Entanglement trapping in structured environments

Abstract

The entanglement dynamics of two independent qubits each embedded in a structured environment under conditions of inhibition of spontaneous emission is analyzed, showing entanglement trapping. We demonstrate that entanglement trapping can be used efficiently to prevent entanglement sudden death. For the case of realistic photonic band-gap materials, we show that high values of entanglement trapping can be achieved. This result is of both fundamental and applicative interest since it provides a physical situation where the entanglement can be preserved and manipulated, e.g. by Stark-shifting the qubit transition frequency outside and inside the gap.PACS numbers: 03.67. Mn, 03.65.Yz, 71.55.Jv Entanglement preservation is an important challenge in quantum information and computation technologies [1]. Realistic quantum systems are affected by decoherence and entanglement losses because of the unavoidable interaction with their environments [2]. For example in Markovian (memoryless) environments, in spite of an exponential decay of the single qubit coherence, the entanglement between two qubits may completely disappear at a finite time [3,4]. This phenomenon, known as "entanglement sudden death" and proven to occur in a quantum optics experiment [5], in turn limits the time when entanglement could be exploited for practical purposes. It is therefore of interest to examine the possibility to preserve entanglement. In the case of environments with memory (non-Markovian), such as imperfect cavities supporting a mode resonant with the atomic transition frequency, revivals of two-qubit entanglement have been found [6,7,8]. These revivals, although effectively extending the possible usage time of entanglement, decrease with time and eventually disappear after a certain critical time. Moreover, when the qubits interact with a common environment, it has been shown that entanglement can be preserved by means of the quantum Zeno effect [8].In this paper we continue the investigation on physical systems and physical effects that may lead to effective long time entanglement protection. Since entanglement evolution and population decay have been previously shown to be related [7], one is led to investigate situations where population trapping occurs. This can happen in structured environments where the density of states presents a dip which can inhibit spontaneous emission in the region of the dip [9]. Among realistic physical situations, this effect is known to occur in photonic band-gap (PBG) materials [10]. Entanglement can be generated when a pair of atoms near-resonantly coupled to the edge of a PBG present direct dipole-dipole interaction [11]. On the other hand, a way to produce entangled independent atoms in PBG materials is to consider a three-dimensional photonic crystal single-mode cavity with a sufficiently high-quality Q factor where Rydberg atoms can freely travel through the connected void regions [12]. The atoms exchange photons with the cavity, represented by a single defect mode of the crystal resonant with t...

Mechanism of entanglement preservation

“…In short, different to the need for a structured environment as emphasized in Ref. [7], our discussion clearly reveals two essential conditions to preserve the entanglement: the availability of the bound state and the non-Markovian effect. This discussion focused on an almost maximally entangled initial state by taking α = 0.7.…”

“…However, in many cases the finite extension of the entangled time is not enough and thus it is desired to preserve a significant fraction of the entanglement in the longtime limit. Indeed, it was shown [7] that some noticeable fraction of entanglement can be obtained by engineering structured environment such as photonic band-gap materials [8,9]. According to these works, it is still unclear whether the residual entanglement is fundamentally due to the specific structured materials or due to certain physical mechanisms.…”

Revival of quantum correlations without system-environment back-action

“…The quantum part of the correlations, quantified by quantum discord, includes not only entanglement but also correlations that may occur in separable states. For bipartite open quantum systems in quantum environments, entanglement may display phenomena such as sudden death, revivals, and trapping [5][6][7]. Revivals of entanglement, after finite time periods when it completely disappears, can be expected when either direct two-qubit interactions [8,9] or indirect effective interaction is present, as in the case of two qubits in a common quantum reservoir [10].…”

Preservation of quantum correlation between separated nitrogen-vacancy centers embedded in photonic-crystal cavities

“…The underlying physical picture is that during the evolution the NVC's excited level |A 2 experiences an anomalous "giant" Lamb shift and splits into doublet levels only when the NVC's transition frequency ω 0 lies inside or near the band gap [41][42][43]. One of the doublet levels retains in EFBS lying within the gap, whereas the other is shifted out of the gap and exhibits resonance fluorescence.…”