum states and measurements. We argue that nonclassical correlations are naturally related to Bell nonlocality, the former being a more general class of quantum correlations. Indeed, it is known that local realistic as well as noncontextual models correspond to non-negative solutions to a system of linear equations for the joint probab…
We demonstrate the generation of multi-photon quantum states of light by cavity-enhanced parametric down-conversion in the high-repetition-rate pulsed regime. An external enhancement cavity resonant with the spectral comb of modes of a mode-locked pump laser provides a coherent build-up of the pump intensity and greatly enhances the parametric gain without sacrificing its high repetition rate and comb structure. We probe the parametric gain enhancement by the conditional generation and tomographic analysis of two-photon Fock states. Besides its potential impact to efficiently generate highly-n…
Thermal or chaotic light sources emit radiation characterized by a slightly enhanced probability of emitting photons in bunches, described by a zero-delay second-order correlation function $g^{(2)}(0) = 2$. Here we explore photon-coincidence counting statistics of thermal cavities in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. We find that, depending on the system temperature and coupling rate, thermal photons escaping the cavity can display very different statistical behaviors, characterised by second-order correla…
We propose a scheme to achieve a uniform cross phase modulation (XPM) for two nonclassical light pulses and study its application for quantum non-demolition measurements of the photon number in a pulse and for controlled phase gates in quantum information. We analyze the scheme by quantizing a common phenomenological model for classical XPM. Our analysis first treats the ideal case of equal cross-phase modulation and pure unitary dynamics. This establishes the groundwork for more complicated studies of non-unitary dynamics and difference in phase shifts between the two pulses where decohering …
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual…
We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters of an unknown Gaussian process, considering a noisy source of radiation the phase of which is not locked to the pump of the process. We verify the sufficiency of passive optical elements in the interferometer, active optical elements do not improve the quality of the estimation. We also prove the robustness of the method against the noise and loss in both i…
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the direct detection followed by the spectral analysis of the recorded photocurrents. As an example, the squeezing spectra of the atomic resonance fluorescence are studied for both types of filtering procedures. The conditions for which the detection of the nonclassical signatures of the radiation is possible are analyzed. For the considered example, photocurrent f…
We propose a protocol for quantum state tomography of nonclassical states in optomechanical systems. Using a parametric drive, the procedure overcomes the challenges of weak optomechanical coupling, poor detection efficiency, and thermal noise to enable high efficiency homodyne measurement. Our analysis is based on the analytic description of the generalized measurement that is performed when optomechanical position measurement competes with thermal noise and a parametric drive. The proposed experimental procedure is numerically simulated in realistic parameter regimes, which allows us to show…
Emergence of nonclassical radiation in strongly laser-driven quantum systems
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Institute of Physical Chemistry, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学物理化学研究所）；Fraunhofer Institute for Applied Optics and Precision Engineering（弗劳恩霍夫应用光学和精密工程研究所）
We analyze a quantum reservoir engineering method, originally introduced by [Sarlette et al. in Phys. Rev. Lett. 107, 010402 (2011) -- arXiv 1011.5057], for the stabilization of non-classical field states in high quality cavities. We generalize the method to the protection of mesoscopic entangled field states shared by two non-degenerate field modes. The reservoir is made up of a stream of atoms undergoing successive composite interactions with the cavity, each combining resonant with non-resonant parts. We get a detailed insight into the competition between the engineered reservoir and decohe…
Quantum enhanced sensing is a powerful technique in which nonclassical states are used to improve the sensitivity of a measurement. For enhanced mechanical displacement sensing, squeezed states of light have been shown to reduce the photon counting noise that limits the measurement noise floor. It has long been predicted, however, that suppressing the noise floor with squeezed light should produce an unavoidable increase in radiation pressure noise that drives the mechanical system. Such nonclassical radiation pressure forces have thus far been hidden by insufficient measurement strengths and …
We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize quantum correlations by the statistics measured with systems of on-off detectors. Additionally, we generalize our method to multiple detector systems for measurements of correlations between light fields. We also consider multi-mode radiation fields and isolate nonclassicality in terms of the space time correlations. Finally, we present results for the quantum…
We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap and its relation to the Uhlmann fidelity are interestingly illustrated by our approach.
The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states(arbitrary number or photons, pure or mixed) of quantised radiation and their violation is connected to other nonclassical properties of the field. Classical states are shown to obey these inequalities and for the family of centered Gaussian states the direct connection between violation of Bell-type inequalities and squeezing is established.
Experimental investigation of nonclassicality in the simplest scenario via the degrees of freedom of light
Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）；Instituto Federal do Rio de Janeiro（里约热内卢联邦学院）
Nonclassical microwave radiation from the parametric dynamical Casimir effect in the reversed-dissipation regime of circuit optomechanics
University of Isfahan（伊斯法罕大学）；Center of Quantum Science and Technology, University of Isfahan（伊斯法罕大学量子科学与技术中心）；Department of Physics, College of Science, University of Tehran（德黑兰大学理学院物理系）；Quantum Remote Sensing Lab, Quantum Metrology Group, Iranian Center for Quantum Technologies（伊朗量子技术中心量子计量组量子遥感实验室）；Quantum Optics Group, Department of Physics, University of Isfahan（伊斯法罕大学物理系量子光学小组）；Laboratory of Photonics and Quantum Measurement, Swiss Federal Institute of Technology Lausanne（洛桑联邦理工学院光子学与量子测量实验室）；EDWATEC SA
Localized radiation sources are analyzed with respect to the relation of nonclassicality and quantum entanglement of the emitted light. The source field parts of the radiation emitted in different directions are closely related to each other. As a consequence, nonclassicality of the light fields in one direction directly implies entanglement of the field modes in different directions. This implication can be extended to multipartite-entanglement and multi-time quantum correlations. Given that a nonclassical effect is observed, our approach explicitly yields the multipartite entanglement witnes…
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, …
We introduce an experimentally accessible method to measure a unique degree of nonclassicality, based on the quantum superposition principle, for arbitrary quantum states. We formulate witnesses and test a given state for any particular value of this measure. The construction of optimal tests is presented as well as the general numerical implementation. We apply this approach on examples such as squeezed states, and we show how to formulate conditions to certify a particular degree of nonclassicality for single- and multimode radiation fields.
