Initial Photon Number Research Articles

Analysis of Transmission Depth and Photon Number in Monte Carlo Simulation for Underwater Laser Transmission

The modeling of laser transmission characteristics in complex seawater is fundamental for bathymetric and oceanographic laser detection systems. Because the factors affecting laser transmission in seawater are independent of one another, firstly, in this paper, a Monte Carlo model of laser propagation in seawaters with suspended matter was established to study the influence of suspended matter with specific radius on the underwater laser transmission. Secondly, the influence of transmission depth and the number of photons on the laser extinction coefficients of seawater containing different concentrations of suspended matter were analyzed, respectively. Thirdly, the relationships between maximum transmission depth, the number of initial photons, and the concentrations were built and verified by simulations. Lastly, an experimental platform was set up and experiments were carried out to verify the Monte Carlo model and the relationships. Results show that (1) both the minimum initial photon number and maximum transmission depth depend exponentially on the concentrations of the suspended matter; (2) the extinction coefficients obtained by the Monte Carlo model and those obtained by experiments are consistent. The absolute values of the differences are less than 0.028 m−1, implying that (1) the proposed Monte Carlo model is effective for simulating laser propagation in seawaters with suspended matter; (2) the established relationships between maximum transmission depth, the minimum initial photon number, and the concentrations of suspended matter have better accuracies, which are valuable for the simulations on attenuation of laser transmission in seawater. The method of this paper can also be extended to the study of suspended solids with other radii and improve the simulation accuracy and decrease simulation time consumption.

Extreme expected values and their applications in quantum metrology

We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable $X$. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we find that after dividing the non-monotone function $H(X)$ into multiple monotone intervals, the problem of solving the maximum and minimum expected values of $H(X)$ can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve three problems in quantum information processing. When studying the quantum parameter estimation in Mach-Zehnder interferometer, for an equal total input photon number, we find an optimal path-symmetric input state that makes the quantum Fisher information take the maximum value, and we prove that the NOON state is the path-symmetric state that makes the quantum Fisher information takes the minimum value. When studying the quantum parameter estimation in Landau-Zener-Jaynes-Cummings model, we find the optimal initial state of the cavity field that makes the system obtain the maximum quantum Fisher information. Finally, for an equal initial average photon number, we find the optimal initial state of the cavity field that makes the Tavis-Cummings quantum battery have the maximum stored energy and the maximum average charging power.

Effects of ocean turbulence on photon orbital angular momentum quantum communication

The effect of the turbulent motion of ocean on the quantum communication based on the orbital angular momentum in an underwater quantum channel is studied in this work. Based on the power spectrum model of ocean turbulence proposed by Elamassie, the quantitative relationships of different ocean turbulence parameters with the single photon detection probability of orbital angular momentum photons, the channel capacity, the key generation rate, the concurrence of two entangled photons are proposed. The maximum entanglement distance of the orbital angular momentum entangled photon-pairs in the ocean turbulence is further studied by the universal entanglement decay of the concurrence of entangled photon-pairs in the ocean turbulence. The results show that the detection probability of single photon, the channel capacity, the key generation rate, and the concurrence of entangled photon-pairs decrease with the increase of the dissipation rate of turbulent kinetic energy and the decrease of the rate of dissipation of mean-squared temperature. The influence of the temperature and salinity balance parameter of ocean turbulence on the performance of underwater quantum communication are significantly different under the condition of whether the stable stratification of seawater is assumed or not. In the ocean turbulent environment, the increasing of the initial orbital angular momentum quantum number of signal photons can improve the key generation rate of quantum key distribution and the resistance of entangled photons to entanglement decay.

Optimal state for a Tavis-Cummings quantum battery via the Bethe ansatz method

In this paper, we investigate the effect of different optical field initial states on the performance of the Tavis-Cummings (T-C) quantum battery. In solving the dynamical evolution of the system, we found a fast way to solve the Bethe ansatz equation. We find that the stored energy and the average charging power of the T-C quantum battery are closely related to the probability distribution of the optical field initial state in the number states. We define a quantity called the number-state stored energy. With this prescribed quantity, we only need to know the probability distribution of the optical field initial state in the number states to obtain the stored energy and the average charging power of the T-C quantum battery at any time. We propose an equal probability and equal expected value splitting method by which we can obtain two inequalities, and the two inequalities can be reduced to Jensen's inequalities. By this method, we found the optimal initial state of the optical field. We found that the maximum stored energy and the maximum average charging power of the T-C quantum battery are proportional to the initial average photon number, and the quantum battery can be fully charged when the initial average photon number is large enough. We found two phenomena, which can be described by two empirical inequalities. These two phenomena imply the hypersensitivity of the stored energy of the T-C quantum battery to the number-state cavity field. Finally, we discussed the impact of decoherence on battery performance.

