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arXiv:0811.1844 · Physical Review A

Quantum simulations based on measurements and feedback control

K. G. H. Vollbrecht, J. I. Cirac

Published Apr 3, 2009• 9 citations
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Abstract

We propose a scheme for performing quantum simulations with atoms in cavities based on a photon detection feedback loop that requires only linear optical elements. Atoms can be stored individually without the need of directly interacting with one another. The scheme is able to simulate any time evolution that can be written as a sum of two-qubit Hamiltonians, e.g., any nearest-neighbor interaction on a lattice. It can also be made robust against photon losses.

DOI
10.1103/physreva.79.042305

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We propose a scheme for performing quantum simulations with atoms in cavities based on a photon detection feedback loop that requires only linear optical elements. Atoms can be stored individually without the need of directly interacting with one another. The scheme is able to simulate any time evolution that can be written as a sum of two-qubit Hamiltonians, e.g., any nearest-neighbor interaction on a lattice. It can also be made robust against photon losses.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions). Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions). Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions) Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.