A recently introduced hierarchy of states of a single mode quantised radiation field is examined for the case of centered Guassian Wigner distributions. It is found that the onset of squeezing among such states signals the transition to the strongly nonclassical regime. Interesting consequences for the photon number distribution, and explicit representations for them, are presented.
We study su(2) and su(1,1) displaced number states. Those states are eigenstates of density-dependent interaction systems of quantized radiation field with classical current. Those states are intermediate states interpolating between number and displaced number states. Their photon number distribution, statistical and squeezing properties are studied in detail. It is show that these states exhibit strong nonclassical properties.
Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan $P$ function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistic…
In this review, we introduce the notion of quantum nonclassicality of light, and the role of nonclassicality in optical quantum metrology. The first part of the paper focuses on defining and characterizing the notion of nonclassicality and how it may be quantified in radiation fields. Several prominent examples of nonclassical light is also discussed. The second part of the paper looks at quantum metrology through the lens of nonclassicality. We introduce key concepts such as the Quantum Fisher information, the Cram{é}r-Rao bound, the standard quantum limit and the Heisenberg limit, and discus…
A new operator based condition for distinguishing classical from non-classical states of quantised radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalisation of the notion of subpoissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuat…
Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of identical two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled $W$ states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations as one needs to e…
We briefly review the ideas that have shaped modern optics and have led to various applications of light ranging from spectroscopy to astrophysics, and street lights to quantum communication. The review is primarily focused on the modern applications of classical light and nonclassical light. Specific attention has been given to the applications of squeezed, antibunched, and entangled states of radiation field. Applications of Fock states (especially single photon states) in the field of quantum communication are also discussed.
We present a conditional experiment involving a parametric amplifier and an avalanche photodetector to generate highly nonclassical states of the radiation field. The nonclassicality is robust against amplifier gain, detector efficiency and dark counts. At the output all the generalized Wigner functions have negative values, and this is exploited in order to reveal the nonclassicality through quantum homodyne tomography.
Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results are compared with those of the corresponding separable state. In both…
We study the evolution of higher-order nonclassicality and entanglement criteria in atmospheric fluctuating-loss channels. By formulating input-output relations for the matrix of moments, we investigate the influence of such channels on the corresponding quantumness criteria. This generalization of our previous work on Gaussian entanglement [M. Bohmann et al., Phys. Rev. A 94, 010302(R) (2016)] not only exploits second-order-based scenarios, but it also provides a detailed investigation of nonclassicality and entanglement in non-Gaussian and multimode radiation fields undergoing a fluctuating …
Detailed derivation of the master equation and the corresponding time evolution of the cavity radiation of a coherent beat laser when the atoms are initially prepared in a partial coherent superposition is presented. It turns out that the quantum features and intensity of the cavity radiation are considerably modified by the phase fluctuation arising due to the practical incapability of preparing atoms in the intended coherent superposition. New terms having an opposite sign with the contribution of the driving radiation emerged in the master equation. This can be taken as an indication for a …
In this paper, we follow our presented model in J. Opt. Soc. Am. B {\bf 30}, 1109--1117 (2013), in which the interaction between a $Λ$-type three-level atom and a quantized two-mode radiation field in a cavity in the presence of nonlinearities is studied. After giving a brief review on the procedure of obtaining the state vector of the atom-field system, some further interesting and important physical features (which are of particular interest in the quantum optics field of research) of the whole system state, i.e., the number-phase entropic uncertainty relation (based on the two-mode Pegg-Bar…
In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via $l$-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. We show that the more the number of the parties in the system the less the amounts of the nonclassical effects exhibited in the entropy squeezing.…
Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photo…
We assess the performance of an entanglement indicator which can be obtained directly from tomograms, avoiding state reconstruction procedures. In earlier work, we have examined this tomographic entanglement indicator, and a variant obtained from it, in the context of continuous variable systems. It has been shown that, in multipartite systems of radiation fields, these indicators fare as well as standard measures of entanglement. In this paper, we assess these indicators in the case of two generic hybrid quantum systems, the double Jaynes-Cummings model and the double Tavis-Cummings model usi…
We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geom…
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a g…
We investigate the generation of higher-order harmonics from a quantum optics perspective via the interaction of a semiconductor with a coherent pump field focusing on the regime where strong-field intraband excitations dominate. The related Schrödinger equation for the system is solved approximately and the classical and quantum characteristics of the fundamental light mode as well as the higher frequency modes are analyzed. We find intricate but sufficiently mild modifications of the fundamental mode and coherent displacements depending on the position quadrature component of the driving las…
