We propose a scheme to realize the fractional quantum Hall system with atoms confined in a two-dimensional array of coupled cavities. Our scheme is based on simple optical manipulation of atomic internal states and inter-cavity hopping of virtually excited photons. It is shown that as well as the fractional quantum Hall system, any system of hard-core bosons on a lattice in the presence of an arbitrary Abelian vector potential can be simulated solely by controlling the phases of constantly applied lasers. The scheme, for the first time, exploits the core advantage of coupled cavity simulations, namely the individual addressability of the components and also brings the gauge potential into such simulations as well as the simple optical creation of particles.The achievement of trapping ultracold atomic gases in a strongly correlated regime has prompted an interest in mimicking various condensed matter systems, thereby allowing one to tackle such complex systems in unprecedented ways [1]. A major class of simulable systems, distinct from the Hubbard model and spin systems, is that in a gauge potential, such as the fractional quantum Hall (FQH) system. The FQH effect arises when a two-dimensional (2D) electron gas is in the presence of a strong perpendicular magnetic field at a low temperature. The Hall resistance of such a system exhibits plateaus when the Landau filling factor ν takes simple rational values [2]. The FQH effect at fundamental filling factors ν = 1/m for odd integers m (even integers for bosons) is accounted for by Laughlin's trial wave function (in the symmetric gauge) [3]where z j = x j + iy j is the 2D position of the jth electron in unit of the magnetic length l B ≡ /eB with B being the magnetic field. The elementary excitation of this state is a quasihole (quasiparticle), which has a fractional charge +e/m (−e/m) and obeys the anyonic statistics [4]. To simulate such a system in trapped atoms, a major challenge is to create an artificial magnetic field as the atoms in consideration have no real charge. This is done with considerable difficulties, for instance, by rapidly rotating the harmonic trap [5], by exploiting electromagnetically induced transparency [6], or by modulating the optical lattice potential [7,8]. Additionally, FQH systems are also simulable in Josephson junction arrays [9].Recently, coupled cavity arrays (CCAs) [10,11,12] have emerged as a fascinating alternative for simulating quantum many-body phenomena, supported by diverse technologies, such as microwave stripline resonators, photonic crystal defects, microtoroidal cavity arrays, and so forth [13,14,15]. CCAs have complementary advantages over optical lattices, such as arbitrary many-body geometries and individual addressability [16]. Recently, theoretical works have shown that the Mott-superfluid phase transition of polaritons [10,11] and the Heisenberg spin chains [12] can be realized in CCAs. These works, however, relied only on globally addressing lasers and thus could not highlight the key advantage of CCAs, namely, t...

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We propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. Our scheme is based on the cavity input-output process and the single photon polarization measurement. We show that, even with the practical imperfections such as atomic spontaneous emission, weak atom-cavity coupling, violation of the Lamb-Dicke condition, cavity photon loss, and detection inefficiency, the proposed gate is feasible for generation of a cluster state in that it meets the scalability criterion and it operates in a conclusive manner. We demonstrate a simple and efficient process to generate a cluster state with our high probabilistic entangling gate.The one-way quantum computation [1,2,3,4,5] has opened up a new paradigm for constructing reliable quantum computers. In their pioneering works [1,2], Raussendorf and Briegel showed that preparation of a particular entangled state, called a cluster state, accompanied with local single-qubit measurements is sufficient for simulating any arbitrary quantum logic operations. Therefore, experimental or intrinsic difficulties in performing two-qubit operations can be substituted with (possibly probabilistic) generation of an entangled state. Especially, Nielsen showed that the resource overhead of a conventional linear optics quantum computer [6] is drastically decreased by combining it with the idea of the one-way quantum computation [4].A cluster state can be visualized as a collection of qubits and lines connecting them. In order to generate a cluster state systematically, one first initializes each qubit in state |+ = 1 √ 2 (|0 + |1 ), where |0 and |1 are the computational basis states, and then performs controlledphase operations between every neighboring qubits connected by the lines. In some previous works [7,8,9], it was shown that in principle there is no threshold value of p required for efficient generation of a cluster state, where p is the success probability of each controlled-phase operation. For a reasonable computational overhead, however, a high success probability p should be attained.In the present work, we propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. The proposed entangling gate is suitable for the systematic generation of a cluster state described above for two reasons. The first is that it works between two individually trapped atoms, thus it meets the scalability criterion. Since a large number of qubits should be entangled in a cluster state to perform a nontrivial quantum computation, entangling gates which work only inside a single trapping structure [10,11,12,13] can not be used directly for our goal. The second is that, in contrast to other scalable two-qubitThe setup for the basic building block. A qubit is encoded in two ground levels |0 and |1 of a 3-level atom trapped in an one-sided optical cavity. The transition between states |1 and |e ...