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arXiv:quant-ph/0502114 · New Journal of Physics

Entanglement of topological phase factors

Dimitris I. Tsomokos

Published Feb 11, 2005• 6 citations
arXivHTMLPDF

Abstract

The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topological phases. The effect is quantified in terms of Weyl functions for the density operators of the photons and illustrated with particular examples. The scheme employs the generalized phase factor as a mechanism for information transfer from the photons to the electric charges. In this sense, the scheme may be useful in the context of flying qubits (corresponding to photons) and stationary qubits (electrons), as well as the conversion from one type to the other.

DOI
10.1088/1367-2630/7/1/050

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The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topological phases. The effect is quantified in terms of Weyl functions for the density operators of the photons and illustrated with particular examples. The scheme employs the generalized phase factor as a mechanism for information transfer from the photons to the electric charges. In this sense, the scheme may be useful in the context of flying qubits (corresponding to photons) and stationary qubits (electrons), as well as the conversion from one type to the other.
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Two electron interference experiments which are far from each other are considered. They are irradiated with correlated nonclassical electromagnetic fields, produced by the same source. The phase factors are in this case operators, and their expectation values with respect to the density matrix of the electromagnetic field quantify the observed electron fringes. The correlated photons create correlations between the observed electron intensities. Both cases of classically correlated (separable) and quantum mechanically correlated (entangled) electromagnetic fields are considered. It is shown that the induced correlation between the distant electron interferences is sensitive to the nature of the correlation between the irradiating photons.
Electron interference in mesoscopic devices irradiated by external monochromatic nonclassical microwaves is considered. The relative phase factor between two electron paths is a quantum mechanical operator whose expectation value with respect to the density matrix of the nonclassical microwaves is studied. It is shown that, due to both classical and quantum noise in the microwaves, the absolute value of the phase factor is less than 1,1,1, causing partial destruction of the interference. Separable and entangled two-mode nonclassical microwaves are also considered and their effect on the expectation value of the phase factor is studied.
In this work we performed two experiments to observe the fractional topological phases in two qudits photonic systems. The qudits are encoded in the transverse position degree of freedom of photon pairs generated by the spontaneous parametric down conversion after being transmitted through multiple slits. The photons in this phenomenon are quantum correlated in momentum and energy. Initially we review the theory about the origin of the phases acquired by the evolving quantum states of one and two qubits, where we identify the dynamic, the geometric and the topological phases. Then we examine the generalization of topological phases for two qudits, and discuss its relation with the concept of connectedness of a space. Next we show a way to measure the topological phase, considering that it must appear as a relative phase between two interfering quantum states. To realize the measurement we build an optical interferometer with a spatial light modulator inside it to implement the necessary unitary operations. The polarization is used as an auxiliary degree of freedom for the operations to act conditionally. The results are close to the theoretical predictions, showing the dependence of the phase with the Hilbert space dimension of the state. In a second setup we measure the topological phase for qudits without using a longitudinal interferometer. A new source of polarization entangled photon pairs is used in this new setup. The entanglement in the auxiliary degree of freedom, polarization, is used as a resource to eliminate the interferometer, propitiating a significant improvement in the visibility of the measured interference curves, and a large increase in the signal to noise ratio. In this new setup, we are also capable of realize the unitary operations in both parts of the two qubit system.
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.
Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results are compared with those of the corresponding separable state. In both cases, the results depend on whether the ratio of the two frequencies is rational or irrational.