The physical origin of a photon-number parity effect in cavity quantum electrodynamics

The rapidly increasing capability to modulate the physicochemical properties of atomic groups and molecules by means of their coupling to radiation, as well as the revolutionary potential of quantum computing for materials simulation and prediction, fuel the interest for non-classical phenomena produced by atom-radiation interaction in confined space. One of such phenomena is a “parity effect” that arises in the dynamics of an atom coupled to two degenerate cavity field modes by two-photon processes and manifests itself as a strong dependence of the field dynamics on the parity of the initial number of photons. Here we identify the physical origin of this effect in the quantum correlations that produce entanglement among the system components, explaining why the system evolution depends critically on the parity of the total number of photons. Understanding the physical underpinnings of the effect also allows us to characterize it within the framework of quantum information theory and to generalize it. Since a single photon addition/removal has dramatic effects on the system behavior, this effect may be usefully applied, also for amplification purposes, to optoelectronics and quantum information processing.

Quantum fluctuations in strong field ionization

Based on the field quantization, the angular distribution of the ionization rate of hydrogen atoms with the effect of a finite number of photons is computed in this letter. We find that the angular distribution of the ionization rate will fluctuate with the initial photon number of the field, and have a peak value higher than that predicted by Keldysh-Faisal-Reiss theory. This ionization peak is the embodiment of quantum effect. Furthermore, our calculations show that the phenomenon of ionization peak also exists when the initial field state is a coherent state.

Optimal estimation of matter-field coupling strength in the dipole approximation

This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting with a single mode of the radiation field. Our estimation strategy is based on the emerging state of the two-level system, whereas we determine both the minimum mean-square error and maximum likelihood estimators for uniform and Gaussian prior probability density functions. In the case of the maximum likelihood estimator, we develop a mathematical method which extends the already existing approaches to the variational problem of the average cost function. We demonstrate that long interaction times, large initial mean photon numbers, and nonzero detuning between two-level system transition and the frequency of the electromagnetic field mode have a deleterious effect on the optimality of the estimation scenario. We also present several cases where the estimation process is inconclusive, despite many ideal conditions being met.

Quantum Entanglement of the Multiphoton Transition Jaynes-Cummings Model

In this paper, we have studied the multiphoton transition Jaynes-Cummings model (N = 1, 2, 3, 4, 5, 6), and researched the effect of initial state superposition coefficient $C_{1}$ , the initial photon number n, the transition photon number N, and the quantum discord $\delta $ on the quantum entanglement degrees, and given the quantum entanglement degrees curves with time evolution. We obtain some results, which should have important significance in the quantum computing and quantum information.

Evaluation of bipartite entanglement between two optical multi-mode systems using mode translation symmetry

Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M-mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.

Quantum phase fluctuations of coherent and thermal light coupled to a non-degenerate parametric oscillator beyond rotating wave approximation

The essence of the rotating wave approximation (RWA) is to eliminate the non-conserving energy terms from the interaction Hamiltonian. The cost of using RWA is heavy if the frequency of the input radiation field is low (e.g. below optical region). The well known Bloch-Siegert effect is the out come of the inclusion of the terms which are normally neglected under RWA. We investigate the fluctuations of the quantum phase of the coherent light and the thermal light coupled to a nondegenerate parametric oscillator (NDPO). The Hamiltonian and hence the equations of motion involving the signal and idler modes are framed by using the strong (classical) pump condition. These differential equations are nonlinear in nature and are found coupled to each other. Without using the RWA, we obtain the analytical solutions for the signal and idler fields. These solutions are obtained up to the second orders in dimensionless coupling constants. The analytical expressions for the quantum phase fluctuation parameters due to Carruther's and Nieto are obtained in terms of the coupling constants and the initial photon numbers of the input radiation field. Moreover, we keep ourselves confined to the Pegg-Barnett formalism for measured phase operators. With and without using the RWA, we compare the quantum phase fluctuations for coherent and thermal light coupled to the NDPO. In spite of the significant departures (quantitative), the qualitative features of the phase fluctuation parameters for the input thermal light are identical for NDPO with and without RWA. On the other hand, we report some interesting results of input coherent light coupled to the NDPO which are substantially different from their RWA counterpart. In spite of the various quantum optical phenomena in a NDPO, we claim that it is the first effort where the complete analytical approach towards the solutions and hence the quantum phase fluctuations of input radiation fields coupled to it are obtained beyond rotating wave approximation. To have the feelings of the analytical solutions, we give few numerical estimates of the quantum phase fluctuation parameters relevant to a real experimental situation.

