Explicit effective Hamiltonians for general linear quantum-optical networks
نویسنده
چکیده
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the network is decomposed into a product of three matrices that can be generated by Hamiltonians.
منابع مشابه
Explicit effective Hamiltonians for linear quantum-optical networks
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for an effective Hamiltonian generating the scattering operator of a general linear quantum network. Our formula shows how to compute the effective Ham...
متن کاملLie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems
We reelaborate on a general method for diagonalizing a wide class of nonlinear Hamiltonians describing different quantum optical models. This method makes use of a nonlinear deformation of the usual su(2) algebra and when some physical parameter, dictated by the particular model under consideration, becomes small, it gives a diagonal effective Hamiltonian that describes correctly the dynamics f...
متن کاملRepulsive interactions in quantum Hall systems as a pairing problem
A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px + ipy) superconductivity. Specifically, we show that general...
متن کاملTime Evolution of States for Open Quantum Systems. The quadratic case∗
Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather general formula for the purity (or the linear entropy) in a short time approximation. For this formula the quadratic assumption is not necessary, more general Ham...
متن کاملSub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer
Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin ...
متن کامل