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

Coherence-induced entanglement

Han Xiong, Tiegang Di, Muhammad Suhail Zubairy

Published Aug 18, 2005• 0 citations
Publisher

Abstract

Several examples that show the relationship between atomic coherence and entanglement productions have been discussed in this paper. The first example shows how atomic coherence can lead to entanglement between two thermal fields at a temperature T ; In the second example, we demonstrate how a cascade correlated spontaneous emission laser can be used as an entanglement amplifier; The last example illustrates how an arbitrary entangled state of two cavity fields can be prepared through atomic coherence. All these examples seem indicate that the two different quantum effects-coherence and entanglement-are closely related.

DOI
10.1117/12.611623

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Several examples that show the relationship between atomic coherence and entanglement productions have been discussed in this paper. The first example shows how atomic coherence can lead to entanglement between two thermal fields at a temperature T ; In the second example, we demonstrate how a cascade correlated spontaneous emission laser can be used as an entanglement amplifier; The last example illustrates how an arbitrary entangled state of two cavity fields can be prepared through atomic coherence. All these examples seem indicate that the two different quantum effects-coherence and entanglement-are closely related.
Spontaneous emission as a potential tool for creation of entanglement between two atoms is investigated. We assume that the atoms are coupled to the same environment and study entanglement engineering between the atoms and its transfer between different states. The role of the atomic coherence induced by spontaneous emission will be explored which, in contrast to what is generally believed, can create entanglement between initially unentangled atoms. We quantify entanglement by the concurrence and find that it exhibits threshold properties that can lead to interesting noncontinuous phenomena of sudden birth and sudden death of entanglement. In addition, we consider the mechanism involved in creation of entanglement between distant atoms coupled to a single-mode cavity field. We include a possible variation of the coupling constants between the atoms and the cavity mode with location of the atoms in a standing-wave cavity mode. Effectively, we engineer two coupled atoms whose the dynamics are analogous to that of interacting and collectively damped two nonidentical atoms. We illustrate the interesting result that spatial variations of the coupling constants can lead to a stationary entanglement between the atoms. We explain this effect in terms of the trapping phenomenon of atomic population in a non-decaying entangled state.
We show how atomic coherence can lead to entanglement between two thermal fields at a temperature TTT. We first show that the passage of a three-level atom in VVV configuration without coherence cannot create entanglement. However, if the excited states are driven by a microwave field, the resulting atomic coherence can lead to entanglement between the thermal fields. We show that, no matter how high the temperature of the fields is, the thermal fields can always be entangled in the presence of atomic coherence.
Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. \n \nWe study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.
We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in V\mathsf{V}V configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.
As discussed in the last three chapters, the fundamental source of noise in a laser is spontaneous emission. A simple pictorial model for the origin of the laser linewidth envisions it as being due to the random phase diffusion process arising from the addition of spontaneously emitted photons with random phases to the laser field. In this chapter we show that the quantum noise leading to the laser linewidth can be suppressed below the standard, i.e., Schawlow–Townes limit by preparing the atomic systems in a coherent superposition of states as in the Hanle effect and quantum beat experiments discussed in Chapter 7. In such coherently prepared atoms the spontaneous emission is said to be correlated. Lasers operating via such a phase coherent atomic ensemble are known as correlated spontaneous emission lasers (CEL). An interesting aspect of the CEL is that it is possible to eliminate the spontaneous emission quantum noise in the relative linewidths by correlating the two spontaneous emission noise events. A number of schemes exist in which quantum noise quenching below the standard limit can be achieved. In two-mode schemes a correlation between the spontaneous emisson events in two different modes of the radiation field is established via atomic coherence so that the relative phase between them does not diffuse or fluctuate. In a Hanle laser and a quantum beat laser this is achieved by pumping the atoms coherently such that every spontaneously emitting atom contributes equally to the two modes of the radiation, leading to a reduction and even vanishing of the noise in the phase difference.