Generation of Nonclassical Light by Unsaturated Two-Photon Absorption

In this paper, we investigate the distribution statistics of photons in a single mode radiation field subjected to two-photon absorption (TPA) and the factors that contribute to squeezing and antibunching of photons, leading to the generation of nonclassical light. TPA is a nonlinear optical phenomenon in which the atoms interact with the light field by absorbing two photons simultaneously. The motivation to study TPA is the recent intense activity on nanocrystallites/quantum dots. Further, it is the only nonlinear optical phenomenon that can be analytically studied. The simultaneous occurrence of squeezing and antibunching is studied with small initial photon numbers by solving the master equation for TPA of a single mode radiation directly by numerical integration, without going through analytical procedure. The results are compared with those of analytical/numerical procedures available. Further, the discussion on the parameters of squeezing and antibunching for short-time (ST) as well as long-time is done comprehensively in the present work by taking up the ST approximation and summation of ST (SST) procedure along with the exact numerical method.

Motion and gravity effects in the precision of quantum clocks

We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state's evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ dt = −κ[a+aρ −a+ρa − aρa+ + ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

Evolution of the quantum fidelity in a system of multimode light field interacting resonantly with a two-level atom through degenerate multi-photon process

The time evolution properties of the quantum fidelity in a system of multi-mode coherent light field resonantly interacting with a two-level atom via any Nj-degenerate N∑-photon transition process are studied by the fully quantum theory and numerical calculations. The analytical expressions of the quantum fidelity of field and atom, and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle, the phase angle of the atom dipole, the field excitation angle, and the atomic degeneracy on the evolution of the quantum fidelity. The results obtained from the numerical calculation indicate that the above factors lead to the quantum fidelity changing with oscillation behavior. The quantum fidelity of field and atom will drastically decrease as the initial light increases, which is correlated sensitively with the fidelity. The speed change of quantum fidelity is strongly dependent on the atomic degeneracy and the intensity coupling between atoms and fields. The value and frequency of the quantum fidelity change lightly with the atomic distribution angle and the angle of light field excitation as well. The phase angles of the atom dipole almost have no influences on the quantum fidelity of field and atom. According to these properties of the quantum fidelity, we can control the speed and value of quantum fidelity in the system by these constraint conditions.

How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters

Up to a few years ago, terrestrial gamma ray flashes (TGFs) were only observed by spaceborne instruments. The aircraft campaign ADELE was able to observe one TGF, and more attempts on aircraft observations are planned. There is also a planned campaign with stratospheric balloons, COBRAT. In this context an important question that arises is what count rates we can expect and how these estimates are affected by the initial properties of the TGFs. Based on simulations of photon propagation in air we find the photon fluence at different observation points at aircraft and balloon altitudes. The observed fluence is highly affected by the initial parameters of the simulated TGFs. One of the most important parameters is the number of initial photons in a TGF. In this paper, we give a semi‐analytical approach to find the initial number of photons with an order of magnitude accuracy. The resulting number varies over several orders of magnitude, depending mostly on the production altitude of the TGF. The initial production altitude is also one of the main parameters in the simulations. Given the same number of initial photons, the fluence at aircraft and balloon altitude from a TGF produced at 10 km altitude is 2–3 orders of magnitude smaller then a TGF originating from 20 km altitude. Other important parameters are altitude distribution, angular distribution and amount of feedback. The differences in altitude, altitude distribution and amount of feedback are especially important for the fluence of photons observed at altitudes less than 20 km, and for instruments with a low‐energy threshold larger than 100 keV. We find that the maximum radius of observation in 14 km for a TGF with the intensity of an average RHESSI TGF is smaller than the results reported by Smith et al. (2011), and our results support the conclusion in Gjesteland et al. (2012) and Østgaard et al. (2012) that TGFs probably are a more common phenomenon than previously reported.

