Mathematical Methods of Quantum Optics

Puri, Rajeev K.

doi:10.1007/978-3-540-44953-9

Cited by 440 publications

(442 citation statements)

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“…While such definitions are not as straightforward in the case of the multivariate distribution considered here, the third and fourth order cumulants still characterize the non-Gaussian character of the field. Indeed, recall that a cumulant of order n is a polynomial of moments of order n and less, and that, for a Gaussian field, only the cumulants of order one and two are non-zero [62]. Fig.…”

Section: Cumulantsmentioning

confidence: 99%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance.

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Section: Cumulantsmentioning

confidence: 99%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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“…and with commutation relations [60], which is fully described by the first and second statistical moments,…”

Section: Explicit Formulae For Dissipative Channelsmentioning

confidence: 99%

Information geometry of Gaussian channels

Monràs

Illuminati

2010

Phys. Rev. A

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We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a byproduct, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications: It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulae for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states, and provide the optimal observables for the estimation of the channel parameters (e.g. bath couplings, squeezing, and temperature).

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“…The noise contribution to the effective hamiltonian takes now the form: 8) while the matrix C ij which characterizes the dissipative term in (2.18) becomes diagonal:…”

Section: Diagonal Correlationsmentioning

confidence: 99%

“…[1][2][3][4] The system plus environment paradigm for the treatment of the so-called open systems is nevertheless very general and has been successfully adopted to model very different physical situations, in laser, atomic and molecular physics. [1][2][3][4][5][6][7][8] In particular, it has been very useful in describing the effects of random media or of stochastic external fields in particle propagation inside interferometric devices. [9][10][11][12][13] Indeed, for weakly-coupled systems, the decoherence and dissipative phenomena induced by the media are in general very small, so that the most suited way to study them is through appropriate interferometric set-ups.…”

Section: Introductionmentioning

confidence: 99%