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arXiv:0805.3056 · Physical Review A

Entanglement trapping in structured environments

Bruno Bellomo, Rosario Lo Franco, Sabrina Maniscalco, Giuseppe Compagno

Published Dec 12, 2008• 222 citations
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Abstract

We highlight the direct link between the time-dependent entanglement and single-qubit excited-state population for two independent qubits, each coupled to a zero-temperature bosonic environment. We show that, in environments structured so as to inhibit spontaneous emission, entanglement trapping and thus prevention of entanglement sudden death occur. We explicitly show that, for photonic band-gap materials as environment, high values of entanglement trapping can be achieved. We finally discuss how, under these conditions, coherent quantum operations can be implemented.

DOI
10.1103/physreva.78.060302

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We highlight the direct link between the time-dependent entanglement and single-qubit excited-state population for two independent qubits, each coupled to a zero-temperature bosonic environment. We show that, in environments structured so as to inhibit spontaneous emission, entanglement trapping and thus prevention of entanglement sudden death occur. We explicitly show that, for photonic band-gap materials as environment, high values of entanglement trapping can be achieved. We finally discuss how, under these conditions, coherent quantum operations can be implemented.
We investigate the roles of different qubit—environment decoherence models on the entanglement trapping of two qubits. By considering three environmental models (the single photonic band gap model, the common photonic band gap model, and the two independent photonic band gaps model), we note that the final values of entanglement trapping are determined by these different models. We also give the conditions of obtaining the larger entanglement trapping by comparing two-qubit entanglement dynamics in different decoherence models. Moreover, the comparison of entanglement trapping between two Bell-like states in the same decoherence model are also carried out.
Abstract We investigate the time evolution of a general two-qubit pure entangled state in different structured environments. A general expression is obtained to evaluate the entanglement dynamics of two-qubit systems for two different dissipative environments in the non-Markovian regime. In one case it is single Lorentzian and is detuned from the system while in the other case two Lorentzians form a photonic band gap and is resonant with the system. In the first case, we show that entanglement can be generated from the initial separable state in the non-Markovian regime. Compared to our earlier work under Markov approximation (Tahira et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 205501), we show that disentanglement rates as well as sudden death times are modified in structured environments. Therefore, we can retain the entanglement for a longer time by controlling the system–environment coupling parameters.
We investigate how nonlocal entanglement, as identified by violations of a Bell inequality, may be protected during the evolution. Our system consists of two qubits each embedded in a bosonic reservoir evolving independently and initially in an entangled mixed state. We show that the violation of the Bell inequality can be related to the single-qubit population of excited state in such a way that, by appropriately choosing structured environments that give rise to sufficiently high values of population trapping, long-time protection of nonlocal entanglement can be correspondingly achieved.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
Any quantum system inevitably interacts with its natural environment, which can be modeled as a Markovian reservoir consisting of a continuum of electromagnetic field modes. The quantum coherence of qubits in a zero-temperature natural reservoir decays asymptotically, whereas the quantum entanglement of two qubits coupled to such reservoirs may disappear in a finite time. This phenomenon, referred to as entanglement sudden death (ESD), has been simulated with artificially engineered dissipative channels, but ESD induced by natural dissipative channels has not been confirmed. We here present the first demonstration of natural-dissipation-induced ESD for two photonic qubits, each stored in a leaky resonator of a superconducting circuit. The disentanglement dynamics of the two photonic qubits is monitored with two ancilla superconducting qubits, which can be controllably coupled to the corresponding leaky resonators. The techniques developed in our experiment pave the way for experimental exploration of entanglement dynamics in natural environments.