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Register a new userFast simulation of a quantum phase transition in an ion-trap realisable unitary map
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Added by
John Paul Barjaktarevic
Publication date
2004
fields
Physics
and research's language is
English
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We demonstrate a method of exploring the quantum critical point of the Ising universality class using unitary maps that have recently been demonstrated in ion trap quantum gates. We reverse the idea with which Feynman conceived quantum computing, and ask whether a realisable simulation corresponds to a physical system. We proceed to show that a specific simulation (a unitary map) is physically equivalent to a Hamiltonian that belongs to the same universality class as the transverse Ising Hamiltonian. We present experimental signatures, and numerical simulation for these in the six-qubit case.
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We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around 10$^{-4}$.
Quantum simulations of spin systems could enable the solution of problems which otherwise require infeasible classical resources. Such a simulation may be implemented using a well-controlled system of effective spins, such as a two-dimensional lattice of locally interacting ions. We propose here a layered planar rf trap design that can be used to create arbitrary two-dimensional lattices of ions. The design also leads naturally to ease of microfabrication. As a first experimental demonstration, we confine strontium-88 ions in a mm-scale lattice trap and verify numerical models of the trap by measuring the motional frequencies. We also confine 440 nm diameter charged microspheres and observe ion-ion repulsion between ions in neighboring lattice sites. Our design, when scaled to smaller ion-ion distances, is appropriate for quantum simulation schemes, e.g. that of Porras and Cirac (PRL 92 207901 (2004)). We note, however, that in practical realizations of the trap, an increase in the secular frequency with decreasing ion spacing may make a coupling rate that is large relative to the decoherence rate in such a trap difficult to achieve.
Two-dimensional crystals of trapped ions are a promising system with which to implement quantum simulations of challenging problems such as spin frustration. Here, we present a design for a surface-electrode elliptical ion trap which produces a 2-D ion crystal and is amenable to microfabrication, which would enable higher simulated coupling rates, as well as interactions based on magnetic forces generated by on-chip currents. Working in an 11 K cryogenic environment, we experimentally verify to within 5% a numerical model of the structure of ion crystals in the trap. We also explore the possibility of implementing quantum simulation using magnetic forces, and calculate J-coupling rates on the order of 10^3 / s for an ion crystal height of 10 microns, using a current of 1 A.
The optimisation of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimised for the highest ratio of ion-ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a Biot-Savart like law method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimisation. A method for maximising the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the polygon radii and separations scale to optimise the ratio between the interaction and decoherence rate. The optimal polygon radius and separation for a 2D lattice is found to be a function of the ratio between rf voltage and drive frequency applied to the array. We then provide a case study for 171Yb+ ions to show how a two-dimensional quantum simulator array could be designed.
We have observed a metal-insulator transition of a quasi-two dimensional electronic system in transition metal dichalcogenide $2H$-TaSe$_2$ caused by doping iron. The sheet resistance of $2H$-Fe$_x$TaSe$_2$ ($0 leq x leq 0.120$) single crystals rises about $10^6$ times with the increasing of $x$ at the lowest temperature. We investigated the temperature dependence of the resistance and found a metal-insulator transition with a critical sheet resistance $11.7 pm 5.4$ k$rm{Omega}$. The critical exponent of the localization length $ u$ is estimated $0.31 pm 0.18$. The values of the critical sheet resistance and $ u$ are accordant to those of the textit{chiral unitary class} (less than $h/1.49e^2=17.3$ k$rm{Omega}$ and $0.35 pm 0.03$, respectively). We suggest that $2H$-Fe$_x$TaSe$_2$ is classified as the chiral unitary class, not as standard unitary class.
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