Effective cross-Kerr nonlinearity and robust phase gates with trapped ions

We derive an effective Hamiltonian that describes a cross-Kerr type interaction in a system involving a two-level trapped ion coupled to the quantized field inside a cavity. We assume a large detuning between the ion and field (dispersive limit) and this results in an interaction Hamiltonian involving the product of the (bosonic) ionic vibrational motion and field number operators. We also demonstrate the feasibility of operation of a phase gate based on our hamiltonian. The gate is insensitive to spontaneous emission, an important feature for the practical implementation of quantum computing.Comment: Included discussion of faster gates (Lamb-Dicke regime), Corrected typos, and Added reference

Signatures of the super fluid-insulator phase transition in laser driven dissipative nonlinear cavity arrays

We analyze the non-equilibrium dynamics of a gas of interacting photons in an array of coupled dissipative nonlinear cavities driven by a pulsed external coherent field. Using a mean-field approach, we show that the system exhibits a phase transition from a Mott-insulator-like to a superfluid regime. For a given single-photon nonlinearity, the critical value of the photon tunneling rate at which the phase transition occurs increases with the increasing photon loss rate. We checked the robustness of the transition by showing its insensitivity to the initial state prepared by the the pulsed excitation. We find that the second-order coherence of cavity emission can be used to determine the phase diagram of an optical many-body system without the need for thermalization.Comment: 4 pages, 4 figure

Topology by dissipation

Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure

Perturbation Theory for Quantum Computation with Large Number of Qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.Comment: 8 pages RevTex including 2 figure

Single-photon tunneling

Strong evidence of a single-photon tunneling effect, a direct analog of single-electron tunneling, has been obtained in the measurements of light tunneling through individual subwavelength pinholes in a thick gold film covered with a layer of polydiacetylene. The transmission of some pinholes reached saturation because of the optical nonlinearity of polydiacetylene at a very low light intensity of a few thousands photons per second. This result is explained theoretically in terms of "photon blockade", similar to the Coulomb blockade phenomenon observed in single-electron tunneling experiments. The single-photon tunneling effect may find many applications in the emerging fields of quantum communication and information processing.Comment: 4 pages, 4figure

Quantum Bit Regeneration

Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error caused by loss (amplitude damping to a reservoir at T=0), based on using a dual-rail representation of a quantum bit. This is possible because (1) balanced loss does not perform a ``which-path'' measurement in an interferometer, and (2) balanced quantum nondemolition measurement of the ``total'' photon number can be used to detect loss-induced quantum jumps without disturbing the quantum coherence essential to the quantum bit. Our results are immediately applicable to optical quantum computers using single photonics devices.Comment: 4 pages, postscript only, figures available at http://feynman.stanford.edu/qcom

Nonperturbative Coherent Population Trapping: An Analytic Model

Coherent population trapping is shown to occur in a driven symmetric double-well potential in the strong-field regime. The system parameters have been chosen to reproduce the $0^{-}\leftrightarrow 3^{+}$ transition of the inversion mode of the ammonia molecule. For a molecule initially prepared in its lower doublet we find that, under certain circumstances, the $3^{+}$ level remains unpopulated, and this occurs in spite of the fact that the laser field is resonant with the $0^{-}\leftrightarrow 3^{+}$ transition and intense enough so as to strongly mix the $0^{+}$ and $0^{-}$ ground states. This counterintuitive result constitutes a coherent population trapping phenomenon of nonperturbative origin which cannot be accounted for with the usual models. We propose an analytic nonperturbative model which accounts correctly for the observed phenomenon.Comment: 5 pages, 2 figure

Non-ideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system

We examine a 31P donor electron spin in a Si crystal to be used for the purposes of quantum computation. The interaction with an uncontrolled system of 29Si nuclear spins influences the electron spin dynamics appreciably. The hyperfine field at the 29Si nuclei positions is non-collinear with the external magnetic field. Quantum operations with the electron wave function, i.e. using magnetic field pulses or electrical gates, change the orientation of hyperfine field and disturb the nuclear spin system. This disturbance produces a deviation of the electron spin qubit from an ideal state, at a short time scale in comparison with the nuclear spin diffusion time. For H_ext=9 T, the estimated error rate is comparable to the threshold value required by the quantum error correction algorithms. The rate is lower at higher external magnetic fields.Comment: 11 pages, 2 figure