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arXiv:1508.02457 · Physical Review Letters

Carving Complex Many-Atom Entangled States by Single-Photon Detection

Wenlan Chen, Jiazhong Hu, Yiheng Duan, Boris Braverman, Hao Zhang, Vladan Vuletić

Published Dec 18, 2015• 71 citations
arXivHTMLPDF

Abstract

We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multifrequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trial, and can generate complex entangled states such as mesoscopic superposition states of coherent spin states with high fidelity.

DOI
10.1103/physrevlett.115.250502

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We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multifrequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trial, and can generate complex entangled states such as mesoscopic superposition states of coherent spin states with high fidelity.
We propose and analyze a probabilistic but heralded scheme to generate pure, entangled, non-Gaussian states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while two or more photons announce Schr\"odinger cat states. The method produces pure states even for finite photon detection efficiency and weak atom-photon coupling. The entanglement generation can be made quasideterministic by means of repeated trial and feedback, enabling metrology beyond the standard quantum limit.
We propose a simple and efficient method for generating metrologically useful quantum entanglement in an ensemble of spin-1 atoms that interacts with a high-finesse optical cavity mode. It requires straightforward preparation of N atoms in the m_{F}=0 sublevel, tailoring of the atom-field interaction to give an effective Tavis-Cummings model for the collective spin-1 ensemble, and a photon counting measurement on the cavity output field. The photon number provides a projective measurement of the collective spin length S, which, for the chosen initial state, is heavily weighted around values S≃sqrt[N], for which the corresponding spin states are strongly entangled and exhibit Heisenberg scaling of the metrological sensitivity with N, as quantified by the quantum Fisher information.
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 the optical generation and characterization of entanglement in atomic ensembles under nonuniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of nonuniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the average total spin remains large, and the detection does not resolve single spins. Furthermore, we derive an analytic formula for determining the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.
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.
The so-called state-carving protocol generates high-fidelity entangled states at an atom-cavity interface without requiring high cavity cooperativity. However, this protocol is limited to 50% efficiency, which restricts its applicability. We propose a simple modification to the state-carving protocol to achieve efficient entanglement generation, with unit probability in principle. Unlike previous two-photon schemes, ours employs only one photon which interacts with the atoms twice-avoiding separate photon detections which causes irrecoverable probability loss. We present a detailed description and performance evaluation of our protocol under nonideal conditions. High fidelity of 0.999 can be achieved with cavity cooperativity of only 34. Efficient state carving paves the way for large-scale entanglement generation at cavity interfaces for modular quantum computing, quantum repeaters, and creating arbitrary shaped atomic graph states, essential for one-way quantum computing.