The nonclassical effect of photon anti-bunching is observed in the mixed field of a narrow band two-photon source and a coherent field under certain condition. A variety of different features in photon statistics are found to be the consequence of a two-photon interference effect with dependence on the relative phase of the fields. Besides the anti-bunching effect, we find another one of the features to be also nonclassical. These features emphasize the importance of quantum entanglement.
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
We present an experiment of nonclassical interference between a pure heralded single-photon state and a weak coherent state. Our experiment is the first to demonstrate that spectrally pure single photons can have high interference visibility, 89.4 \pm 0.5%, with weak coherent photons. Our scheme lays the groundwork for future experiments requiring quantum interference between photons in nonclassical states and those in coherent states.
We theoretically generate nonclassical states from coherent state heralded by Knill-Laflamme-Milburn (KLM)-type SU(3) interference. Injecting a coherent state in signal mode and two single-photon sources in other two auxiliary modes of SU(3) interferometry, a broad class of useful nonclassical states are obtained in the output signal port after making two single-photon-counting measurements in the two output auxiliary modes. The nonclassical properties, in terms of anti-bunching effect and squeezing effect as well as the negativity of the Wigner function, are studied in detail by adjusting the…
We study first-order interference in spontaneous parametric down-conversion generated by two pump pulses that do not overlap in time. The observed modulation in the angular distribution of the signal detector counting rate can only be explained in terms of a quantum mechanical description based on biphoton states. The condition for observing interference in the signal channel is shown to depend on the parameters of the idler radiation.
It is shown that both the visibility ${\cal V} = 1/2$ predicted for two-photon interference experiments with two independent sources\textcolor{black}{, like the Hanbury Brown-Twiss experiment,} and the visibility ${\cal V} = 1$ predicted for two-photon interference experiments with a parametric down-conversion source\textcolor{black}{, like the Ghosh-Mandel experiment,} can be explained \textcolor{black}{by a discrete event simulation. This simulation approach reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whol…
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization…
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…
The Berry phase acquired by an electromagnetic field undergoing an adiabatic and cyclic evolution in phase space is a purely quantum-mechanical effect of the field. However, this phase is usually accompanied by a dynamical contribution and cannot be manifested in any light-beam interference experiment because it is independent of the field state. We here show that such a phase can be produced using an atom coupled to a quantized field and driven by a slowly changing classical field, and it is manifested in atomic Ramsey interference oscillations. We also show how this effect may be applied to …
In this paper, we demonstrate a source of photon pairs based on four-wave-mixing in photonic crystal fibres. Careful engineering of the phase matching conditions in the fibres enables us to create photon pairs at 597 nm and 860 nm in an intrinsically factorable state showing no spectral correlations. This allows for heralding one photon in a pure state and hence renders narrow band filtering obsolete. The source is narrow band, bright and achieves an overall detection efficiency of up to 21% per photon. For the first time, a Hong-Ou-Mandel interference with unfiltered photons from separate fib…
The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor on the electric charges. This phase factor, which is a generalization of the standard Aharonov-Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons destroys slightly the electron i…
A corpuscular simulation model for second-order intensity interference phenomena is discussed. It is shown that both the visibility ${\cal V}=1/2$ predicted for two-photon interference experiments with two independent sources and the visibility ${\cal V}=1$ predicted for two-photon interference experiments with a parametric down-conversion source can be explained in terms of a locally causal, modular, adaptive, corpuscular, classical (non-Hamiltonian) dynamical system. Hence, there is no need to invoke quantum theory to explain the so-called nonclassical effects in the interference of signal a…
Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ${ψ_{AB}} = {ψ_A} + {ψ_B}$ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-s…
Using the theoretical model of the optical beam-splitter, the interference of the self-phase modulated ultrashort light pulse (SPM-USP) with the coherent one is investigated. It is found that, the choice of the coefficient of transmission of the beam-splitter allows one to get the spectra of quadrature fluctuations with forms of interest to us. It is shown that the choice of the geometrical phase gives one the control of the position of the ellipse of squeezing in the quadrature space XY. The extended Mandel parameter is introduced and the photon statistics is scanned at all frequencies. It is…
We develop a technique for generating multi-photon nonclassical states via interference between coherent and Fock states using quantum catalysis. By modulating the coherent field strength, the number of catalyst photons and the ratio of the beam splitter upon which they interfere, a wide range of nonclassical phenomena can be created, including squeezing of up to 1.25 dB, anti- and super-bunched photon statistics and states exhibiting over 90% fidelity to displaced coherent superposition states. We perform quantum catalysis experimentally, showing tunability into the nonclassical regime. Our p…
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.
We use photon counters to obtain the joint photon counting statistics from twin-beam non-degenerate parametric down conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical.
Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of multiple observables. This requires enlarged spaces and couplings with auxiliary degrees of freedom so it must be followed by an inversion procedure to infer system properties from the observed statistics. In particular this discloses nonclassical properties of standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. Moreover, when c…
Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as classical-like, such as SU(2) and Glauber coherent states. We show that this holds because we can always find a joint measurement whose statistics is not separable.