Detection of an Absorbing Heterogeneity in a Biological Object during Recording of Scattered Photons

A rapid method for detection of an optical heterogeneity in a biological object on the basis of diffuse optical tomography (DOT) is described. The method utilizes late arriving photons (LAP) that are scattered and diffusely transmitted through a phantom or a biological object. The technique was validated experimentally using a near infrared femtosecond laser as the source. A streak camera was used as the radiation detector. Satisfactory agreement between the experimental data and a numerical diffusion model is demonstrated. The initial relative number of photons in a single pulse (virtual isotropic source) uniformly fills the object in the same manner as a diffusing droplet moving toward the center of an object.

Geometric phase and entanglement for a single qubit interacting with deformed-states superposition

The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrodinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.

Dynamics of photon–photon entanglement in a bimodal nonlinear nanocavity

The photon–photon entanglement dynamics in a bimodal nanocavity, filled with a centrosymmetric nonlinear medium, is studied. In the present study, we have included the first and third order susceptibilities, giving rise to linear and the Kerr-type couplings. With no restrictions placed on the relative strength of these effects, we prove that the corresponding Hamiltonian is block-diagonal, each with ever-growing dimensions. We then show that, depending upon the initial total photon number, one needs to diagonalize a specific low-dimensional block, leading to the time evolution operator. Consequently, the time-evolution of the von Neumann entropy, as a measure of entanglement, is determined. From an analysis of the von Neumann entropy, we show that the entanglement exhibits oscillations, with plateaus, whose characteristics (period, duration, … ) strongly depend upon the strength of third order susceptibility. Moreover, it is shown that the entanglement is enhanced as the linear coupling is increased. The effect of detuning between photon's frequencies is also discussed.

Time-dependent transport of electrons through a photon cavity

We use a non-Markovian master equation to describe the transport of Coulomb-interacting electrons through an electromagnetic cavity with one quantized photon mode. The central system is a finite-parabolic quantum wire that is coupled weakly to external parabolic quasi-one-dimensional leads at $t=0$. With a stepwise introduction of complexity to the description of the system and a corresponding stepwise truncation of the ensuing many-body spaces, we are able to describe the time-dependent transport of Coulomb-interacting electrons through a geometrically complex central system. We take the full electromagnetic interaction of electrons and cavity photons without resorting to the rotating-wave approximation or reduction of the electron states to two levels into account. We observe that the number of initial cavity photons and their polarizations can have important effects on the transport properties of the system. The quasiparticles formed in the central system have lifetimes limited by the coupling to the leads and radiation processes active on a much longer time scale.

大豆愈伤组织超弱光子辐射的双指数模型

Double-exponential model of ultraweak photon emission of soybean callus was proposed based on the mechanism of ultraweak photon emission in biological system. Treated soybean callus by UV-B radiation (20 μW/cm^2) for 2 h, ultraweak photon emission of soybean callus treated by UV-B for 4 d after was measured. The results show that double-exponential model accurately describes the characteristics of ultraweak photon emission of soybean callus and its changes, delayed luminescence of ultraweak photon emission of soybean callus is composed by both fast and slow phase. Spontaneous luminescence in ultraweak photon emission of soybean callus and some parameters of delayed luminescence such as initial photon number I(0), integrated intensity I(T) and decay parameters of delayed luminescence are obtained through analysis of the double-exponential model, the characteristics of ultraweak photon emission of soybean callus can be quantitative expressed by these parameters. The studies also find that there is an excellent positive correlation between initial photon number I(0) and integrated intensity I(T), and I(0) or I(T) can be used to measure the metabolic intensity of soybean callus. Induced by UV-B radiation (20 μW/cm^2) for 2 h, the decay parameter of fast phase in delayed luminescence decreases first and then increases, the change of spontaneous luminescence is opposite, it suggests that fast phase of delayed luminescence is sensitive to the UV-B radiation and membrane lipid peroxidation could be the reason of the drastic change of fast phase in delayed luminescence of soybean callus.