Efficient Quantum Computation with Probabilistic Quantum Gates

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability p. The required computational overhead scales efficiently both with 1/p and n, where n is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantum computation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability 1-p far beyond any threshold requirement

Efficient engineering of multi-atom entanglement through single-photon detections

We propose an efficient scheme to engineer multi-atom entanglement by detecting cavity decay through single-photon detectors. In the special case of two atoms, this scheme is much more efficient than previous probabilistic schemes, and insensitive to randomness in the atom's position. More generally, the scheme can be used to prepare arbitrary superpositions of multi-atom Dicke states without the requirements of high-efficiency detection and separate addressing of different atoms.Comment: 5 pages, 2 figure

Superfluidity of fermions with repulsive on-site interaction in an anisotropic optical lattice near a Feshbach resonance

We present a numerical study on ground state properties of a one-dimensional (1D) general Hubbard model (GHM) with particle-assisted tunnelling rates and repulsive on-site interaction (positive-U), which describes fermionic atoms in an anisotropic optical lattice near a wide Feshbach resonance. For our calculation, we utilize the time evolving block decimation (TEBD) algorithm, which is an extension of the density matrix renormalization group and provides a well-controlled method for 1D systems. We show that the positive-U GHM, when hole-doped from half-filling, exhibits a phase with coexistence of quasi-long-range superfluid and charge-density-wave orders. This feature is different from the property of the conventional Hubbard model with positive-U, indicating the particle-assisted tunnelling mechanism in GHM brings in qualitatively new physics.Comment: updated with published version

Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.Comment: 5 pages, 6 figures, typos corrected, references adde

BCS-BEC crossover and quantum phase transition for 6Li and 40K atoms across Feshbach resonance

We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold 6Li and 40K atoms across a wide Feshbach resonance. The background scattering lengths for 6Li and 40K have opposite signs, which lead to very different behaviors for these two types of atoms. For 40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For 6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of 40K, there is a quantum phase transition at zero temperature from the superfluid to the normal fermi gas at the positive detuning of the magnetic field where the s-wave scattering length passes its zero point. For 6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.Comment: 7 pages, 6 figure

Three-dimensional theory for interaction between atomic ensembles and free-space light

Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently-discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles. For description of these interactions, one assumed either a cavity-QED model or a one-dimensional light propagation model, which is still inadequate for a full prediction and understanding of most of the current experimental efforts which are actually taken in the three-dimensional free space. Here, we propose a perturbative theory to describe the three-dimensional effects in interaction between atomic ensembles and free-space light with a level configuration important for several applications. The calculations reveal some significant effects which are not known before from the other approaches, such as the inherent mode-mismatching noise and the optimal mode-matching conditions. The three-dimensional theory confirms the collective enhancement of the signal-to-noise ratio which is believed to be one of the main advantage of the ensemble-based quantum information processing schemes, however, it also shows that this enhancement need to be understood in a more subtle way with an appropriate mode matching method.Comment: 16 pages, 9 figure

Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap

We derive an effective low-dimensional Hamiltonian for strongly interacting ultracold atoms in a transverse trapping potential near a wide Feshbach resonance. The Hamiltonian includes crucial information about transverse excitations in an effective model with renormalized interaction between atoms and composite dressed molecules. We fix all the parameters in the Hamiltonian for both one- and two-dimensional cases.Comment: v2: 5 pages, 1 figure; expanded presentation of the formalis