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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Orthogonal and polarization-entangled photon-pair arrangement for decoherence-free quantum measurement

Patrick D. Kumavor, Eric Donkor, Bing Wang

Published Aug 24, 2004• 0 citations
Publisher

Abstract

A theoretical model is presented for the interaction of a quantum system with an orthogonal polarized entangled photon-pair measurement probe. The theoretical framework is based on solving the generalized Jaynes-Cummings and Shroeder's equations to determine the phase evolution of the interacting system. The measurement-induced decoherence is expressed in terms of the temporal evolution of the relative phases of the superposition states induced by the measurement probe. The method is applied to determine the rate of decoherence of a two-qubit rubidium quantum system. Quantitative results are given to contrast measurement-induced of (i) single photon probe and (ii) orthogonal polarized and entangled probe.

DOI
10.1117/12.542936

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A theoretical model is presented for the interaction of a quantum system with an orthogonal polarized entangled photon-pair measurement probe. The theoretical framework is based on solving the generalized Jaynes-Cummings and Shroeder's equations to determine the phase evolution of the interacting system. The measurement-induced decoherence is expressed in terms of the temporal evolution of the relative phases of the superposition states induced by the measurement probe. The method is applied to determine the rate of decoherence of a two-qubit rubidium quantum system. Quantitative results are given to contrast measurement-induced of (i) single photon probe and (ii) orthogonal polarized and entangled probe.
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We report a new method for generation of polarization-entangled photon pairs in maximally entangled polarization states. Our approach is based on quantum interference between two polarization states which are non-orthogonal. We present necessary and sufficient conditions for generation the photon pair in a maximally entangled state. The effect of dependence of entanglement on the phase between the interfering states of photons is investigated theoretically and demonstrated experimentally with quantum states produced via spontaneous parametric down-conversion in the double-crystal scheme.
We have performed a series of experiments using a spontaneous parametric down-conversion source to produce pairs of photons in either entangled or non-entangled polarization states. We determine the full quantum mechanical polarization state of one photon, conditioned on the results of measurements performed on the other photon. For non-entangled states, we find that the measured state of one photon is independent of measurements performed on the other. However, for entangled states, the measured state does depend on the results of measurements performed on the other photon. This is possible because of the nonlocal nature of entangled states. These experiments are suitable for an undergraduate teaching laboratory.
In this thesis a theoretical framework for a spin-1 exchange dynamics is developed by the use of effective Hamiltonian theory. We develop this framework through several applications beginning with the standard Jaynes-Cummings model, which under the method of time-averaging leads to the Hamiltonian described by one-axis twisting in a more efficient manner than standard adiabatic elimination. The process of developing effective many-body spin Hamiltonian’s is then applied in several contexts. The robustness of the systems we studied are demonstrated through the generation of entangled states under various constraints.\nWe find that when fixed within a sub-manifold of the collective angular momentum states the time evolution of minimally uncertain atomic states results in atomic cat states, which have been utilized in a variety of contexts for precision measurements. More so, when the initial state is given freedom to evolve between all angular momentum sub-manifolds large degrees of entanglement results. We give analytic results for the case of two-atoms where the entanglement quantification is given through the fidelity, and Schmidt number. This gives implications for measurement protocols through Ramsey pulses, quantum simulators, and creation of spin-1 Bell states for teleportation.\nUnder different operating conditions, we demonstrate the emergence of electromagnetically induced transparency(EIT) which provides a platform for quantum memory, polarization conversion, and state transfer. A limitation of photonic processes is the short optical resonance lifetime, however, our system is free of this issue due to the dispersive approximation constraining the system to a decoherence free ground state manifold. As a result our EIT scheme can result in longer storage times, and more efficient state transfer as decoherence due to spontaneous emission is not the limiting factor.
In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz