High Intensity Generation of Entangled Photons in a Two‐Mode Electromagnetic Field

2018

Sci Rep

At present, there are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. Quantum entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.

Section: Exact Solution Of the Schrodinger Equationmentioning

confidence: 64%

“…In order to calculate (16) with the wave function (18), the results of previous research [17] must be used where an integral of this kind was calculated. As a result, we obtain A s 1 ,s 2 n,m = i s 1 −n (−1) s 2 +m α s 2 +m √ n!m!…”

Section: Exact Solution Of the Schrodinger Equationmentioning

confidence: 99%

Quantum entanglement of a harmonic oscillator with an electromagnetic field

2018

Sci Rep

“…Furthermore Eq. (2) is more convenient to consider in the form of a differential equation (which was the approach taken in [21][22][23] ), going from the operators â = 1…”

Section: Photons In Bsmentioning

confidence: 99%

“…Furthermore Eq. ( 2 ) is more convenient to consider in the form of a differential equation (which was the approach taken in 21 – 23 ), going from the operators to the electromagnetic field variables q 9 , 10 . As a result, the Hamiltonian of Eq.…”

Section: Photons In Bsmentioning

confidence: 99%

Fluctuations in the detection of the HOM effect

2020

Sci Rep

Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. It is believed that the effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. In this work, it is shown that these fundamental provisions of the HOM interference may not always be fulfilled. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection $$R = 1/2$$ R = 1 / 2 and transmission $$ T = 1/2 $$ T = 1 / 2 . Here we consider the general mechanism of the interaction of two photons in a beam splitter, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only $$ R = 1/2 $$ R = 1 / 2 and $$ T = 1/2 $$ T = 1 / 2 , but also their root-mean-square fluctuations $$ \Delta R ^ 2, \Delta T ^ 2 $$ Δ R 2 , Δ T 2 , which arise due to the dependence of $$R = R(\omega _1, \omega _2) $$ R = R ( ω 1 , ω 2 ) and $$ T = T (\omega _1, \omega _2) $$ T = T ( ω 1 , ω 2 ) on the frequencies where $$\omega _1, \omega _2$$ ω 1 , ω 2 are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations $$ \Delta R^2 $$ Δ R 2 and $$ \Delta T^2 $$ Δ T 2 can be neglected and $$ R=T=1/2 $$ R = T = 1 / 2 is chosen, the developed theory coincides with previously known results.

“…In expression (16), proceeding from the properties of the integral considered in [27], it should be noted that k + p = s 1 + s 2 . Then, using the density matrix and the Schmidt mode definition, as the latter is an eigenvalue of the reduced density matrix, it is easy to obtain λ k (t) = |c k,s 1 +s 2 −k (t)| 2 .…”

Section: Quantum Entanglement Of the Dynamic Systemmentioning

confidence: 99%

Coupled harmonic oscillators and their quantum entanglement

2018

Phys. Rev. E

A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.