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arXiv:1510.04217

How subtraction of a single photon affects many quantum modes

Valentin Averchenko, Clément Jacquard, Valérian Thiel, Claude Fabre, Nicolas Treps

Published Oct 14, 2015• 0 citations
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Abstract

The subtraction of a single photon from a multimode quantum field is analyzed as the conditional evolution of an open quantum system. We develop a theory describing different subtraction schemes in a unified approach and we introduce the concept of subtraction modes intrinsic to the process. The matching between the subtraction modes and the modes of the field defines different possible scenarios for the photon subtraction. In particular, our framework identifies: the conditions of pure photon subtraction, the quantum states of the field modes conditioned to the photon subtraction, the mode with the highest fidelity with a single-photon state when the subtraction is performed on multimode squeezed light. We use our theory to analyze the photon subtraction from a highly multimode quantum resource - a train of quantum squeezed or correlated optical pulses. Performing the photon subtraction optimally on various multimode light field has the potential to implement a number of quantum information protocols in a multiplexed and scalable way.

DOI
10.48550/arxiv.1510.04217

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The subtraction of a single photon from a multimode quantum field is analyzed as the conditional evolution of an open quantum system. We develop a theory describing different subtraction schemes in a unified approach and we introduce the concept of subtraction modes intrinsic to the process. The matching between the subtraction modes and the modes of the field defines different possible scenarios for the photon subtraction. In particular, our framework identifies: the conditions of pure photon subtraction, the quantum states of the field modes conditioned to the photon subtraction, the mode with the highest fidelity with a single-photon state when the subtraction is performed on multimode squeezed light. We use our theory to analyze the photon subtraction from a highly multimode quantum resource - a train of quantum squeezed or correlated optical pulses. Performing the photon subtraction optimally on various multimode light field has the potential to implement a number of quantum information protocols in a multiplexed and scalable way.
We develop a general theory to describe the manipulation of a multimode quantum state of light via the subtraction of a single photon. The theory is applicable for various types of subtraction schemes independent of the physical nature of the light modes, their number or the embedded quantum states. We show that different subtraction schemes can be described in a unified approach through the characterization of their intrinsic subtraction modes. The conditional state of the multimode quantum light after the photon subtraction is defined by the number of subtraction modes and their matching with the light modes. We propose the manipulation of light states by controlling the subtraction modes. Performing a photon subtraction on a multimode quantum resource is promising for the implementation of a number of quantum information protocols in all-optical, multiplexed and scalable way.
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.
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation.
Multimode photon subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the payoff for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in nnn-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.
Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.
The nature of a quantum network, in particular in the continuous variable regime, is governed not only by the light quantum state but also by the measurement process. It can then be chosen after the light source has been generated. Multimode entanglement is not anymore an intrinsic property of the source but a complex interplay between source, measurement and eventually post processing. This new avenue paves the way for adaptive and scalable quantum information processing. However, to reach this ambitious goal, multimode degaussification has to be implemented. Single-photon subtraction and addition have proved to be such key operations, but are usually performed with linear optics elements on single-mode resources. We present a device able to perform mode dependant non Gaussian operation on a spectrally multimode squeezed vacuum states. Sum frequency generation between the state and a bright control beam whose spectrum has been engineered through ultrafast pulse-shaping is performed. The detection of a single converted photon heralds the success of the operation. The resulting multimode quantum state is analysed with standard homodyne detection whose local oscillator spectrum is independently engineered. The device can be characterized through quantum process tomography using weak multimode coherent states as inputs. Its single-mode character can be quantified and its inherent subtraction modes can be measured. The ability to simultaneously control the state engineering and its detection ensures both flexibility and scalability in the production of highly entangled non-Gaussian quantum states.