Journal ArticleDOI
Generalised P-representations in quantum optics
P D Drummond,Crispin W. Gardiner +1 more
TLDR
In this article, a class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators.Abstract:
A class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators. These are shown to have practical application to the solution of quantum mechanical master equations. Different representations have different domains of integration, on a complex extension of the usual canonical phase-space. The 'complex P-representation' is the case in which analytic P-functions are defined and normalised on contours in the complex plane. In this case, exact steady-state solutions can often be obtained, even when this is not possible using the Glauber-Sudarshan P-representation. The 'positive P-representation' is the case in which the domain is the whole complex phase-space. In this case the P-function may always be chosen positive, and any Fokker-Planck equation arising can be chosen to have a positive-semidefinite diffusion array. Thus the 'positive P-representation' is a genuine probability distribution. The new representations are especially useful in cases of nonclassical statistics.read more
Citations
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Journal ArticleDOI
Quantum fluids of light
Iacopo Carusotto,Cristiano Ciuti +1 more
TL;DR: In this paper, a review of recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems is presented, from the superfluid flow around a defect at low speeds to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles.
Journal ArticleDOI
Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
TL;DR: In this article, phase-space techniques based on the Wigner representation of dilute ultra-cold Bose gases are presented, where the quantum field evolution is represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation.
Journal ArticleDOI
Quantum mechanical pure states with gaussian wave functions
TL;DR: In this article, the authors examined single-mode and two-mode Gaussian pure states (GPS), quantum mechanical pure states with Gaussian wave functions, and derived many of the important properties of GPS and of the Hamiltonians and unitary operators associated with them.
Journal ArticleDOI
Sub-Poissonian processes in quantum optics
TL;DR: In this article, a review of methods for generating sub-Poissonian light and related concepts is presented. But the authors focus on the conceptual foundations and developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-poissonic light generation in lasers and masers.
Journal ArticleDOI
Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
TL;DR: In this paper, phase space techniques based on the Wigner representation of dilute ultra-cold Bose gases are presented, where the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation.
References
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The Quantum Theory of Optical Coherence
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Journal ArticleDOI
Density operators and quasiprobability distributions.
Kevin Cahill,Roy J. Glauber +1 more
TL;DR: In this paper, the problem of expanding a density operator in forms that simplify the evaluation of important classes of quantum-mechanical expectation values is studied from a unified point of view, where the weight function $P(ensuremath{\alpha})$ of the $P$ representation, the Wigner distribution $W(\ensureMath{\alpha), and the function $
Journal ArticleDOI
Ordered Expansions in Boson Amplitude Operators
Kevin Cahill,Roy J. Glauber +1 more
TL;DR: In this article, a parametric ordering convention is introduced according to which normal, symmetric, and antinormal ordering correspond to the values $s=+1,0,\ensuremath{-}1, respectively, of an order parameter $s$.