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arXiv:0704.0641

Quantum engineering of photon states with entangled atomic ensembles

Diego Porras, J. I. Cirac

Published Apr 4, 2007• 2 citations
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Abstract

We propose and analyze a new method to produce single and entangled photons which does not require cavities. It relies on the collective enhancement of light emission as a consequence of the presence of entanglement in atomic ensembles. Light emission is triggered by a laser pulse, and therefore our scheme is deterministic. Furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain atomic states using simple sequences of quantum gates. We analyze the feasibility of our scheme, and particularize it to: ions in linear traps, atoms in optical lattices, and in cells at room temperature.

DOI
10.48550/arxiv.0704.0641

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We propose and analyze a new method to produce single and entangled photons which does not require cavities. It relies on the collective enhancement of light emission as a consequence of the presence of entanglement in atomic ensembles. Light emission is triggered by a laser pulse, and therefore our scheme is deterministic. Furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain atomic states using simple sequences of quantum gates. We analyze the feasibility of our scheme, and particularize it to: ions in linear traps, atoms in optical lattices, and in cells at room temperature.
The deterministic generation of collimated single and entangled photons is of crucial importance in several applications in quantum information. Most of the methods require the use of high-Q cavities, something which is very demanding in practice. In this work we propose a new method to produce single-and entangled-photons in a deterministic way which does not require the use of cavities. It relies on the collective light emission in some particular directions as a consequence of the presence of entanglement in an atomic ensemble. This light emission is triggered by a laser pulse, and therefore our scheme is deterministic. Furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain classes of atomic entangled states.
We consider different ways of engineering quantum states of light and atoms via their interaction. First, we show that with atoms in optical lattices one may induce quantum gates between two photons. Then, I will give some procedures to create entangled states of ions and atoms in optical lattices. Those states have the property that can be mapped into photonic states by using interference, in such a way that one ends up with several entangled photons. The mapping is triggered by a laser pulse, and the emerging photons are collimated even in the absence of a cavity.
We propose the implementation of a light source that can deterministically generate a rich variety of multimode quantum states.The desired states are encoded in the collective population of different ground hyperfine states of an atomic ensemble and converted to multimode photonic states by excitation to optically excited levels followed by cooperative spontaneous emission.Among our examples of applications, we demonstrate how twophoton-entangled states can be prepared and implemented in a protocol for a reference-frame-free quantum key distribution and how one-dimensional as well as higher-dimensional cluster states can be produced.
We present a theoretical framework to describe the collective emission of light by entangled atomic states. Our theory applies to the low-excitation regime, where most of the atoms are initially in the ground state, and relies on a bosonic description of the atomic excitations. In this way, the problem of light emission by an ensemble of atoms can be solved exactly, including dipole-dipole interactions and multiple light scattering. Explicit expressions for the emitted photonic states are obtained in several situations, such as those of atoms in regular lattices and atomic vapors. We determine the directionality of the photonic beam, the purity of the photonic state, and the renormalization of the emission rates. We also show how to observe collective phenomena with ultracold atoms in optical lattices and how to use these ideas to generate photonic states that are useful in the context of quantum information.
We propose an optical scheme to generate cluster states of atomic qubits, with each trapped in separate optical cavity, via atom-cavity-laser interaction. The quantum information of each qubit is encoded on the degenerate ground states of the atom, hence the entanglement between them is relatively stable against spontaneous emission. A single-photon source and two classical fields are employed in the present scheme. By controlling the sequence and time of atom-cavity-laser interaction, we show that the atomic cluster states can be produced deterministically.
In Chapter 7 we discussed the interaction between atoms and photons. We found that the coupling between a single atom and a single photon is rather weak, unless the atom and the photon are contained within a small cavity. The only way to significantly affect a free atom with light is to use a state of light with many photons, and in particular we showed how to use classical laser fields to prepare particular atomic states. However, there is another way of enhancing the interaction in a useful way. We can use many atoms rather than a single one. In this chapter, we will show that the interaction between a single photon and an ensemble of atoms can be greatly increased through the phenomenon of collective enhancement. We will show that this gives an atomic ensemble a relatively large susceptibility, and that multilevel atoms can be used to generate large optical nonlinearities. These offer the possibility of slowing, and even stopping, a beam of light; a phenomenon that goes hand in hand with electromagnetically induced transparency. We will discuss how a quantum state of light can be stored in and retrieved from an ensemble of atoms, and how the states of different atomic ensembles can be entangled with one another. We will show that collective states of atoms can even be used as a single qubit or several qubits, and finally, we will show that atomic ensembles can be use to mediate a photon–photon interaction.