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arXiv:1007.2209 · Physical Review A

Dissipatively driven entanglement of two macroscopic atomic ensembles

Christine A. Muschik, Eugene Simon Polzik, J. I. Cirac

Published May 17, 2011• 155 citations

Abstract

Up to now, the lifetime of experimentally demonstrated entangled states has been limited due to their fragility under decoherence and dissipation. Therefore, they are created under strict isolation conditions. In contrast, new approaches harness the coupling of the system to the environment, which drives the system into the desired state. Following these ideas, we present a robust method for generating steady-state entanglement between two distant atomic ensembles. The proposed scheme relies on the interaction of the two atomic systems with the common vacuum modes of an electromagnetic field which act as an engineered environment. We develop the theoretical framework for two-level systems, including dipole-dipole interactions, and complement it by considering its implementation in multilevel ground states. Based on these results, the realization of entanglement generation by engineered dissipation has been experimentally demonstrated [H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, e-print arXiv:1006.4344].

DOI: 10.1103/physreva.83.052312

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Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment, where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser- and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04s at room temperature. Our system consists of two ensembles containing about 10^{12} atoms and separated by 0.5m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to an hour.

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.

Following a recent proposal (Muschik et al 2011 Phys. Rev. A 83 052312), engineered dissipative processes have been used for the generation of stable entanglement between two macroscopic atomic ensembles at room temperature (Krauter et al 2011 Phys. Rev. Lett. 107 080503). This experiment included the preparation of entangled states which are continuously available during a time interval of 1 h. Here, we present additional material, further-reaching data and an extension of the theory developed in Muschik et al (2011 Phys. Rev. A 83 052312). In particular, we show how the combination of the entangling dissipative mechanism with measurements can give rise to a substantial improvement of the generated entanglement in the presence of noise.

We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.

We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short-lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Waals interaction range with perspectives for entangling atoms in separate ensembles.

We propose a scheme that is able to generate on demand a steady-state entanglement between two nondegenerate cavity modes. The scheme relies on the interaction of the cavity modes with driven two- or three-level atoms, which act as a coupler to build entanglement between the modes. We show that, in the limit of a strong driving, it is crucial for the generation of entanglement between the modes to imbalance populations of the dressed states of the driven atomic transition. In the case of a three-level

V

-type atom, we find that a stationary entanglement can be created on demand by tuning the Rabi frequency of the driving field to the difference between the atomic transition frequencies. The resulting degeneracy of the energy levels, together with the spontaneously generated coherence, generate a steady-state entanglement between the cavity modes. It is shown that the condition for the maximal entanglement coincides with the collapse of the atomic system into a pure trapping state. We also show that the creation of entanglement depends strongly on the mutual polarization of the transition atomic dipole moments.