We study the possibility of affecting the entanglement in a two-qubit system consisting of two photons with different fixed frequencies but with two arbitrary linear polarizations, moving in the same direction, with the help of an applied external magnetic field. The interaction between the magnetic field and the photons in our model is achieved through intermediate electrons that interact both with the photons and the magnetic field. The possibility of an exact theoretical analysis of this scheme is based on well-known exact solutions that describe the interaction of an electron subjected to an external magnetic field (or a medium of electrons not interacting with each other) with a quantized field of two photons. We adapt these exact solutions to the case under consideration. Using explicit wave functions for the resulting electromagnetic field, we calculate the entanglement measures (the information and the Schmidt ones) of the photon beam as functions of the applied magnetic field and the parameters of the electron medium.
We study the possibility of affecting the entanglement in a two-qubit system consisting of two photons with different fixed frequencies but with two arbitrary linear polarizations, moving in the same direction, with the help of an applied external magnetic field. The interaction between the magnetic field and the photons in our model is achieved through intermediate electrons that interact both with the photons and the magnetic field. The possibility of an exact theoretical analysis of this scheme is based on well-known exact solutions that describe the interaction of an electron subjected to an external magnetic field (or a medium of electrons not interacting with each other) with a quantized field of two photons. We adapt these exact solutions to the case under consideration. Using explicit wave functions for the resulting electromagnetic field, we calculate the entanglement measures (the information and the Schmidt ones) of the photon beam as functions of the applied magnetic field and the parameters of the electron medium.
In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.
Abstract In spite of the fact that photons do not interact with an external magnetic field unless nonlinearity of QED is taken into account, the latter field may indirectly affect photons in the presence of a charged environment. This opens up an interesting possibility to continuously control the entanglement of photon beams without using any crystalline devices. We study this possibility in the framework of an adequate QED model. In an approximation it was discovered that such entanglement has a resonant nature, namely, a peak behavior at certain magnetic field strengths, depending on characteristics of photon beams direction of the magnetic field and parameters of the charged medium. Numerical calculations illustrating the above-mentioned resonant behavior of the entanglement measure and some concluding remarks are presented.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
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.
We study the dynamics of a two-qubit system coupled through time dependent anisotropic XYZ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the system under certain integrability conditions. Furthermore, the corresponding entanglement of the system is studied for different values of the involved parameters. We found that the time evolution and different properties of entanglement such as amplitude, frequency and profile can be finely tuned by the interplay of the characteristics of the time-dependent magnetic field and exchange coupling. Also we show how the discrete symmetries of the system Hamiltonian, which splits its Hilbert space into two distinct subspaces, can be utilized to deduce the dynamics in one of its two distinct subspaces from the other one. Moreover, approximate results for the time evolution are provided utilizing the rotating wave as well as the perturbation approximations for the special case of either static magnetic field or exchange coupling. We compare the range of validity of the two approximation methods and their effectiveness in treating the considered system and determine their critical parameters.
The interaction of electrons and photons lies at the heart of quantum physics. The \nmost notable phenomena which are described by quantum physics but which obviously \ninvalidate a classical description of the electromagnetic field - the photoelectric \neffect, the Compton effect, or the antibunching of photons emitted from a single atom, \nto mention a few - are intimately related to the interaction of electrons and photons. \nElectrons possess an internal degree of freedom, the spin. The spin S of an electron \ncan be described as an internal angular momentum, leading to a magnetic moment \nm due to the electric charge of the electron. Stern and Gerlach have shown that \nthe projection of m onto a quantization axis (defined by an external magnetic field \nin their experiment), e.g., along the z axis, is either mz = g�μB/2 (\\spin up") or \nmz = g�μB=2 (\\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton \nand g is the g-factor of the electron (g = 2 for free electrons). \n \n An electron spin \nis therefore usually referred to as a two-level system. Due to this property, the \nspin of electrons which are localized in semiconductor quantum dots has recently \nattracted significant attention regarding the implementation of quantum information \nprocessing: Electron spins can be used as carriers of quantum information. One \ncan define that the spin pointing "up" corresponds to the logical value "0" and \nthe spin pointing "down" corresponds to "1". Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. A system with this property is called a quantum \nbit (qubit). The additional possibilities due to quantum superpositions of qubits are \nexploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks \nmuch more efficiently than with a classical computer (i.e., the prime factorization of \nlarge numbers for Shor's algorithm and the search within an unstructured database for \nGrover's algorithm). While quantum computation has presently only been achieved \nin prototypical experiments with few qubits, the implementation of efficient largescale \nquantum computation with many qubits still remains an extremely demanding \ntask. Yet, other quantum mechanical properties of qubits, such as entanglement, \nhave already been exploited experimentally with photons in quantum communication \nschemes, for example, quantum teleportation and quantum data compression. \nIn this thesis, we investigate the interaction of electrons and photons in semiconductor \nquantum dots. Optical transitions in quantum dots enable a direct link between \nelectron spins and photon polarizations due to conservation laws. We show that \n \nentanglement can be transferred from electron spin qubits to qubits defined by the \nphoton polarization, enabling the measurement of entangled spin states via photons. \nThe mechanism under study can also be used for the production of entangled photons, \nfor instance for the implementation of quantum communication protocols. In contrast \nto the presently used sources of entangled photons, the photon source we propose here \nis deterministic, providing entangled photons on demand. It has been demonstrated \nin several recent experiments that the most obvious way to achieve such a transfer of \nentanglement - using the recombination of biexcitons in a single quantum dot - fails \nin the presently available quantum dot structures. We have analyzed the problems \nof this approach. As a solution, we propose schemes based on charged excitons in \nsingle or coupled quantum dots. We discuss the generation of entangled two- and \nfour-photon states. \nIn addition to the transfer of quantum states, photons can also be used to probe \nelectron spin states. We investigate in detail different methods to optically measure \nthe decoherence time of a single electron spin in a quantum dot. The decoherence time \nof a spin establishes the time scale during which coherent manipulation is possible. \nMeasurements of the electron spin decoherence time are therefore highly desirable \nin view of the implementation of spin-based quantum information processing. We \nshow that the schemes we propose can be implemented with current experimental \ntechniques. \nWe then study the magneto-optical effect called Faraday rotation. Using the technique \nof time-resolved Faraday rotation, a recent experiment has demonstrated the \ncoherent transfer of spin between quantum dots coupled by molecules. We calculate \nthe Faraday rotation signal for a coupled dot system and show that a two-site \nHamiltonian with a transfer term captures the essential features observed in this experiment. \nWe also present results for a system of two coupled dots doped with a \nsingle electron. \nWe finally show that the coupled states of two qubits can be detected via the optical \ninteraction with a cavity in the dispersive regime. We present a Schrieffer-Wolff \ntransformation which removes the coupling of the two qubits to the cavity in leading \norder. The different two-qubit states lead to a different spectral shift of the cavity \nline. For a sufficiently low cavity linewidth, this enables the direct readout of a \ntwo-qubit system.