We demonstrate, theoretically and experimentally, that statistical mixtures of the vacuum state |0> and the single-photon Fock state |1> are nonclassical according to the Vogel criterion (W. Vogel, Phys. Rev. Lett. 84, 1849 (2000)), regardless of the vacuum fraction. The ensembles are synthesized via conditional measurements on biphotons generated by means of parametric downconversion, and their quadrature statistics are measured using balanced homodyne detection. A comparative review of various quantum state nonclassicality criteria is presented.
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 …
With a product state of the form $ρ_{in} = ρ_a\otimes|0>_b_b< 0|$ as input, the output two-mode state $ρ_{\rm out}$, of the beam splitter is shown to be NPT whenever the photon number distribution (PND) statistics $\{p(n_a) \}$ associated with the possibly mixed state $ρ_a$ of the a_mode is antibunched or otherwise nonclassical, i.e., if $\{p(n_a)\}$ fails to respect any one of an infinite of classicality conditions.
Using cumulant expansion in Gaussian approximation, the internal quantum statistics of damped soliton-like pulses in Kerr media are studied numerically, considering both narrow and finite bandwidth spectral pulse components. It is shown that the sub-Poissonian statistics can be enhanced, under certain circumstances, by absorption, which damps out some destructive interferences. Further, it is shown that both the photon-number correlation and the correlation of the photon-number variance between different pulse components can be highly nonclassical even for an absorbing fiber. Optimum frequency…
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single- and two-mode fields, o…
We experimentally investigate a method of directly characterizing the photon number distribution of nonclassical light beams that is tolerant to losses and makes use only of standard binary detectors. This is achieved in a single measurement by calibrating the detector using some small amount of prior information about the source. We demonstrate the technique on a freely propagating heralded two-photon number state created by conditional detection of a two-mode squeezed state generated by a parametric downconverter.
A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $τ$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures di…
It is often asserted that quantum effects can be observed in coincidence detection rates or other correlations, but never in the rate of single-photon detection. We observe nonclassical interference in a singles rate, thanks to the intrinsic nonlinearity of photon counters. This is due to a dependence of the effective detection efficiency on the quantum statistics of the light beam. Such measurements of detector response to photon pairs promise to shed light on the microscopic aspects of silicon photodetectors, and on general issues of quantum measurement and decoherence.
Nonclassical photocounting statistics with a single on-off detector
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Quantum Technology Laboratories GmbH（量子技术实验室有限公司）；Kyiv Academic University（基辅学术大学）；Kyiv School of Economics（基辅经济学院）
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical ligh…
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 measurement of joint signal-idler photon-number distribution of a field obtained from spontaneous parametric downconversion using an intensified CCD camera is presented. It is shown that a classicality criterion is violated directly by the measured data. Characteristic dimensions of the area of correlation are determined in the same experimental setup.
We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong-Ou-Mandel interference or sum-frequency generation. We measure the quantum state of the broadband bi-photons, amplitude and phase, with a pairwise "Mach-Zehnder" quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of …
Broadband light sources play essential roles in diverse fields, such as high-capacity optical communications, optical coherence tomography, optical spectroscopy, and spectrograph calibration. Though an ultrabroadband nonclassical state from standard spontaneous parametric down-conversion may serve as a quantum counterpart, its detection and quantum characterization have been a challenging task. Here we demonstrate the quantitative characterization of a multimode structure in such an ultrabroadband (150 nm FWHM) squeezed state at telecom wavelength (1.5 μm). The nonclassical photon distribution…
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically coupled optomechanical system which contains a thin dielectric membrane quadratically coupled to the cavity field. A decorrelation method is employed to solve for a larger number of coupled equations. Transient mean numbers of cavity photons and phonons that provide dynamical behaviour are computed for different coupling regime. We have also obtained the two-boson…
Dirac has written "Each photon then interferes only with itself. Interference between two different photons never occurs." Indeed, a practical definition is that "classical" optics consists of phenomena due to the interference of photons only with themselves. However, photons obey Bose statistics which implies a ``nonclassical'' tendency for them to ``bunch''. For a simple example of nonclassical optical behavior, we consider two pulses of photons of a single frequency that are simultaneously incident on two sides of a lossless, 50:50 beam splitter.
According to Born's rule quantum probabilities are given by the overlap between the system state and measurement states in a quite symmetrical way. This means that both contribute to any observed nonclassical effect that is usually attributed just to the observed light state. This is relevant since typical measurement are highly nonclassical by themselves, such as number states and quadrature eigenstates. We show that nonclassical effects only arise provided that the measurement is itself nonclassical. Otherwise there is a classical-like model accounting for the observed statistics.
