Photon blockade induced Mott transitions, spin models, and QIP in coupled micro-cavity arrays.

The studies of insulator to superfluid transitions in many body systems and their realization in optical lattices have opened great possibilities for simulating many body systems. It is thus interesting to explore which other systems permit such phases and simulations, especially if the problem of accessibility of the individual sites is not present. Particularly arresting will be to find such phases in a system of photons which, by being non-interacting, are unlikely candidates for the studies of many-body phenomena.

Together with M. Santos(Univ. of Minas Gerais) and S. Bose(UCL) I have managed to show , that a Mott phase can arise in an array of coupled high Q electromagnetic cavities between which photons can hop, when each cavity is coupled to a single two level system. The latter could be an atom or a quantum dot or even a Cooper pair box. In this phase each atom-cavity system has the same integral number of polaritonic (atomic plus photonic) excitations. It occurs for resonant photonic and atomic frequencies when photon blockade provides an effective repulsion between the excitations in each atom-cavity system. Detuning the atomic and photonic frequencies suppresses this repulsion and induces a transition from the Mott phase to a photonic superfluid. We have also shown that for zero detuning, the system can simulate the dynamics of a spin chain with arbitrary number of excitations. This could be used for various quantum information processing

The most promising technologies for implementing these ideas are shown in the illustration above. In the first, an array of coupled defects in a photonic band gap material is shown. These could be doped with single atoms, or quantum dots already existing in the substrate. The second one is showing a series of coupled toroidal microresonators. Here single atoms could be trapped near the surface and coupled with the resonator’s circulating light modes. The third one describes a circuit quantum electrodynamics architecture. There two superconducting charged qubits-Cooper pair boxes-are coupled strongly to a coplanar transmission line resonator.

Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays.

quant-ph/0606159 also in  Phys. Rev. A (Rap. Com.) vol. 76, 031805 (2007)

Presentation on the above work

Media coverage

This work was the subject of an exclusive feature article in New Scientist, 13 January 2007, p. 42, by Mark Buchanan entitled

‘Engaging photons in light conversation’

It has also appeared in the news section of the

UK Quantum Information Processing Interdisciplinary Research Collaboration (QIPIRC)

Reproducing spin lattice models in strongly coupled atom-cavity systems

http://arxiv.org/abs/0802.0488

 In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing phenomena in condensed matter physics, such as the spin-1/2 Ising, XX, Heisenberg, and XXZ models. The ability to construct networks of arbitrary geometry also allows for the simulation of topological effects. By tuning the number of excitations present, the dimension of the spin to be simulated can be controlled, and mixtures of different spin types produced. The facility of single-site addressing, the use of only the natural hopping photon dynamics without external fields, and the recent experimental advances towards strong coupling, makes the prospect of using these arrays as efficient quantum simulators promising.

http://arxiv.org/abs/0712.2413

We propose a scheme to generate two-photon polarization entangled states with a coupled system of two cavities. In our scheme, two cavity photons are mediated by the direct inter-cavity coupling, while atoms introduced into the cavities simply play the role of generating and probing them. In virtue of the high efficiency of atomic state measurement, this method enables the realization of a heralded entanglement source, which greatly facilitates

quantum communication and quantum computation based on single photons.

Simulation of high-spin Heisenberg chains in coupled cavities 

http://arxiv.org/abs/0802.3365

We propose a scheme to realize the antiferromagnetic Heisenberg model of any spin in an array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a regime where both atomic and cavity excitations are suppressed. It is shown that as well as optically controlling the effective spin-chain Hamiltonian, it is also possible to engineer the magnitude of the spin. Our scheme would open up an unprecedented way to simulate otherwise intractable high-spin problems in many-body physics.

Steady state entanglement between distant hybrid light-matter qubits under classical driving

http://arxiv.org/abs/0711.1830

 We study the case of two polaritonic qubits localized in two separate cavities coupled by a fiber/additional cavity. We show that surprisingly enough, even a coherent classical pump in the intermediate cavity/fiber can lead to the creation of entanglement between the two ends in the steady state. The stationary nature of this entanglement and its survival under dissipation opens possibilities for its production under realistic laboratory conditions. To facilitate the verification of the entanglement in an experiment we also construct the relevant entanglement witness measurable by accessing only a few local variables of each polaritonic qubit.