Approximate quantum statistical properties of a nonlinear optical coupler (original) (raw)
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Joint photon and wave statistics in nonlinear optical couplers
Optics Communications, 2014
Nonlinear optical couplers based on optical parametric processes and Raman-Brillouin scattering are discussed from the point of view of their nonclassical behaviour using joint photon-number and integrated-intensity probability distributions and derived quantum statistical quantities. Employing these tools quantum entanglement of modes and their nonclassical properties are demonstrated by means of conditional probability distributions and their Fano factors, difference-number probability distributions, quantum oscillations, squeezing of vacuum fluctuations and negative values of the joint wave probability quasidistributions in time evolution. Sub-Poissonian and sub-shot-noise properties are determined for initial coherent, chaotic and squeezed light.
Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher order antibunching, higher order squeezing, higher order two-mode and multi-mode entanglement in the asymmetric nonlinear optical coupler. It is also shown that nonclassical properties of light can transfer from a nonlinear wave guide to a linear wave guide.
Modern Physics Letters B, 2003
The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.
Nonclassical properties of a contradirectional nonlinear optical coupler
We investigate the nonclassical properties of output fields propagated through a contradirectional asymmetric nonlinear optical coupler consisting of a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation. In contrast to the earlier results, all the initial fields are considered weak and a completely quantum mechanical model is used here to describe the system. Perturbative solutions of Heisenberg's equations of motion for various field modes are obtained using Sen-Mandal technique. Obtained solutions are subsequently used to show the existence of single-mode and intermodal squeezing, single-mode and intermodal antibunching, two-mode and multi-mode entanglement in the output of contradirectional asymmetric nonlinear optical coupler. Further, existence of higher order nonclassicality is also established by showing the existence of higher order antibunching, higher order squeezing and higher order entanglement. Variation of observed nonclassical characters with different coupling constants and phase mismatch is discussed.
Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler
International Conference on Optics and Photonics 2015, 2015
Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler are studied. The asymmetric nonlinear optical coupler is composed of a linear waveguide (χ (1)) and a nonlinear waveguide (χ (2)) interacting with each other through the evanescent waves. The nonlinear waveguide has quadratic nonlinearity and it operates under second harmonic generation. A completely quantum mechanical description is used to describe the system. The closed form analytic solutions of Heisenberg's equations of motion for the different field modes are obtained using Sen-Mandal perturbative approach. In the coupler, the linear waveguide acts as a probe on the system (nonlinear waveguide). The effect of the presence of the probe (linear waveguide) on the photon statistics of the second harmonic mode of the system is considered as quantum Zeno and anti-Zeno effects. Further, it is also shown that in the stimulated case, it is easy to switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the asymmetric coupler.
Kerr nonlinear coupler and entanglement induced by broadband laser light
PHOTONICS LETTERS OF POLAND, 2016
We consider the model of a Kerr-like nonlinear coupler linearly excited by an external classical field, involving a coherent part and white noise, solving a set of coupled stochastic integro-differential equations, and deriving exactly analytical formulae for the probability amplitudes of n-photon Fock states. As a consequence, the nonlinear coupler in question behaves as a two-qubit system. The effects of dissipation on entanglement of formation parameterised by concurrence are also analyzed and the results compared with those obtained previously in the literature. Interestingly, initially for a period of time the entanglement is enlarged when the chaotic parameter increases. One of the central problems in quantum information theory is quantum state engineering which leads to finite-dimensional states generation. Such states can exhibit several interesting properties as they are able to produce various kinds of quantum correlations. The most important type of these for quantum computing is quantum entanglement. It is one of the most basic concepts of the theory of quantum information and allows us to study many features of nonlocal properties of quantum systems [1]. Different aspects of entanglement and its generation have been considered in numerous works. Quantum optical systems based on Kerr nonlinearities are those which allow for creation of entangled states. Such a system can be found in various physical situations and referred to as Kerr-like couplers. It has been shown that the quantum evolution of the system can be closed in a two-qubit Hilbert space and can lead to Bell states generation [2-3]. It is shown that the coupler evolution governed by the same effective Hamiltonians as usual optical Kerr couplers (discussed for instance in [4]) can be closed within a finite set of n-photon states. After "truncation" of the wave function describing the system, the coupler can be treated as two-qubit and treated as a Bell-like state generator that can create maximally entangled states even if the system exhibits its energy dissipating nature [5]. The system behaves similar to nonlinear quantum scissors and maximally entangled Bell states can be generated with high efficiency [6]. * In previous papers, including these mentioned above, it was assumed that the laser light is monochromatic. However, a real laser is never perfectly monochromatic and it is interesting to include fluctuations of a laser beam. In the present paper we model laser beam fluctuations with a Gaussian process. The exact analytical averaging of stochastic equations with a Gaussian process is a difficult task. Hence, it is worthwhile to start with an extreme case of white noise. Even in this case we can obtain several interesting results [7-9]. Here we extend the formalism given in [10] to a more realistic case, when the laser width is taken into account and discuss a simple quantum information application of Kerr nonlinearities, namely for generation of entangled optical qubits from classical light. We consider here a simple model including two quantum nonlinear oscillators located inside one cavity. These oscillators are linearly coupled to each other, while one of the oscillators is excited by an external coherent field, which is assumed to be decomposed into two parts: a coherent part and white noise. Then a set of stochastic differential equations of motion describing the system dynamics will be obtained and analytically solved. The plot of probabilities corresponding to the Bell-like states and concurrence for the excited nonlinear coupler will be calculated analytically and compared with the results obtained in [10]. In this paper we investigate the model of a Kerr-like nonlinear coupler comprising two nonlinear oscillators linearly coupled to each other. One of these nonlinear oscillators is coupled to an external classical field. Such a system is depicted by the Hamiltonian of the form [10]:
Nonclassical light in a three-waveguide coupler with second-order nonlinearity
EPJ Quantum Technology 11, 51, 2024
Possible squeezed states generated in a three-waveguide nonlinear coupler operating with second harmonic generation is discussed. This study is carried out using two well-known techniques; the phase space method (based on positive-P representation) and the Heisenberg-based analytical perturbative (AP) method. The effects of key design parameters were investigated under various conditions, including full frequency matching, symmetrical and asymmetrical waveguide initialization, and both codirectional and contr-adirectional propagation. The system consistently produced long-lasting oscillatory squeezed states across all three waveguides, even when only one waveguide was pumped with coherent light while the others were in a vacuum state. Also, the performance and capacities of both methods are critically evaluated. For low levels of key design parameters and in the early stages of evolution, a high level of agreement between the two methods is noticed. In the new era of quantum-based technology, the proposed system opens a new avenue for utilising nonlinear couplers in nonclassical light generation.
Quantum correlations in optics
Pramana, 1998
In many nonlinear optical problems, for example in down-conversion and four-wave mixing, the photons are generated in pairs. The strong correlation between the photons in a pair, characterized by either the correlations between operators corresponding to observables associated with individual photons, or the correlated state describing the two photons, may lead to various nonclassicalities. We discuss some of these nonclassical effects and their experimental demonstrations in nonlinear optical processes.
Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators
Optics Communications, 2016
The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anharmonic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear nonclassical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode.
Quantum-statistical properties of two coupled modes of electromagnetic field
1998
Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q1 and q2 is examined. The δ- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.