We study an optomechanical system for the purpose of generating a nonclassical mechanical state when a mechanical oscillator is quadratically coupled to a single-mode cavity field driven by a squeezed optical field. The system corresponds to a regime where the optical dissipation dominates both the mechanical damping and the optomechanical coupling. We identify that multi-phonon processes emerge in the optomechanical system and show that a mechanical oscillator prepared in the ground state will evolve into an amplitude-squared squeezed vacuum state. The Wigner distribution of the steady state …
Interference lies at the heart of the behavior of classical and quantum light. It is thus crucial to understand the boundaries between which interference patterns can be explained by a classical electromagnetic description of light and which, on the other hand, can only be understood with a proper quantum mechanical approach. While the case of two-mode interference has received a lot of attention, the multimode case has not yet been fully explored. Here we study a general scenario of intensity interferometry: we derive a bound on the average correlations between pairs of output intensities for…
We perform a phase-space analysis of strong-field enhanced ionisation in molecules, with emphasis on quantum-interference effects. Using Wigner quasi-probability distributions and the quantum Liouville equation, we show that the momentum gates reported in a previous publication [N. Takemoto and A. Becker, Phys. Rev. A \textbf{84}, 023401 (2011)] may occur for static driving fields, and even for no external field at all. Their primary cause is an interference-induced bridging mechanism that occurs if both wells in the molecule are populated. In the phase-space regions for which quantum bridges …
Machine-learning and neural-network approaches have gained huge attention in the context of quantum science and technology in recent years. One of the most essential tasks for the future development of quantum technologies is the verification of nonclassical resources. Here, we present an artificial neural network approach for the identification of nonclassical states of light based on recorded measurement statistics. In particular, we implement and train a network which is capable of recognizing nonclassical states based on the click statistics recorded with multiplexed detectors. We use simu…
Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\fracπ{2}$ out of phase. The formalism has then been applied to a few physical systems as "harmonious states", "SU(1,1) coherent states" and "the center of mass motion of trapped ion". Finally, the nonclassical properties such as sub-Poissonian statistics, quadrature squeezing, amplitude-squared squeezing and Wigner distribution function of the superposed states have been investigated, numerically. E…
We theoretically study the emission statistics of a weakly nonlinear photonic dimer during coherent oscillations. We show that the phase and population dynamics allow to periodically meet an optimal intensity squeezing condition resulting in a strongly nonclassical emission statistics. By considering an exciton-polariton Josephson junction resonantly driven by a classical source, we show that a sizeable antibunching should emerge in such semiconductor system where intrinsic nonclassical signatures have remained elusive to date.
Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of incompatible observables requires different experimen-tal procedures, which no necessarily must share a common joint statistics. In this work, we avoidthese difficulties by proposing a joint simultaneous measurement experiment. We can obtain theexact individual statistics of all the observables involved in the Bell inequalities after a suitable datainversion. A lack …
Two-photon interference of multimode two-photon pairs produced by an optical parametric oscillator has been observed for the first time with an unbalanced interferometer. The time correlation between the multimode two photons has a multi-peaked structure. This property of the multimode two-photon state induces two-photon interference depending on delay time. The nonclassicality of this interference is also discussed.
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…
We develop a nonclassicality criterion for the interference of three delayed, but otherwise identical, light fields in a three-mode Bell interferometer. We do so by comparing the prediction of quantum mechanics with those of a classical framework in which independent sources emit electric fields with random phases. In particular, we evaluate third-order correlations among output intensities as a function of the delays, and show how the presence of a correlation revival for small delays cannot be explained by the classical model of light. The observation of a revival is thus a nonclassicality s…
In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coher- ent states. The suQ(1;1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have been also introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete non-degenerate spectrum" en. As some physical appearances, a …
Nonclassical state is an essential resource for quantum-enhanced communication, computing and metrology to outperform their classical counterpart. The nonclassical states that can operate at high bandwidth and room temperature while being compatible with quantum memory are highly desirable to enable the scalability of quantum technologies. Here, we present a direct observation of broadband nonclasscal states in a room-temperature light-matter interface, where the atoms can also be controlled to store and interfere with photons. With a single coupling pulse and far off-resonance configuration, …
Single photons and single-photon pairs, inherently nonclassical in their nature, are fundamental elements of quantum sciences and technologies. Here, we propose to realize the nonclassical correlated deterministic photon pairs at the single-photon level for a single atom trapped in bimodal cavities. It is shown that the photon emissions for bimodal cavities exhibit a high single photon purity and relatively large intracavity photon numbers, which are ascribed to the combination of optical Stark shift enhanced energy-spectrum anharmonicity and quantum interference suppressed two-photon excitati…
The quantum statistics of damped higher-order optical solitons are analyzed numerically, using cumulant-expansion techniques in Gaussian approximation. A detailed analysis of nonclassical properties in both the time and the frequency domain is given, with special emphasis on the role of absorption. Highly nonclassical broadband spectral correlation is predicted.
We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of …
We discuss a simple search problem which can be pursued with different methods, either on a classical or on a quantum basis. The system is represented by a chain of trapped ions. The ion to be searched is a member of that chain, consists, however, of an isotopic species different to the others. It is shown that the classical imaging may lead as fast to the final result as the quantum imaging. However, for the discussed case the quantum method gives more flexibility and higher precision when the number of ions considered in the chain is increasing. In addition, interferences are observable even…
