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arXiv:quant-ph/0512073 · Physical Review A

Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula

Masahide Sasaki, Shigenari Suzuki

Published Apr 19, 2006• 72 citations
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Abstract

We develop a multimode theory to design the frequency mode matching in the photon-subtracting operation by an on/off-type photon detector on a wideband squeezed light. The output state thus generated is known to be the Schr\"odinger-cat-like state. Its Wigner function constructed by the homodyne tomography must have a negative dip around the phase space origin. In order to observe this nonclassical effect, however, one must achieve good mode matching between the fields observed by the on/off and homodyne detectors, those are quite different types from each other. The events are defined for finite measurement time duration $T$, and are measured by the homodyne detector with finite bandwidth $B$. We provide an explicit formulus to calculate the Wigner function of the state, taking into account multimode aspects of the squeezed light and the time and band limitation to the quantum states. A unified picture of the mode matching in terms of the single parameter $BT$ is presented, covering the cw and pulsed schemes. The nonclassical effect can be realized and measured most remarkably when the modes excited in the detectors could be restricted to a single mode by taking $BT$ as small as possible, and could reduce dark counts in the on/off detector and the vacuum noise invasion in the homodyne detector. Practical design of experimental setup is described based on presently available technologies.

DOI
10.1103/physreva.73.043807

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We develop a multimode theory to design the frequency mode matching in the photon-subtracting operation by an on/off-type photon detector on a wideband squeezed light. The output state thus generated is known to be the Schr"odinger-cat-like state. Its Wigner function constructed by the homodyne tomography must have a negative dip around the phase space origin. In order to observe this nonclassical effect, however, one must achieve good mode matching between the fields observed by the on/off and homodyne detectors, those are quite different types from each other. The events are defined for finite measurement time duration TTT, and are measured by the homodyne detector with finite bandwidth BBB. We provide an explicit formulus to calculate the Wigner function of the state, taking into account multimode aspects of the squeezed light and the time and band limitation to the quantum states. A unified picture of the mode matching in terms of the single parameter BTBTBT is presented, covering the cw and pulsed schemes. The nonclassical effect can be realized and measured most remarkably when the modes excited in the detectors could be restricted to a single mode by taking BTBTBT as small as possible, and could reduce dark counts in the on/off detector and the vacuum noise invasion in the homodyne detector. Practical design of experimental setup is described based on presently available technologies.
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Optical non-Gaussian quantum states can be generated in a heralded manner by applying a photon subtraction operation to a Gaussian input state. In our work, we develop a theoretical framework to describe this operation in the case where the input state is spectrally multimode. This framework allows the optimal design of photon subtraction experiments. We give the exact expression of the generated non-Gaussian state in the general case. We apply this framework to the case of Schrodinger kitten state generation using a multimode squeezed vacuum as input state. We show that the quality of the generated state (in terms of fidelity and Wigner function negativity) can be enhanced by adapting the different experimental parameters.
This paper establishes a versatile theoretical framework that explicitly describes single-photon subtraction from multimode quantum light in the context of non-Gaussian state generation and manipulation. The treatment focuses on easy-to-implement configurations in which no mode-selective operation is available and evaluates features and advantages of schemes where only simple filtering stages are employed on the experiments. Such configuration, by considerably reducing the experimental overheads, makes experiments involving single-photon subtraction easier to be implemented. The obtained theoretical framework allows retrieving, given a multimode input state, optimal conditions required to herald and then to detect non-Gaussian states, providing a practical and powerful toolbox for experiments' design. The application of the proposed approach to the case study of Schr\"odinger cat state preparation starting from a frequency multimode squeezed state illustrates the impact of the derived theoretical tools.
The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this paper we derive the truncated correlations, which are multimode generalizations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.
We experimentally verify the quantum non-Gaussian character of a conditionally generated noisy squeezed single-photon state with a positive Wigner function. Employing an optimized witness based on probabilities of squeezed vacuum and squeezed single-photon states, we prove that the state cannot be expressed as a mixture of Gaussian states. In our experiment, the non-Gaussian state is generated by conditional subtraction of a single photon from a squeezed vacuum state. The state is probed with a homodyne detector and the witness is determined by averaging a suitable pattern function over the measured homodyne data. Our experimental results are in good agreement with a theoretical fit obtained from a simple yet realistic model of the experimental setup.
We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-Gaussian states are produced conditionally. These are useful states for continuous-variable quantum-information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric down-conversion, thereby improving the analysis of existing experimental results. The main improvement is that spatial and frequency filters before the photon detector are taken into account explicitly. We find excellent agreement with previously published experimental results, using fewer free parameters than before, and discuss the implications of our analysis for the optimized production of states with negative Wigner functions.