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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Continuous measurements of photon number and field quadratures

Vlasta Peřinová, A. Lukš

Published Nov 18, 2003• 0 citations
Publisher

Abstract

Continuous quantum measurement of photon number is shown to be a quantum state reconstruction of limited, but appropriate, scope. Operation valued generating functionals are used for deriving models of continuous measurement of one and two field quadratures. Statistical properties are compared and solvable models are discussed. (Summary only available)

DOI
10.1117/12.524163

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Continuous quantum measurement of photon number is shown to be a quantum state reconstruction of limited, but appropriate, scope. Operation valued generating functionals are used for deriving models of continuous measurement of one and two field quadratures. Statistical properties are compared and solvable models are discussed. (Summary only available)
This paper describes the model of a compound Poisson distribution for photon statistics with regard to their bunching in Fock states, thermal states, and others. The method of generating functions is used to calculate the probability distributions, moments, and correlation functions. The parameters of conditional states arising from the subtraction of photons by splitting the beam are determined. The problem of state reconstruction with regard to quadrature quantum measurements is considered. The study is aimed at developing high-precision methods for generating and controlling optical quantum states.
Quantum processes involving single-photon states are of broad interest, in particular, for quantum communications. Extending to continuous values a recent proposal by Yuan et al. [Phys. Rev. A94, 062305 (2016)PLRAAN1050-294710.1103/PhysRevA.94.062305], we show that single-photon quantum processes can be characterized using phase-randomized coherent states (PRCS) as inputs. As a proof of principle, we present the experimental investigation of single-photon tomography using PRCS. The probability distribution of field quadrature measurements for single-photon states can be accurately derived from the PRCS data. As a consequence, the Wigner function and the density matrix of single-photon states are reconstructed with good precision. The sensitivity of the reconstruction to experimental errors and the number of PRCS used is addressed.
The theory of continuous measurement is generalized so as to be applicable to a two-mode radiation field whose properties are monitored by using a \ensuremath{\Lambda} system with initial coherence between two ground states. The two-mode system is shown to offer the possibility of generating a number of new quantum states. Quantum statistics of the field following continuous measurements is calculated. Results for the phase distribution, quasiprobability distribution, and the photon-number distribution of the resulting field are also presented.
Basic concepts of quantum optics are introduced in this chapter. In the beginning, we give a review of the basic quantum mechanics. Then, we perform quantization of an electromagnetic field, which naturally introduces the concept of mode and quadrature. After that, we introduce basic quantum states of light and their phase space representation. Quantum operations in the continuous-variable system and their universality are also explained. To obtain the values of the physical quantities, we have to measure our quantum systems. In the optical continuous-variable system, homodyne measurement and photon number measurement are among the most common measurements that are also discussed here. Finally, we introduce the concept of quantum entanglement, which is one of the central concepts in quantum computation.
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.